Article

# Tidal Resonance in the Bay of Fundy and Gulf of Maine

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## Abstract

Tidal ratios outside and inside the Bay of Fundy/Gulf of Maine system fall into two distinct groups. The period of the free mode oscillation in the bay is 13.3 h, and this is forced by the lunar M2 tide of the North Atlantic to produce the unusually high tides recorded in the area.

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... Resonant effect is the main mechanism for anomalously strong tides in many bays and shelf sea straits, for example, Ungava Bay, Canada (Arbic et al., 2007); the Bay of Fundy (Garrett, 1972); Shark Bay, Western Australia (Burling et al., 2003), and the Taiwan Strait (Lin et al., 2001). Resonance tide occurs if the tidal period is close to one of the eigenmodes of the basin. ...
... In bays or shelf seas open at one end, the superposition of incident and reflected waves produces standing waves through quarter-wave resonance phenomena, in which the nodal point (or section) occurs at the mouth (or shelf edge) and the anti-node occurs at the head (or on the coast). The quarter-wave resonance phenomenon generates large tides in the Bay of Fundy, whose length is nearly equal to one-quarter of the semidiurnal tides' wavelength (Garrett, 1972). In shallow coastal bays, tidal propagation has often been viewed as the superposition of incident and reflected waves under the influence of friction, for example, San Francisco Bay (Walters et al., 1985) and Puttalam Lagoon, Sri Lanka (Wijeratne and Rydberg, 2007). ...
... The half-wavelength resonance period (T) for an open-end canal is given as T ¼ ð1=nÞ2L = ffiffiffiffiffiffi gh p , where L is the canal length and n is the mode number, with n ¼ 1 for the fundamental mode; hence the fundamental mode of the half-wavelength resonance period in the strait is w12.5 h. Another approach to determine the dominant resonant frequency of a system is to examine its response to a range of forcing frequencies (Garrett, 1972;Godin, 1988). Our results for simulation 3, which included only DGT forcing (Table 1), revealed the M 2 tide was stronger than the other tidal frequencies and that the strait's fundamental period was almost semidiurnal. ...
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The relative contribution of tides, atmospheric surges, long period waves, seasonal, decadal and inter-annual variability to coastal flooding along the Western Australian coast were examined. The nature of these sources of sea level variability and phase relationships were explored using a state-wide network of 26 coastal tide gauges. Assessment at a regional scale showed the coherence or divergence of sea level processes around the State’s coastline. Anomalous surge events in the southwest, unrelated to local meteorological forcing, were identified as continental shelf waves generated by tropical cyclones on the Northwest Shelf and propagating thousands of kilometres. Spatial variation in the phase and amplitude of water level processes was observed over both seasonal and inter-annual time scales. These differences affect the nature and likelihood of flood events. Over decadal time scales, the relative influence of storminess, climate-related mean sea level variation and tidal modulations was examined. A relationship to tidal form was established, with the 18.6 year lunar nodal cycle affecting flood recurrence in regions where diurnal tidal conditions were dominant and the 4.4 year sub-harmonic of lunar perigee dominating flooding occurrence in regions of semi-diurnal tidal conditions. Results confirmed the importance of multiple processes that influence coastal flooding occurrence. Within the Swan River Region, flooding increased substantially between 1990 and 2006 due to mean sea level variability, tidal modulation and the seasonal timing of severe storms. However, these processes were not directly coincident and there is potential for secular change if they peaked simultaneously, although this has not occurred over the historic period.
... Wu et al. (2013) reproduced the tidal system well with superimposed incident and reflected Kelvin waves and a series of Poincare modes. This result raises the question of whether the quarter-wavelength resonant theory can explain the tidal resonance in the gulf, as is the case with other areas (Miles and Munk, 1961;Garrett, 1972;Sutherland et al., 2005). According to quarter-wavelength theory, because the distance from the head of the gulf to the mouth is approximately 660 km and the mean depth is approximately 36 m, the resonant frequency should be 0.61 cpd, which is much lower than the estimates by Cui et al. (2015) and Tomkratoke et al. (2015). ...
... According to the theories of Garrett (1972) and Miles and Munk (1961), tidal oscillations are limited to a specific area. In contrast, Godin (1993) proposed that tides are a global phenomenon that cannot be separated into independent subdomains. ...
... In this paper, we use the Princeton Ocean Model (POM) for numerical investigation, but we partially modify its code to meet the needs of the present study. This study is limited to the main mechanism of diurnal tidal resonance; accordingly, the elimination of tide-generating forces and nonlinear terms and the linearization of bottom friction in the control equation will not affect the problem we are studying, and the twodimensional model effectively suits our purpose, as shown in a number of previous studies (e.g., Garrett, 1972;Godin, 1993;Webb, 2014;Cui et al., 2015). The general forms of the equation of continuity and the equation of motion used in this study are as follows: ...
Article
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The Gulf of Thailand is dominated by diurnal tides, which might be taken to indicate that the resonant frequency of the gulf is close to one cycle per day. However, when applied to the gulf, the classic quarter-wavelength resonance theory fails to yield a diurnal resonant frequency. In this study, we first perform a series of numerical experiments showing that the gulf has a strong response near one cycle per day and that the resonance of the South China Sea main area has a critical impact on the resonance of the gulf. In contrast, the Gulf of Thailand has little influence on the resonance of the South China Sea main area. An idealized two-channel model that can reasonably explain the dynamics of the resonance affecting the Gulf of Thailand is then established in this study. We find that the resonant frequency around one cycle per day in the main area of the South China Sea can be explained with the quarter-wavelength resonance theory, and the large-amplitude response at this frequency in the Gulf of Thailand is basically a passive response of the gulf to the increased amplitude of the wave in the southern portion of the main area of the South China Sea.
... When children learn to pump at or near the natural frequency of a swing, they can attain large amplitudes; until they do, amplitudes remain small (e.g., Case & Swanson 1990). Similarly, when gravitational forcing occurs near the natural resonance frequency of a channel-like basin, large-amplitude tides occur (e.g., at the Bay of Fundy; Garrett 1972). Continuing the analogy, frictional forces tend to reduce or damp out oscillations on a swing, when forcing is diminished or removed. ...
... Globally, many semienclosed basins exhibit amplified tides due to the constructive interference of an incoming and reflected tide wave, with modifications due to convergent geometry. Examples of near resonance at the semidiurnal frequency include Bristol Bay and Cook Inlet in Alaska (Fong & Heaps 1978, Danielson et al. 2011), Long Island Sound (Wong 1990, Kemp et al. 2017, the Gulf of Maine (Marmer 1922, Duff 1970, Garrett 1972, Godin 1993, the Chilean Inland Sea (Aiken 2008), and the Gulf of California (Godin 1993). For diurnal tides (once daily), examples of resonant systems include the Sea of Okhotsk, the Sahul Shelf, and the Gulf of Tonkin (Skiba et al. 2013). ...
... Because the Gulf of Maine resonance period is 12.5-13.3 h (see Garrett 1972, Greenberg et al. 2012, it is within the region of large sensitivity to length changes for the M 2 tidal frequency, as shown in Figure 3. Therefore, decreases in length caused by road construction and morphological changes in the 1960s and 1970s (Daborn & Dadswell 1988) may have increased M 2 amplification. Conversely, numerical models suggest that flooding induced by sea-level rise in the Gulf of Maine could increase length and decrease the amount of amplification (Pelling & Green 2013). ...
Article
Tides are changing worldwide at rates not explained by astronomical forcing. Rather, the observed evolution of tides and other long waves, such as storm surges, is influenced by shelf processes and changes to the roughness, depth, width, and length of embayments, estuaries, and tidal rivers. In this review, we focus on processes in estuaries and tidal rivers, because that is where the largest changes to tidal properties are occurring. Recent literature shows that changes in tidal amplitude have been ubiquitous worldwide over the past century, often in response to wetland reclamation, channel dredging, and other environmental changes. While tidal amplitude changes are sometimes slight (<1%) or even negative, we identify two types of systems that are particularly prone to tidal amplification: ( a) shallow, strongly damped systems, in which a small increase in depth produces a large decrease in effective friction, and ( b) systems in which wave reflection and resonance are strongly influenced by changes to depth, friction, and convergence. The largest changes in amplitude occur inland, some distance from the coast, and can sometimes be measured in meters. Tide changes are a leading indicator that the dynamics of storm surges and river flood waves have also changed and are often associated with shifts in sediment transport, salinity intrusion, and ecosystem properties. Therefore, the dynamics of tidal evolution have major implications for coastal management, particularly for systems that are sensitive to changes in geometry induced by sea-level rise and anthropogenic development. Expected final online publication date for the Annual Review of Marine Science, Volume 12 is January 3, 2020. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
... Such behavior is typical for resonant systems (cf. Garrett, 1972;Sutherland et al., 2005). We may assume that diurnal and semidiurnal tides in the Adriatic Sea have a resonant character. ...
... As indicated by Garrett (1972), tides in gulfs and marginal seas, such as the Adriatic Sea, are mainly induced by tidal waves incoming from the open basin, rather than by direct forcing from the Sun and Moon. According to Garrett (1972), Sutherland et al. (2005), and Arbic et al. (2007), in that case the tidal frequency response of a near-resonant system can be presented as ...
... As indicated by Garrett (1972), tides in gulfs and marginal seas, such as the Adriatic Sea, are mainly induced by tidal waves incoming from the open basin, rather than by direct forcing from the Sun and Moon. According to Garrett (1972), Sutherland et al. (2005), and Arbic et al. (2007), in that case the tidal frequency response of a near-resonant system can be presented as ...
Article
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Tides in the Adriatic Sea are anomalously strong in comparison with most of other parts of the Mediterranean Sea. Consequently, tides play a fundamental role in the hydrodynamics of this sea and in the formation of destructive floods in its northernmost part. The resonant character of the Adriatic tides is evident, but the exact mechanism of their formation has never been thoroughly examined. In the present study, we used multidecadal tide gauge data from 10 stations located along the basin's coastline to examine the spectral properties of the Adriatic Sea and to provide high‐resolution tidal analysis. Our results demonstrate that both diurnal and semidiurnal tidal harmonics are resonantly amplified due to the proximity of tidal periods to the periods of the fundamental (21.5 hr) and first (10.9 hr) Adriatic eigen modes, respectively. The constructed resonance models were found to closely describe specific features of the observed tides in the Adriatic Sea, including both major and minor harmonics, and therefore help to explain the dominant physical mechanism driving the floods in the northernmost part of the basin, including the Venice Lagoon.
... The ECS features large tidal elevations and intense tidal currents in the BoF and the northwestern GSL (Garrett, 1972;Greenberg, 1979;Saucier and Chassé, 2000). The tidal range in the upper BoF reaches about 16 m, among the largest in the world, due to the resonant frequency of the BoF being close to the frequencies of the semi-diurnal tides (Garrett, 1972). ...
... The ECS features large tidal elevations and intense tidal currents in the BoF and the northwestern GSL (Garrett, 1972;Greenberg, 1979;Saucier and Chassé, 2000). The tidal range in the upper BoF reaches about 16 m, among the largest in the world, due to the resonant frequency of the BoF being close to the frequencies of the semi-diurnal tides (Garrett, 1972). Strong tidal currents affect sub-tidal circulation and hydrography through the nonlinear tidal rectification and tidal mixing (Garrett et al., 1978;Pingree and Griffiths, 1980;Loder, 1980;Loder and Wright, 1985;Loder and Greenberg, 1986;Tee et al., 1993;Xue et al., 2000;Lu et al., 2001;Hannah et al., 2001;Chegini et al., 2018). ...
Article
A coupled circulation and sea ice model is used to examine the tidal impacts on the seasonal variability of circulation, hydrography and sea ice over the eastern Canadian shelf (ECS). The model performance is assessed using in-situ and satellite remote sensing observations. The tidal impacts have significant spatial variability, which are relatively small over the Labrador and Newfoundland Shelves, moderate over the Scotian Shelf (ScS), and significant over the St. Lawrence River Estuary (SLRE), northwestern Gulf of St. Lawrence (GSL), southwestern ScS, Gulf of Maine (GoM), Bay of Fundy (BoF), and the northern flank of Georges Bank (GeB). The tidal impacts on the seasonal mean circulation are greater in winter than in summer in the SLRE, while greater in summer than in winter over several other areas in the GSL, the GoM-BoF and the southwest ScS. The tidal impacts on temperature and salinity are the most significant near fronts, where both tidal mixing and frontal circulation play important roles. The tidal residual circulation, especially that due to tidal rectification in the GSL and GoM-BoF, spreads the large tidal impacts generated near fronts into broader areas. The changes in circulation and stratification also account for the reduced sea ice concentrations in the GSL.
... The Bay of Fundy, together with the Gulf of Maine, is a near-resonant system with an extreme tidal range at the M 2 tidal frequency (Garrett, 1972). The present study will focus on Minas Channel, Minas Basin, and Cobequid Bay (Figure 1) where the highest tides in the world have been observed. ...
... The amplitude and phase of the M 2 tidal elevations predicted by CTRL are shown in Figure 2. Along the open boundary (clockwise from x 0 to x E ), the predicted mean M 2 amplitude is 4.07 m and it increases to 5.96 m at the head of Cobequid Bay (x H ). The tidal phase also increases toward the head with high water arriving at x H with a delay of about 1.5 hr relative to the open boundary. The predicted increase in M 2 amplitude and phase toward the head is consistent with previous studies (e.g., Greenberg, 1969;Hasegawa et al., 2011;Karsten et al., 2008;Tee, 1976;Wu et al., 2011) and has been explained in terms of the resonant character of the Bay of Fundy system (Garrett, 1972). ...
Article
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In shallow, tidally dominated regions, overtides and the mean state of the ocean are coupled through their simultaneous generation by nonlinear processes. We present a new method that uses observed overtides (e.g., M4) and mean currents to independently assess the accuracy of mean dynamic topography (MDT) predicted by ocean models. This is useful in regions where no sufficiently long, geodetically referenced sea level records are available for validation of the predicted MDT. We apply the new method to a regional model of the Gulf of Maine/Scotian Shelf region (GoMSS) and a barotropic, higher resolution model focused on the upper Bay of Fundy (UBoF). We first show that the tides and mean circulation predicted by UBoF are in good agreement with observations and a significant improvement over GoMSS. Next, we use UBoF to demonstrate that observed overtides are useful in selecting the optimal bathymetry and constraining parameters of an ocean model. An accurate bathymetry is critical for capturing the dominant nonlinear processes that generate overtides and control the form of MDT in shallow, tidally dominated regions. Finally, we use the observed overtides to argue that the MDT predicted by UBoF is more realistic than the prediction by GoMSS. In the vicinity of headlands, both horizontal advection and bottom friction in UBoF generate harmonics of the tidal flow and local setdowns of coastal MDT of O $\mathcal{O}$(10 cm). The prediction of such features, validated by observed overtides, can provide guidance in future deployments of tide gauges in support of geoid and ocean model validation.
... Largely because of the macrotidal environment (Garrett, 1972) and the rapid overturn of Maine bay waters, along with a lack of large influent rivers, the GOM, with its distinctive oceanography, has strong control over most coastal bays. In brief, as a result of the shallow terminal moraines of Georges and Browns Banks, the Gulf is a semi-enclosed body of water. ...
... In the twentieth century, winter air temperatures often dipped below -10°C at night and most bays froze over during the winter, while daytime summer air temperatures were typically warm, in the 20°-25°C range. On the other hand, as we briefly describe below, the peculiar oceanography of the GOM (Bigelow, 1927;Graham, 1970;Lynch et al., 1996), coupled with a tidal regime driven by the shape of the GOM (Garrett, 1972), provided a water climate that is mixed Subarctic/ FIGURE 2. Idealized representational cross sections of Gouldsboro-Dyer Bay complex. Top: Upper bay. ...
Article
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In the early 1980s, the National Oceanic and Atmospheric Administration (NOAA) initiated an ecosystem analysis of Gouldsboro Bay in eastern Maine as part of a planned marine sanctuary. The original report to NOAA by Walter H. Adey was not published after the sanctuary concept for Maine was abandoned. Because significant human-related climatic and ecosystem changes are underway in the Gulf of Maine, that report provides valuable baseline data and is included as the Appendix to this volume. After qualitatively describing the geological, physical, chemical, and biogeographical features of Gouldsboro Bay and adjacent Dyer Bay, we quantitatively describe the principal bay ecological communities with data collected during the 1981–1983 ecosystem assessment as well as additional measurements taken within the past decade. We then undertake a comparison of the primary productivity of these bays with the Google Earth Pro polygon tool to determine component areas. Benthic taxa are the dominant primary producers in both bays: rockweeds (primarily Ascophyllum nodosum, with Fucus vesiculosus secondary) in the intertidal; Irish moss (Chondrus crispus, with Fucus distichus secondary) as a near monoculture in the lowest intertidal (infralittoral); kelps (primarily Saccharina latissima, Laminaria digitata, and Agarum clathratum) in the rocky subtidal; and the angiosperm Zostera marina (seagrass) in soft bottom substrate. The rocky intertidal, dominated by Ascophyllum with a specific productivity of 10.6 kg/m2/year, provides nearly one-third of all bay productivity. Because of the proportionally greater shore length relative to area of Dyer Bay, it has 45% greater productivity for its surface area than Gouldsboro Bay. Kelp has a specific productivity value of 7.2 kg/m2/year, and Zostera of 1.2 kg/m2/year. The kelps provide approximately 20% of Gouldsboro Bay’s primary productivity and 35% of that of Dyer Bay. Zostera provides roughly 20% of total primary productivity in Gouldsboro Bay and 12% in Dyer Bay. With a primary productivity of 1.73 kg/m2/year, salt marshes provide only 3.7% (Gouldsboro) and 2.6% (Dyer) of total primary productivity. With a primary productivity of 0.06 kg/m2/year, plankton account for 23.8% of Gouldsboro Bay and 16% of Dyer Bay primary productivity.
... Considering only years with at least 75 % of data resulted in excluding up to 15 years for a given station (Table 1, columns 3 and 4). We care-fully removed the nodal modulation of M 2 amplitude (Simon, 2007(Simon, , 2013, as described briefly in Appendix A. Finally, 3 station-years were discarded due to problems in the record (1953( and 1962( at Delfzijl, 1953 Hoek van Holland), and 2 more station-years due to doubtful M 2 values (1972at Eastport, 1978. ...
... In many semienclosed basins, resonance leads to tidal amplification (Talke and Jay, 2020;Haigh et al., 2019). In the Gulf of Maine, Ray and Talke (2019) reported that the tides in the Gulf are in resonance, with a natural resonance frequency close to the N 2 tide (Garrett, 1972;Godin, 1993). Tides may be then very sensitive to any changes in the environment (e.g. ...
Article
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We investigated the long-term changes of the principal tidal component M2 along North Atlantic coasts, from 1846 to 2018. We analysed 18 tide gauges with time series starting no later than 1940. The longest is Brest with 165 years of observations. We carefully processed the data, particularly to remove the 18.6-year nodal modulation. We found that M2 variations are consistent at all the stations in the North-East Atlantic (Cuxhaven, Delfzijl, Hoek van Holland, Newlyn, Brest), whereas some discrepancies appear in the North-West Atlantic. The changes started long before the 20th century and are not linear. The secular trends in M2 amplitude vary from one station to another; most of them are positive, up to 2.5 mm/yr at Wilmington since 1910. Since 1990, the trends switch from positive to negative values in the North-East Atlantic. Concerning the possible causes of the observed changes, the similarity between the North Atlantic Oscillation and M2 variations in the North-East Atlantic suggests a possible influence of the large-scale atmospheric circulation on the tide. Our statistical analysis confirms large correlations at all the stations in the North-East Atlantic. We discuss a possible underlying mechanism. A different spatial distribution of mean sea level (corresponding to water depth) from one year to another, depending on the low-frequency sea-level pressure patterns, could impact the propagation of the tide in the North Atlantic basin. However, the hypothesis is at present unproven.
... These storms can drive surges that interact with the tides, particularly in basins such as the Bay of Fundy, which has a high tidal range due to natural resonance. This resonance creates the largest tidal environment in the world with a maximum tidal range of 16 m (Garrett 1972), and the combination of a powerful storm surge coinciding with a high tide could be devastating to coastal areas in the Bay of Fundy. This destructive combination occurred in 1869 during the "Saxby Gale" where a storm that was later estimated to be a Category 2 hurricane struck the Gulf of Maine (GOM) and the Bay of Fundy (BOF) during a very high (perigean) spring tide, producing storm surges up to 2 m at high tide (Ruffman 1999) that caused widespread flooding along coastal settlements in the Bay of Fundy. ...
... This system experiences the largest tidal range in the world due to the strong semi-diurnal tidal resonance in the BOF. The large tides are generated due to the similarity in the natural oscillation period of the Bay and the period of the M 2 lunar semi-diurnal tidal constituent (Garrett 1972). These near identical periods cause a resonance within the BOF, yielding the large tidal range and exchange of over 160 billion tons of water twice daily and, therefore, very strong tidal currents (Greenberg 1983). ...
Article
Large waves and storm surge generated by powerful storms can have detrimental impacts on coastal areas. The Gulf of Maine and Bay of Fundy system in the Atlantic Ocean is a particularly dynamic environment where storm surge can synergistically combine with the large tides to yield serious impacts on low-lying coastal areas. In this study, impacts from Hurricane Arthur in 2014 were investigated with observations and numerical simulations using a coupled hydrodynamic-wave model. The results indicate that the storm generated significant wave heights up to 5 m in the Gulf of Maine and a storm surge of over 0.5 m in coastal areas in the Upper Bay of Fundy, however this surge occurred during the neap tide with no associated flooding. Additional simulations, including a historically important event called the Saxby Gale of 1869, were also simulated. This powerful storm occurred during a perigean spring tide, and the model results indicate wave heights of over 10 m and storm surge of over 0.7 m that caused significant flooding. The results indicate that a well-timed tropical cyclone during a high spring tide has the potential to create a storm surge that could overtop existing dyke systems, causing extensive flooding and damage.
... The resonant nature of a tidal system can be examined by field measurements of different tidal constituents and careful comparisons of these with theory (e.g. Garrett 1972;Sutherland et al. 2005). ...
Article
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The Bristol Channel/Severn Estuary has some of the largest tides in the world with a mean spring tidal range of 12.2 m. Numerous proposals have been made to exploit this for energy extraction. However, the large tidal range is partially driven by tidal resonance and such systems can be sensitive to small changes. Thus, it is important to understand the impact of a barrage on the resonance of the system which in turn leads to an understanding of the environmental impact of building a barrage. In this paper, we examine the resonant response of the Bristol Channel system, with and without a barrage structure deployed, using a depth-averaged numerical model. We find that the barrage can alter the response of the Bristol Channel to excitation with higher frequencies than 12 h. However, the barrage causes very little change to the resonant response for longer periods including for the semi-diurnal periods which dominate the tides in the region. We also briefly examine the Swansea Lagoon scheme and find that this is too small to have a significant impact on the resonant response of the channel.
... The amplitudes of the eigenwaves depend on the energy source that generates them and resonance occurs when the dominant frequency of periodic external forcing matches the eigenfrequency of the basin (Rabinovich, 2010). A well-documented example for near resonant forcing of an eigenwave is the amplification of tidal waves in the Bay of Fundy (Garrett, 1972). ...
Article
To analyze the hydrodynamics in an impounded river in response to discharge regulation at upstream and downstream dams, we developed a one-dimensional analytical model. The model provides analytical solutions for discharge and water level fluctuations along the river for periodic discharge boundary conditions at both dams. As a case study, the model was applied to a 38 km long section of the Yangtze River located between the Three Gorges Dam and Gezhouba Dam. The outflow discharge at both dams fluctuated diurnally due to varying demand of hydropower electricity during day and night. In good agreement with observational data, the model results showed significant diurnal variation of water level and discharge along the river. Using the model, we analyzed the sensitivity of the amplitude of diurnal fluctuation of water level and discharge to the parameters describing diurnal discharge regulation. Rapid discharge changes at the dams induced large amplitudes of diurnal variation of water level and discharge in the river. The amplitude of the diurnal wave in the river depends strongly on the lag time between discharge changes at both dams and was lowest if the lag time corresponded to the propagation time of a gravity wave along the river (0.6 h in the case study). In addition to the diurnal wave, high frequency waves were generated, with a period corresponding to the eigenperiod of the impounded river system (1.2 h in our case study). The standing wave is generated by rapid discharge changes at both dams and its amplitude is strongly dependent on the lag time between these changes. The high frequency eigenwave has little influence on water level variation but relative strong influence on discharge variation in the river.
... Tides in the Gulf of Maine and Bay of Fundy are unusual in several respects. In addition to the well-known large tidal range, there is a natural resonance frequency in the Gulf near the frequency of the N 2 tide (Garrett, 1972;Godin, 1993). Observed N 2 amplitudes are larger than S 2 amplitudes, although the opposite is true of the theoretical tidal potential; thus, the classic fortnightly spring-neap modulation is relatively weak and is smaller than the monthly modulation induced by M 2 /N 2 beating. ...
Article
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Astronomical variations in tidal magnitude can strongly modulate the severity of coastal flooding on daily, monthly, and interannual timescales. Here we present a new quasi‐nonstationary skew surge joint probability method (qn‐SSJPM) that estimates interannual fluctuations in flood hazard caused by the 18.6‐ and quasi 4.4‐year modulations of tides. We demonstrate that qn‐SSJPM‐derived storm tide frequency estimates are more precise and stable compared with the standard practice of fitting an extreme value distribution to measured storm tides, which is often biased by the largest few events within the observational period. Applying the qn‐SSJPM in the Gulf of Maine, we find significant tidal forcing of winter storm season flood hazard by the 18.6‐year nodal cycle, whereas 4.4‐year modulations and a secular trend in tides are small compared to interannual variation and long‐term trends in sea‐level. The nodal cycle forces decadal oscillations in the 1% annual chance storm tide at an average rate of ±13.5 mm/year in Eastport, ME; ±4.0 mm/year in Portland, ME; and ±5.9 mm/year in Boston, MA. Currently (in 2020), nodal forcing is counteracting the sea‐level rise‐induced increase in flood hazard; however, in 2025, the nodal cycle will reach a minimum and then begin to accelerate flood hazard increase as it moves toward its maximum phase over the subsequent decade. Along the world's meso‐to‐macrotidal coastlines, it is therefore critical to consider both sea‐level rise and tidal nonstationarity in planning for the transition to chronic flooding that will be driven by sea‐level rise in many regions over the next century.
... The Gulf of Maine (GOM) is a semi-enclosed marginal sea distinctive in the world for having the largest tidal amplitude, over 16 m, due to its shape and length that lead to near resonance of the lunar semi-diurnal M2 constituent of the tide (Garrett, 1972). There are two main oceanic inflows to the Gulf of Maine: Scotian Shelf water flowing southwestward along the coastline from Halifax and originating from the Labrador Current; and Slope Sea water entering through the Northeast Channel that derives from subpolar North Atlantic waters mixed with eddies of the Gulf Stream. ...
Article
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We describe “Doppio”, a ROMS-based (Regional Ocean Modeling System) model of the Mid-Atlantic Bight and Gulf of Maine regions of the northwestern North Atlantic developed in anticipation of future applications to biogeochemical cycling, ecosystems, estuarine downscaling, and near-real-time forecasting. This free-running regional model is introduced with circulation simulations covering 2007–2017. The ROMS configuration choices for the model are detailed, and the forcing and boundary data choices are described and explained. A comprehensive observational data set is compiled for skill assessment from satellites and in situ observations from regional associations of the U.S. Integrated Ocean Observing Systems, including moorings, autonomous gliders, profiling floats, surface-current-measuring coastal radar, and fishing fleet sensors. Doppio's performance is evaluated with respect to these observations by representation of subregional temperature and salinity error statistics, as well as velocity and sea level coherence spectra. Model circulation for the Mid-Atlantic Bight and Gulf of Maine is visualized alongside the mean dynamic topography to convey the model's capabilities.
... The large increase in Portland may be explained by some amplification in the Gulf of Maine. Ray and Talke (2019) reported that the tides in the gulf are in resonance, with a natural resonance frequency close to the N 2 tide (Garrett, 1972;Godin, 1993). Tides may be then very sensitive to any changes in the environment (e.g. ...
Preprint
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We investigated the long-term changes of the principal tidal component M2 over the North Atlantic coasts, from 1846 to 2018. We analysed 9 tide gauges with time series starting no later than 1920. The longest is Brest with 165 years of observations. We carefully processed the data, particularly to remove the 18.6-year nodal modulation. We found that M2 variations are consistent at all the stations in the North East Atlantic (Newlyn, Brest, Cuxhaven), whereas some discrepancies appear in the North West Atlantic. The changes started long before the XXth century, and are not linear. The trends vary from a station to another; they are overall positive, up to 0.7 mm/yr. Since 1990, the trends switch from positive to negative values. Concerning the possible causes of the observed changes, the similarity between the North Atlantic Oscillation and M2 variations in the North East Atlantic suggests a possible influence of the large-scale atmospheric circulation on the tide. We discuss a possible underlying mechanism. A different spatial distribution of water heights from one year to another, depending on the low-frequency sea-level pressure patterns, could impact the propagation of the tide in the North Atlantic basin. However, the hypothesis is at present unproven.
... If a wave approaching the bay has such a long-period component, then the resonance mode of the bay will be excited, explaining the long-duration of oscillations within the bay. The resonant mechanism in combination with local bathymetric features (e.g., focusing) may result in the amplification of tsunami amplitudes, from the entrance of the bay to the innermost part of the embayment, in a way similar to tidal amplification from resonance at longer periods (e.g., Garrett, 1972). This effect might explain some local tsunami wave amplification during the 1960 Chile tsunami in Japan (see Section 2.4, Fig. 5). ...
Article
Far-field tsunamis and their features, as well as methods to quantify trans-oceanic tsunamis are reviewed, with examples of instrumental and historical data. Tsunamis from the 1854 Nankai earthquakes, the 1946 Aleutian tsunami earthquake, the 1960 and 2010 Chile earthquakes, as well as the 2011 Tohoku earthquake, were recorded around the Pacific Ocean. The 1883 Krakatoa volcanic eruption caused volcanic tsunami in the Indian Ocean and meteotsunami in the Pacific Ocean. The 2004 Indian Ocean tsunami was also recorded in the Pacific Ocean. When a tsunami amplitude is larger than that of ocean tides, which usually requires the parent earthquake to be gigantic (Mw ~ 9), it can cause damage and may be historically documented. The trans-Pacific tsunamis described in historical documents include those from the 1700 Cascadia earthquake, the 1730, 1751, 1837, and 1877 earthquakes off Chile, and the 1687 and 1868 earthquakes off Peru. The tsunami record in Japan from the 1586 Peru earthquakes was found to be incorrect and should be discounted. The tsunami magnitude scale relates the tsunami heights to the earthquake size. Tsunami travel time can be computed from actual bathymetry, and the tsunami ray tracing provides relative amplitudes, due to focusing/defocusing caused by irregular bathymetry. Numerical computations from fault models produce tsunami amplitudes and waveforms, and indicate strong directivity due to strike of fault or orientation of subduction zones. Far-field tsunamis are often long-lasting, due to multiple reflections across the basin or on continental shelf, or due to resonance in bays/harbors. These features would provide important criteria to estimate tsunami sources from paleo-tsunami data.
... Ocean tide resonance phenomena are pervasive, especially within coastal and offshore settings. The Bay of Fundy in Canada displays the largest half-diurnal tidal component in the world, and is therefore considered to be the classic example of a bay with tidal resonance (Garrett, 1972;Greenberg, 1979). Prandle and Rahman (1980) postulated that tidal resonance causes a sharp increase in the tidal range. ...
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Coastal lagoon–tidal inlet systems occur worldwide, and each has its own unique evolution characteristics in relation to its geographical location, sediment characteristics, and tidal current and ocean wave conditions. However, insufficient observation data means that it is often difficult to fully understand the long-term and short-term evolution of ebb-tidal deltas, and it is even more difficult to monitor and warn against their evolution. This study uses long time-series remote sensing data for the period 1962–2018 to investigate the evolution of an ebb-tidal delta in Xincun Lagoon, Hainan Island, China. Four shoal-sandbar breaching and tidal-inlet migration events were observed, and the corresponding periodic variation characteristics of the ebb-tidal delta were documented. A conceptual model for the periodic evolution of ebb-tidal deltas was also proposed. The results showed that the long-period (15–20 years) evolution was controlled by the effects of seabed friction and tidal-scale lagoon resonance, while the changes in the length of the east sand-spit could be used as a significant early warning indicator for shoal-sandbar breaching and tidal-inlet migration events. In addition, both types of event were jointly triggered by typhoon storm-surges and the accompanying heavy rainfall, strong winds, and strong waves. Thus, the periodic evolution process of the ebb-tidal delta in Xincun Lagoon was determined to be a systematic process that is either controlled or influenced by a series of interconnecting factors. Moreover, we concluded that it is both feasible and valuable to establish a monitoring and early warning framework of ebb-tidal deltas through the use of time-series remote sensing images. The results of this study can improve the existing understanding of the processes and driving factors of periodic shoal-sandbar breaching and tidal-inlet migration, and can also increase safety nourishment for coastal lagoon–tidal inlet systems.
... The Gulf of Maine (GOM) is a semi-enclosed marginal sea distinctive in the world for having the largest tidal amplitude, over 16 m, due to its shape and length that lead to near resonance of the lunar semi-diurnal M 2 constituent of the tide [Garrett, 1972]. 65 ...
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Abstract. We describe Doppio , a ROMS-based model of the Mid-Atlantic Bight and Gulf of Maine regions of the northwest North Atlantic developed in anticipation of future applications to biogeochemical cycling, ecosystems, estuarine downscaling, and near-real-time forecasting. This free-running regional model is introduced with circulation simulations covering 2007–2017. The ROMS configuration choices for the model are detailed, and the forcing and boundary data choices described and explained. A comprehensive observational data set is compiled for skill assessment from satellites and in situ observations from Regional Associations of the U.S. Integrated Ocean Observing Systems, including moorings, autonomous gliders, profiling floats, surface current measuring coastal radar, and fishing fleet sensors. Doppio's performance is evaluated with respect to these observations by representation of sub-regional temperature and salinity error statistics, as well as velocity and sea level coherence spectra. Model circulation for the Mid-Atlantic Bight and Gulf of Maine is visualized alongside the mean dynamic topography to convey the model's capabilities.
... Parametric resonance Rajasekar Wilfinger et al., 1968Optical resonance Oldenburg et al., 1998 Orbital resonance (mean-motion resonance) Sinclair, 1975;Wang et al., 2021 Plasma resonance Dahm et al., 1968 Quantum resonance Moran et al., 2017Reaction resonance Yang et al., 2015 Tidal resonance Garrett, 1972 Additionally, resonances can emerge from the combinations of basic physical forces, such as those illustrated by the following examples: Electromagnetic resonance Fauché et al., 2017 Nuclear magnetic resonance Hore, 2015 Plasma-electron resonance Tonks, 1931 Spin-mechanical resonance Poshakinskiy and Astakhov, 2019 Magneto-mechanical resonance Grimes et al., 2002 Electromagnetic acoustic resonance Hirao and Ogi, 1997 Nuclear acoustic resonance Sundfors et al., 1983 Williams, 1992 Most of the forms of resonance listed in the PHYSICS category appear to be based upon Helmholtz's (2009) idea of sympathetic resonance. For instance, in a review of magnetic resonance, "the term resonance implies that we are in tune with a natural frequency of the magnetic system" (Slichter, 2013). ...
Article
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Resonance, a powerful and pervasive phenomenon, appears to play a major role in human interactions. This article investigates the relationship between the physical mechanism of resonance and the human experience of resonance, and considers possibilities for enhancing the experience of resonance within human–robot interactions. We first introduce resonance as a widespread cultural and scientific metaphor. Then, we review the nature of “sympathetic resonance” as a physical mechanism. Following this introduction, the remainder of the article is organized in two parts. In part one, we review the role of resonance (including synchronization and rhythmic entrainment) in human cognition and social interactions. Then, in part two, we review resonance-related phenomena in robotics and artificial intelligence (AI). These two reviews serve as ground for the introduction of a design strategy and combinatorial design space for shaping resonant interactions with robots and AI. We conclude by posing hypotheses and research questions for future empirical studies and discuss a range of ethical and aesthetic issues associated with resonance in human–robot interactions.
... Migrants moving from the breeding grounds pass either through the interior or to the east coast of North America. Atlantic Canada holds the most important staging areas (Hicklin, 1987), with numerous potential stopover sites, especially around the Bay of Fundy (Garrett, 1972;Hicklin and Smith, 1984;Sprague et al., 2008;Quinn and Hamilton, 2012). Migrants arrive from the central and eastern portions of the breeding range, load large amounts of fuel, and depart to the south-east over the Atlantic Ocean (Lank, 1983), making a single flight of over 4,000 km directly to South America (Lank, 1979). ...
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Peregrine falcons (Falco peregrinus) have undergone a steady hemisphere-wide recovery since the ban on DDT in 1973, resulting in an ongoing increase in the level of danger posed for migrant birds, such as Arctic-breeding sandpipers. We anticipate that in response migrant semipalmated sandpipers (Calidris pusilla) have adjusted migratory behavior, including a shift in stopover site usage toward locations offering greater safety from falcon predation. We assessed semipalmated sandpiper stopover usage within the Atlantic Canada Shorebird Survey dataset. Based on 3,030 surveys (totalling ~32M birds) made during southward migration, 1974–2017, at 198 stopover locations, we assessed the spatial distribution of site usage in each year (with a “priority matching distribution” index, PMD) in relation to the size (intertidal area) and safety (proportion of a site's intertidal area further than 150 m of the shoreline) of each location. The PMD index value is >1 when usage is concentrated at dangerous locations, 1.0 when usage matches location size, and <1 when usage is concentrated at safer locations. A large majority of migrants were found at the safest sites in all years, however our analysis of the PMD demonstrated that the fraction using safer sites increased over time. In 1974, 80% of birds were found at the safest 20% of the sites, while in 2017, this had increased to 97%. A sensitivity analysis shows that the shift was made specifically toward safer (and not just larger) sites. The shift as measured by a PMD index decline cannot be accounted for by possible biases inherent in the data set. We conclude that the data support the prediction that increasing predator danger has induced a shift by southbound migrant semipalmated sandpipers to safer sites.
... Part of the change may be attributed to the ongoing rise in mean sea level. As is well known, the tides in the gulf, and especially the Bay of Fundy, are in resonance, with a natural resonance frequency sitting near or just below the frequency of the N 2 tide (Garrett, 1972;Godin, 1993). Tides are therefore expected to be sensitive to small changes in basin shape, depth, or friction that might modify the resonance. ...
Article
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Since the early twentieth century, the amplitudes of tidal constituents in the Gulf of Maine and Bay of Fundy display clear secular trends that are among the largest anywhere observed for a regional body of water. The M2 amplitude at Eastport, Maine, increased at a rate of 14.1 ± 1.2 cm per century until it temporarily dropped during 1980–1990, apparently in response to changes in the wider North Atlantic. Annual tidal analyses indicate M2 reached an all‐time high amplitude last year (2018). Here we report new estimates of tides derived from nineteenth century water‐level measurements found in the U.S. National Archives. Results from Eastport, Portland, and Pulpit Harbor (tied to Bar Harbor) do not follow the twentieth century trends and indicate that the Gulf of Maine tide changes commenced sometime in the late nineteenth or early twentieth centuries, coincident with a transition to modern rates of sea‐level rise as observed at Boston and Portland. General agreement is that sea level rise alone is insufficient to cause the twentieth‐century tide changes. A role for ocean stratification is suggested by the long‐term warming of Gulf of Maine waters; archival water temperatures at Boston, Portland, and Eastport show increases of ∼2 °C since the 1880s. In addition, a changing seasonal dependence in M2 amplitudes is reflected in a changing seasonal dependence in water temperatures. The observations suggest that models seeking to reproduce Gulf of Maine tides must consider both sea level rise and long‐term changes in stratification.
... An example where the approximation of Eq. (1a-d) dramatically fails is the Fundy bay in Canada, where h reaches up to 20 m [15]. This amplifying phenomenon (like a water gain) is caused by the superposition of the periodic propagation/reflections of water on the coast borders, which reach up to a hydrological resonance in some cavities. ...
Article
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Two identical homemade prototypes are used to monitoring the tide levels on two strategic points of the Serinhaém estuary. This monitoring was realized along a period close to the new moon phase. From the analysis of the experimental results, the average height of the tide is determined between each period of high-tide and low-tide. These estimations show discrepancies minors than half order of magnitude, compared to the theoretical predictions of the static and dynamic oceanic tide models. Also the amplification effects of the tide in the estuary head can be quantified exhibiting a maximum gain 1.33, which is observed in the new moon phase.
... As displayed in Table 3 range. The Gulf of Maine is highly resonant (Garrett, 1972), but under sea level rise 217 (SLR), the local water level is changing, and Devlin et al. (2019) have shown that this 218 might be reducing the M 2 resonance from what has been a maximum resonance (i.e., 219 the resonance is diminishing in intensity as water level rises), especially in the Bay of 220 ...
Article
Accurate estimation of the changes of tides is important for sea level prediction and fundamental for local coastal planning. Here we use a novel method, enhanced harmonic analysis (EHA), to extract temporal changes in the response of the nodal modulation of the M2 tide in the Gulf of Maine. The results show that the temporal variations of nodal amplitudes at four stations in the Gulf of Maine are similar from 1970s to 2013. They all increase in the 1970s to peak values in the 1985s and in the 2000s they decrease to minimum values. The North Atlantic Oscillation (NAO), which is one of the major climate modes in the North Atlantic Ocean, may be responsible for temporal changes in the response of the nodal modulation of the M2 tide from 1970s to 2013. Also, the results obtained by the new method indicate that the traditional method of harmonic analysis slightly underestimates the trend of M2 amplitude in the Gulf of Maine.
... Maximum depth in the Basin is 17 m at low tide. Minas Basin has the largest recorded tides in the world (mean 11 m, maximum 16 m; Garrett 1972) and at low tide about one third of the Basin area (670 km 2 ) is exposed as tide flat (Bousfield and Liem 1959). The tidal regime is semi-diurnal and an estimated 3 x 10 9 m 3 of water flows in and out of the Basin with each tide (Karsten et al. 2008). ...
... We therefore argue that the control simulation is still a valid baseline for the 400 Ma time slice. Higher-resolution simulations are required to resolve the tides of the BB for the control bathymetry, as it is common for the local full tidal range not to be captured in global tidal simulations, like the Bay of Fundy of the PD, which is dominated by a small-scale resonance [67]. For the 380 Ma time slice, the control simulation also fits well with the three tidal proxies for that period, as does the shallow bathymetry simulation. ...
Article
Tides are a major component of the interaction between the marine and terrestrial environments, and thus play an important part in shaping the environmental context for the evolution of shallow marine and coastal organisms. Here, we use a dedicated tidal model and palaeogeographic reconstructions from the Late Silurian to early Late Devonian (420 Ma, 400 Ma and 380 Ma, Ma = millions of years ago) to explore the potential significance of tides for the evolution of osteichthyans (bony fish) and tetrapods (land vertebrates). The earliest members of the osteichthyan crown-group date to the Late Silurian, approximately 425 Ma, while the earliest evidence for tetrapods is provided by trackways from the Middle Devonian, dated to approximately 393 Ma, and the oldest tetrapod body fossils are Late Devonian, approximately 373 Ma. Large tidal ranges could have fostered both the evolution of air-breathing organs in osteichthyans to facilitate breathing in oxygen-depleted tidal pools, and the development of weight-bearing tetrapod limbs to aid navigation within the intertidal zones. We find that tidal ranges over 4 m were present around areas of evolutionary significance for the origin of osteichthyans and the fish-tetrapod transition, highlighting the possible importance of tidal dynamics as a driver for these evolutionary processes.
... The Q factor is a measure of energy damping in a system (Miles and Munk 1961;Wilson 1972;Rabinovich 2009): the higher the Q factor, the higher the amplification and the ringing of the incoming waves and the lower their energy dissipation. However, high Q factor is just a prerequisite for high amplification, while the amplification factor (H) is taking into account the excitement of bays or harbors by the incoming wave forcing: the closer the frequency of the incoming wave (f ) to the harbor or bay natural frequency of resonance (f 0 ), the higher the amplification H, with H À! f 0 f ð Þ 2 !1 Q. Analogously, for larger basins, the tides in the World Ocean are largest in locations where the frequency of tidal forcing is close to the frequency of natural modes (Garrett 1972;Arbic et al. 2007). Q factor is larger in elongated and narrow inlets and bays (Nakano and Unoki 1962), while the damping is controlled by the wave radiation through the entrance (Rabinovich 2009): the narrower is the entrance, the higher is the Q factor and the larger is the amplification of the fundamental natural mode (Miles and Munk 1961). ...
Chapter
In engineering studies, harbor resonance, including quality and amplification factors, is typically computed for swell and waves with periods shorter than 10 min. However, in various locations around the world, such as Vela Luka Bay in Croatia, meteotsunami waves of periods greater than 10 min can excite the bay or harbor natural modes and produce substantial structural damages. In this theoretical study, the impact of some geomorphological changes of Vela Luka Bay—i.e. deepening of the bay, dredging the harbor, adding a pier or a marina—to the amplification of the meteotsunami waves are presented for a set of 6401 idealized pressure wave field forcing used to derive robust statistics. The most substantial increase in maximum elevation is found when the Vela Luka harbor is dredged to a 5 m depth, which is in contradiction with the calculation of the quality factor showing a decrease of the harbor natural resonance. It has been shown that the forcing energy content at different frequency bands should also be taken into account when estimating the quality and amplification factors, as their typical definitions derived from the peak frequency of the sea level spectrum fail to represent the harbor response during meteotsunami events. New definitions of these factors are proposed in this study and are shown to be in good agreement with the results of the statistical analysis of the Vela Luka Bay maximum elevation results. In addition, the presented methodology can easily be applicable to any other location in the world where meteotsunamis occur.
... The period T and specific dissipation Q −1 of a normal mode are directly related (27,30) to the mode's complex frequency  by T = 2/ Re  and Q −1 = 2 Im / Re . Both were determined in the original (28) eigenmode calculations, but for the sake of argument, T and Q can be treated as free parameters. ...
Article
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The Moon’s tidal potential is slightly asymmetric, giving rise to so-called third-degree ocean tides, which are small and never before observed on a global scale. High-precision satellite altimeters have collected sea level records for almost three decades, providing a massive database from which tiny, time-coherent signals can be extracted. Here, four third-degree tides are mapped: one diurnal, two semidiurnal, and one terdiurnal. Aside from practical benefits, such as improved tide prediction for geodesy and oceanography, the new maps reveal unique ways the ocean responds to a precisely known, but hitherto unexplored, force. An unexpected example involves the two semidiurnals, where the smaller lunar force is seen to generate the larger ocean tide, especially in the South Pacific. An explanation leads to new information about an ocean normal mode that spatially correlates with the third-degree astronomical potential. The maps also highlight previously unknown shelf resonances in all three tidal bands.
... However, acceleration by topographic constriction causes moderate (0.3-0.4 m·s À1 ) and moderately strong (0.5-0.6 m·s À1 ) tidal currents in these areas respectively. The strong tidal current on Georges Bank with its mean tidal range of 1.2 m is probably due to the combination that Georges Bank forms part of the Gulf of Maine -BoF tidal resonance system (Garrett 1972) and the bank also causes topographic acceleration of the tidal flow. ...
Article
Waves and tidal currents can interact to produce strong seabed shear stress and mobilization of sediments on continental shelves. Modelled wave and tidal current data for a 3-year period were used in a combined-flow sediment transport model to simulate the seabed shear stresses and the mobilization of uniform medium sand on the continental shelves of Canada. The modelling results are presented to establish the first national framework of seabed disturbance and sediment mobility on the continental shelves of Canada. Strong waves and tidal currents on the Canadian continental shelves produce mean bed shear velocity >5 cm·s<sup>−1</sup>. Medium sand can be mobilized >50% of the time over many areas on the shelves. The mobilization by tidal currents occurs over 36% and by waves over 50% of the shelf area, demonstrating that mobilization of sediments is dominated by waves on the Canadian continental shelves. Combined shear stresses due to wave and tidal current interaction further increase sediment mobilization to over 68% of the shelf area. The spatial variation of the relative importance of wave and tidal disturbances allows classification of the continental shelves into six disturbance types. Innovative Seabed Disturbance (SDI) and Sediment Mobility (SMI) indices are proposed to quantify the seabed exposure to oceanographic processes and sediment mobilization, incorporating both the magnitude and frequency of these processes. The proposed SDI and SMI, together with the disturbance type classification, can be used as standard parameters to best quantify seabed disturbance and sediment mobility on other shelves of the world.
... For present-day conditions, numerous coastal locations, such as Hudson Strait, the English Channel, the Bay of Fundy, the Patagonian Shelf, etc., resonate near the semi-diurnal and diurnal tidal frequencies (C. Garrett, 1972;Wunsch, 1972;Webb, 1976;Arbic et al., 2007Arbic et al., , 2009Arbic & Garrett, 2010;Heath, 1981;Skiba et al., 2013). Arbic et al. (2009) and Arbic and Garrett (2010) modeled global tides as a system of two coupled oscillators, one (the open-ocean) with much greater mass than the other (the coast), and demonstrated that regions of large coastal tides have a substantial back-effect on the open-ocean tides. ...
Article
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Tides and Earth-Moon system evolution are coupled over geological time. Tidal energy dissipation on Earth slows Earth's rotation rate, increases obliquity, lunar orbit semi-major axis and eccentricity, and decreases lunar inclination. Tidal and core-mantle boundary dissipation within the Moon decrease inclination, eccentricity and semi-major axis. Here we integrate the Earth-Moon system backwards for 4.5 Ga with orbital dynamics and explicit ocean tide models that are “high-level” (i.e., not idealized). To account for uncertain plate tectonic histories, we employ Monte Carlo simulations, with tidal energy dissipation rates (normalized relative to astronomical forcing parameters) randomly selected from ocean tide simulations with modern ocean basin geometry and with 55, 116, and 252 Ma reconstructed basin paleogeometries. The normalized dissipation rates depend upon basin geometry and Earth’s rotation rate. Faster Earth rotation generally yields lower normalized dissipation rates. The Monte Carlo results provide a spread of possible early values for the Earth-Moon system parameters. Of consequence for ocean circulation and climate, absolute (un-normalized) ocean tidal energy dissipation rates on the early Earth may have exceeded today’s rate due to a closer Moon. Prior to urn:x-wiley:21699097:media:jgre21740:jgre21740-math-00043 Ga, evolution of inclination and eccentricity is dominated by tidal and core-mantle boundary dissipation within the Moon, which yield high lunar orbit inclinations in the early Earth-Moon system. A drawback for our results is that the semi-major axis does not collapse to near-zero values at 4.5 Ga, as indicated by most lunar formation models. Additional processes, missing from our current efforts, are discussed as topics for future investigation.
... Such resonance effects famously occur in several sites across the globe. In particular, the highest tidal range has been observed in the Bay of Fundy, Canada where the natural frequency has been calculated to be T b % 13.3h leading to similar tidal amplifications (Garrett, 1972). ...
Chapter
Tides present enormous opportunities to serve as a source of marine renewable energy. This chapter outlines resource and exploitation considerations associated with the marine energy available in areas exhibiting a high tidal range. Initially, a brief introduction to this particular form of tidal power is presented, highlighting the characteristics of the resource and its global distribution. In turn, key elements of the technology required to harness this resource are described, demonstrating both progress made to-date and drivers towards the development of tidal range projects. An overview of existing tidal range power plants is provided as well as a summary of recent proposals for locations where the technology can be deployed. The focus then shifts towards technical constraints and feasibility challenges that must be considered, followed by the methods currently used to address these. Finally, further aspects of tidal range energy assessment are discussed by means of practical case studies.
... The dynamism of the Bay of Fundy is important to understand for its coastal management. The Bay's geometry creates tidal resonance, resulting in mega-tidal conditions with the tidal ranges of up to 17 m (Garrett 1972;Godin 1988) and extensive intertidal zones grading from sand to mudflats and vegetated wetland surfaces (Desplanque and Mossman 2004), making them unique in the context of coastal restoration. The Bay of Fundy has a relatively high but spatially variable sediment supply, which is essential in helping its tidal wetlands keep pace with sea-level rise (storm buffering ES) and which influences restoration trajectories. ...
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We review what is known about ecosystem service (ES) delivery from agricultural dykelands and tidal wetlands around the dynamic Bay of Fundy in the face of climate change and sea-level rise, at the outset of the national NSERC ResNet project. Agricultural dykelands are areas of drained tidal wetland that have been converted to agricultural lands and protected using dykes and aboiteaux (one-way drains or sluices), first introduced by early French settlers (Acadians). Today, Nova Scotia’s 242 km system of dykes protect 17,364 ha of increasingly diverse land uses—including residential, industrial, and commercial uses as well as significant tourism, recreational, and cultural amenities—and is undergoing system modernization and adaptation. Different ES are provided by drained and undrained landscapes such as agriculture from dykelands and regulating services from wetlands, but more complex dynamics exist when beneficiaries are differentiated. This review reveals many knowledge gaps about ES delivery and dynamics, including around net greenhouse gas implications, storm protection, water quality, fish stocks, pollination processes, sense of place, and aesthetics, some of which may reveal shared ES or synergies instead of trade-offs. We emphasize the need to be open to adapting ES concepts and categorizations to fully understand Indigenous implications of these land use decisions.
... It consists of the central Minas Basin proper, Cobequid Bay (the eastern extremity inside Economy Point), and the Southern Bight. Minas Basin has the largest recorded tides in the world (16 m; Garrett 1972), and at low tide maximum depth is only 17 m, while more than one-third of the basin area (670 km 2 ) is exposed as tidal flat (Parker et al. 2007). Numerous rivers and streams are tributary to Minas Basin, the largest of which are the Salmon and Shubenacadie rivers discharging into Cobequid Bay, and the Avon, Gaspereau, and Cornwallis rivers discharging into the Southern Bight ( Figure 2). ...
Article
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Little information is available concerning the seasonal demographics of marine migrating Alewife Alosa pseudo-harengus and Blueback Herring A. aestivalis, reported in commercial fisheries as "gaspereau" in Canada and "river herring" in the USA. Once adults and age-0 juveniles depart from coastal spawning rivers, they migrate along the North American Atlantic coast and are difficult to access for scientific analysis. During June-October 1985, a total of 3,785 Alewife and 2,343 Blueback Herring were examined for length, sex, and gonadal stage from commercial intertidal fishing weirs in Minas Basin and Cobequid Bay, Bay of Fundy, Nova Scotia. Of these, 999 adults were sub-sampled for total weight and body cavity fat deposits. Both species first appeared in the weirs during June, when Blueback Herring generally dominated catches. By July, catches were evenly divided between the two species, and Alewife dominated after mid-August. Most adults were mature, and there was no discernable sex ratio pattern during the sampling period. Sampled fish exhibited abrupt changes in length, gonadal stage, condition factor, and abdominal wall and visceral mesentery fat deposits in relation to season (week), moon phase, and time of low tide. Sudden shifts in average lengths and fat deposits suggested that migrating Alewife were from different stocks. For Blueback Herring , the condition and status of fat deposits during June suggested that they were probably long-distance adult migra-tors. Blueback Herring in Cobequid Bay weirs during July were probably from local stocks. Results from a total of 12,422 tagged adults that were released in Minas Basin and Cobequid Bay during 1985 supported these findings. We propose that shifts in condition and fat deposits can be used to estimate migration distance, discriminating among local, regional, and long-distance movements.
... The Bay of Fundy tidal channels, in eastern Canada, are widely known for their large tidal range and strong tidal currents [9], resulting in one of the largest hydrokinetic energy resources in the world [10]. However, this great resource is at the same time challenging and difficult to exploit, in part because strong tidal currents are accompanied by high levels of turbulence resulting from their interaction with the channel's bathymetric features; conditions which have proven difficult to overcome in the most energetic of the Bay of Fundy tidal channels, Minas Passage. ...
Article
In this investigation, instrumented mobile platforms are used to spatially map the turbulent flows in Grand Passage, one of the Bay of Fundy’s more energetic tidal channels in Nova Scotia, Canada. The aim is to characterize the flow around the PLAT-I floating tidal energy platform developed by Sustainable Marine Energy Canada (SMEC). GPS-tracked surface drifters equipped with fast-sampling acoustic Doppler current profilers (ADCPs) provide turbulence-resolving vertical profiles of velocity and turbulent kinetic energy dissipation rate along drifter trajectories, while vessel-mounted ADCP transects complement the mean flow velocity measurements. These data are used to construct tridimensional quasi-synoptic maps of mean velocities and turbulence parameters for several stages of the tide around PLAT-I’s location including peak ebb and flood currents. The data set includes measurements under natural flow conditions, and while the turbines installed on PLAT-I were both not operational and operational. The measurement techniques and resulting maps successfully capture the spatial and temporal structure of the flow for unsteady conditions for various tidal conditions. The combined wake of the four 6.3 m operational PLAT-I turbines was measured for a single tidal stage. Closer to the turbines, the vertical extent of the wake is about 6 m (approximately one turbine diameter), increasing with distance downstream, while the maximum observed velocity deficit is 26% relative to not operating conditions, decreasing with distance downstream.
... The Bay of Fundy, which separates the eastern Maritime Provinces of Nova Scotia and New Brunswick, Canada, is characterized by the world's largest tidal ranges. High tide can be up to over 16 m higher than low tide [1]. The tides in the Bay of Fundy are so high because of an unusual combination of factors: the shape of the bay and the seiches. ...
Article
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The extreme values of high tides are generally caused by a combination of astronomical and meteorological causes, as well as by the conformation of the sea basin. One place where the extreme values of the tide have a considerable practical interest is the city of Venice. The MOSE (MOdulo Sperimentale Elettromeccanico) system was created to protect Venice from flooding caused by the highest tides. Proper operation of the protection system requires an adequate forecast model of the highest tides, which is able to provide reliable forecasts even some days in advance. Nonlinear Autoregressive Exogenous (NARX) neural networks are particularly effective in predicting time series of hydrological quantities. In this work, the effectiveness of two distinct NARX-based models was demonstrated in predicting the extreme values of high tides in Venice. The first model requires as input values the astronomical tide, barometric pressure, wind speed, and direction, as well as previously observed sea level values. The second model instead takes, as input values, the astronomical tide and the previously observed sea level values, which implicitly take into account the weather conditions. Both models proved capable of predicting the extreme values of high tides with great accuracy, even greater than that of the models currently used.
... In this case, the natural period of the oscillating system equals the exciter period of the tidal wave and resonance occurs [1]. An example is the Bay of Fundy in the west of Nova Scotia (Canada), where a fulfilled quarter-wavelength criterion causes tidal ranges more than 12 m, in extreme cases more than 16 m [1][2][3][4]. Over the last century, an increasing number of tidal rivers and basins, e.g. ...
Article
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Many tidal influenced estuaries and coastal basins feature tidal amplification because of, e.g., convergence and reflection. Increasing amplification rates were observed in the Elbe estuary, with consequences for construction measures, nautical manoeuvring, flood protection, riverbed morphology and ecosystems. Although many studies were conducted investigating the tidal wave transformation in estuaries, studies based on spatially well-distributed empirical data covering periods over more than a year are rare. To fill this gap, a self-developed adapted harmonic analysis method of least squares was applied to hydrographs from 25 gauges, distributed over the tidal influenced estuary from the river mouth to the tidal border which is given by the weir 160 km upstream of the river mouth. The investigation period for the harmonic analyses covers a whole nodal cycle of 18.613 a beginning in the year 2000. The tidal constituents’ oscillatory behaviour including the appearance of compound tides, generated by nonlinear shallow water processes, and the formation of reflection induced partially standing waves are determined. The tidal constituents show shared frequency-group specific partial clapotis, but also have significant differences in amplification within those groups. The latter fact contributes to the detected inverse proportionality of tidal range amplification inside the estuary to incoming tidal wave height. As reflection can cause resonance in tidal influenced rivers, tests are developed to analyse whether criteria for resonance are met. To determine the system’s specific resonance frequency, a new method was introduced with the three-parameter Lorentzian curve-fitting. As the detected resonance frequency is not close to tidal frequencies, full-established resonance of the tidal wave and of the tidal constituents is not observed in the Elbe estuary. Migrating nodes of the partially standing tidal wave hint at increasing latent resonance.
... Tidal resonance occurs when the tidal frequency is synchronized with the natural frequency of an estuary (Garrett, 1972;Le Souëf and Allen, 2014;Sutherland et al., 2005). For a frictionless prismatic channel, the amplitude of the water surface elevation (called resonance amplitude L R ) can theoretically tend to infinity, as below: ...
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Sea level rise (SLR) poses a hazard to ecosystems and economies in low-lying coastal and estuarine areas. To better understand the potential impacts of SLR in estuaries, a comprehensive review of existing theory, literature, and assessment tools is undertaken. In addition, several conceptual models are introduced to assist in understanding interlinked estuarine processes and their complex responses to SLR. This review indicates that SLR impacts in estuaries should not be assessed via static (bathtub) approaches as they fail to consider important hydrodynamic effects such as tidal wave amplification, dampening, and reflection. Where hydrodynamic models are used, the existing literature provides a relatively detailed understanding of how SLR will affect estuarine hydrodynamics (e.g., tides and inundation regimes). With regards to the current understanding of, and ability to model, the connections between altered hydrodynamics (under SLR) and dependent geomorphic, ecological, and bio-geochemical processes, significant knowledge gaps remain. This is of particular concern as there is currently a paradigm shift towards more integrated and holistic management of estuaries. Estuarine management under accelerating SLR is likely to become increasingly complex, as decision-making will be undertaken with high uncertainty. As such, this review highlights that there is a fundamental requirement for more sophisticated and interdisciplinary studies that integrate physical, ecological, bio-geochemical, and geomorphic responses of estuaries to SLR.
... Such resonance effects occur in several sites across the globe. In particular, the highest tidal range has been observed in the Bay of Fundy, Canada where the basin natural frequency has been calculated to be T b ≈ 13.3h leading to amplifications Garrett (1972) for the M 2 and S 2 tidal wave constituents. In the UK, equivalent conditions emerge within the Severn Estuary, known for hosting one of the highest tidal ranges in the world. ...
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Can satellite data be used to address challenges currently faced by the Offshore Renewable Energy (ORE) sector? What benefit can satellite observations bring to resource assessment and maintenance of ORE farms? Can satellite observations be used to assess the environmental impact of offshore renewables leading towards a more sustainable ORE sector? This review paper faces these questions presenting a holistic view of the current interactions between satellite and ORE sectors, and future needs to make this partnerships grow. The aim of the work is to start the conversation between these sectors by establishing a common ground. We present offshore needs and satellite technology limitations, as well as potential opportunities and areas of growth. To better understand this, the reader is guided through the history, current developments, challenges and future of offshore wind, tidal and wave energy technologies. Then, an overview on satellite observations for ocean applications is given, covering types of instruments and how they are used to provide different metocean variables, satellite performance, and data processing and integration. Past, present and future satellite missions are also discussed. Finally, the paper focuses on innovation opportunities and the potential of synergies between the ORE and satellite sectors. Specifically, we pay attention to improvements that satellite observations could bring to standard measurement techniques: assessing uncertainty, wind, tidal and wave conditions forecast, as well as environmental monitoring from space. Satellite-enabled measurement of ocean physical processes and applications for fisheries, mammals and birds, and habitat change, are also discussed in depth.
... Maximum depth in the Basin is 17 m at low tide. Minas Basin has the largest recorded tides in the world (mean 11 m, maximum 17 m ;Garrett 1972) and at low tide about one third of the Basin area (670 km 2 ) is exposed as tide flat (Parker et al. 2007). The tidal regime is semidiurnal and an estimated 3 x 10 9 m 3 of water flows in and out of the Basin with each tide (Parker et al. 2007). ...
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A total of 85 species of fish are known or suspected from Minas Basin and Minas Passage, Nova Scotia, Canada. This systematic review details their seasonal occurrence, habitat, abundance, migratory behavior, fisheries and potential impact from tidal power development. The fish assemblage is a mixture of species common to the Bay of Fundy and the Atlantic coast of Nova Scotia as well as numerous warm-and cold-water visitors seldom found elsewhere in Canada. Minas Basin fisheries exploit some species especially those that migrate through the Basin during summer. Fishes were captured or observed using angling, seines, benthic long lines, drift and fixed gill nets, intertidal fish weirs, bottom trawls and sightings while on vessels. Fishes are categorized with respect to their taxonomic diversity, seasonal occurrence, status, fisheries and the potential impact from tidal lagoons and propeller turbines resulting from development of tidal power in Minas Basin and Minas Passage.
... This effect is larger in shallower systems, e.g., 1.5% for 30 m and 4.5% for 10 m deep systems, as shown in Fig. 4(a). Therefore, estuaries close to resonance are most sensitive to length and/or depth variations [29,30,50,94], and often experience a tidal range amplification in the upstream sections of the estuary [46], such as in the Bay of Fundy with a resonance period of 13.3 ± 0.4 h [95]. In the Chesapeake Bay, which is a shallow system, 1 m of SLR has been shown to reduce the resonant period and shift the system closer to a resonant state [96]. ...
Article
Climate change induced sea level rise (SLR) is likely to impact estuarine hydrodynamics and associated processes, including tidal energy. In this study, a hierarchy of factors influencing the future of estuarine tidal energy resources is proposed based on their relevance to SLR. These include primary factors (e.g., tidal prism, tidal range, tidal current, tidal asymmetry), secondary factors (e.g., sediment transport), and tertiary factors (e.g., shifts in estuarine shape/landform). The existing uncertainty regarding SLR impacts on tidal energy resource is high, given the spatial variability of estuaries. SLR may cause tidal ranges or currents to strengthen or weaken, depending on estuarine shape and boundary conditions (e.g., presence or absence of levees and adjacent low-lying areas). To date, local site studies have not resulted in an overarching assessment of SLR effects on tidal energy resources and comparative studies encompassing different regions and estuary types are recommended in order to address the existing knowledge gaps and provide insights for policymakers and stakeholders. SLR implications to estuarine tidal energy resources may be particularly important as SLR-induced changes can alter the available resource within a renewable energy development's operational lifetime (∼20–30 years for tidal stream devices and ∼120 years for tidal barrages). In this regard, broader environmental impacts, as well as techno-economic assessments, are difficult to predict and long-term management decisions associated with harnessing the potential of tidal energy schemes within estuaries should be made with caution.
... Differing from the Gulf of Mexico, the GoM is an M 2 tidal resonance region (Garrett 1972;Brown 1984;Chen et al. 2011), in which the tidal elevation is much higher than the subtidal elevation. As pointed out by Greenberg et al. (2012), in the GoM, "the determination of changing flood risk over the next century will be more complex than simply adding future contributions determined from climate models." ...
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Hurricanes (tropical cyclones) and nor'easters (extratropical cyclones) are two major storm systems for flood risk over the Massachusetts coast. Severe coastal inundation usually happens when wind-induced waves and storm surges coincide with high tides. A Northeast Coastal Ocean Forecast System (NECOFS) was established and placed into the 24/7 forecast operations starting in 2007. Using a well-validated “end to end” FVCOM inundation model of NECOFS, we examined the impact of climate change-induced sea-level rise (SLR) on the future extratropical storms-induced coastal inundation over the Massachusetts coast. The assessment was done by making the model experiments to project the storm-induced inundation over the coastal areas of Scituate and Boston Harbors with different SLR scenarios under a hundred-year storm condition. The results suggest that with sustained SLR, the northeastern US coast will be vulnerable more severely to wave runup-induced splashing/overtopping than wind-induced storm surges. This finding is consistent with the change in the intensity of storm-generated surface waves in the last decade. The model also suggests that the responses of surge and surface waves to SLR are fully nonlinear. The assessment of the impacts of SLR on the future storm-induced coastal inundation should be investigated with a model including wave-current interactions.
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Cambridge Core - Thermal-Fluids Engineering - An Introduction to Tides - by Theo Gerkema
Article
Three-dimensional numerical simulations of a tidally dominated estuary within the Gulf of Maine are performed using the Regional Ocean Modeling System (ROMS) and validated with observations of sea surface elevation and velocity time series obtained between 1975 and 2016. The model is forced at the ocean boundary with tidal constituents (M2, S2, N2, O1, K1), a time series of observed subtidal elevations and discharge from seven rivers that drain into the estuary. Harmonic analysis is used to determine the tidal dissipation characteristics and generation of overtides within the system. Amplitude decay and phase shift of the dominant semidiurnal (M2) tidal component shows good agreement with observations throughout the main channel of the Piscataqua River and over the channels and mudflats of the Great Bay. The model simulates harmonic growth of the overtides across the spectrum, and indicates a spatial evolution of the tide consistent with a shoaling wave that evolves from a skewed elevation profile with ebb dominance in the lower parts of the estuary, to a more asymmetric, pitched-forward shape consistent with flood dominance. The M4 constituent has spatial variation qualitatively similar to the observations but has magnitudes that are under-predicted in the complex bathymetric region of the Piscataqua River where much of the M2 tidal dissipation occurs. The M6 tidal constituent agrees well with the observations throughout the estuary suggesting that frictional effects on harmonic growth are well modeled. Root-mean-square model-data differences in velocities (~0.05 m/s) and sea surface elevation (~0.1 m) agree to within about 10% of the tidal amplitudes. Differences between model simulations with and without subtidal oscillations in the estuary are small, suggesting that interactions between the tide and other low frequency (subtidal) mean flows are weak and can be ignored when considering tidal dynamics. Including average fresh water discharge in the model does not affect the behavior of the tidal flows, but can generate high frequency baroclinic velocities potentially important to mixing within the estuary.
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Ancient shoreline–shelf depositional systems are influenced by an unusually wide array of geological, biological and hydrodynamic processes, with sediment transport and deposition primarily determined by the interaction of river, wave (including storm) and tidal processes, and changes in relative sea level. Understanding the impact of these processes on shoreline–shelf morphodynamics and stratigraphic preservation remains challenging. Numerical modelling integrated with traditional facies analysis provides an increasingly viable approach, with the potential to quantify, and thereby improve understanding of, the impact of these complex coastal sedimentary processes. An integrated approach is presented here that focuses on palaeotidal modelling to investigate the controls on ancient tides and their influence on sedimentary deposition and preservation – one of the three cornerstones of the ternary process classification scheme of shoreline-shelf systems. Numerical tidal modelling methodology is reviewed and illustrated in three palaeotidal model case studies of different scales and focus. The results are synthesised in the context of shoreline–shelf processes, including a critique and modification of the process-based classification scheme. The emphasis on tidal processes reflects their global importance throughout Earth’s history. Ancient palaeotidal models are able to highlight and quantify the following four controls on tidal processes: (1) the physiography (shape and depth) of oceans (1000s km scale) determines the degree of tidal resonance; (2) the physiography of ocean connections to partly enclosed water bodies (100–1000s km scale) determines the regional-scale flux of tidal energy (inflow versus outflow); (3) the physiography of continental shelves influences shelf tidal resonance potential; and (4) tides in relatively local-scale embayments (typically 1–10s km scale) are influenced by the balance of tidal amplification due to funnelling, shoaling and resonance effects versus frictional damping. In deep time, palaeogeographic and palaeobathymetric uncertainty can be accounted for in palaeotidal models by performing sensitivity analyses to different scenarios, across this range of spatial scales. These tidal process controls are incorporated into an updated predictive decision tree for determining shoreline–shelf process regime in terms of the relative interaction of wave, fluvial and tidal processes. The predictive decision tree considers the effects of basin physiography, shelf width and shoreline morphology on wave, fluvial and tidal processes separately. Uncertainty and ambiguity in applying the widely used three-tier process classification scheme are reduced by using the decision tree in conjunction with a proposed two-tier classification of process regime that is limited to primary and secondary processes. This two-tier classification scheme is illustrated in the three case studies, showing how integration of numerical modelling with facies analysis of the preserved stratigraphic record improves confidence in prediction of tide-influenced shoreline-shelf process regimes. Wider application of this approach will further improve process-based classifications and predictions of modern and ancient shoreline–shelf systems.
Chapter
There is significant global potential for power generated from the tides. Tidal stream energy exploits the natural ebb and flow of the tides by extracting kinetic energy from tidal currents. By situating a tidal energy converter underwater and within the tidal stream, it is possible to generate reliable, renewable, low carbon power. In this article the basic principles of the tides, tidal stream energy and tidal energy converter designs are presented. Resource characterization is explained alongside challenges faced by the tidal stream industry and considerations of physical and environmental impacts of tidal stream energy developments.
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The benthic impact of aquaculture waste depends on the area and extent of waste accumulation on the sediment surface below and around the farm. In this study we investigated the effect of flow on biodeposit transport and initial deposition by calculating a rough aquaculture “footprint” around an oyster aquaculture farm in the Damariscotta River, ME. We also compared a site under the farm to a downstream “away” site calculated to be within the footprint of the farm. We found similar sediment biogeochemical fluxes, geochemical properties and macrofaunal communities at the site under the farm and the away site, as well as low organic enrichment at both sites, indicating that biodeposition in this environment likely does not have a major influence on the benthos. To predict accumulation of biodeposits, we measured sediment erodibility under a range of shear stresses and found slightly higher erosion rates at the farm than at the away site. A microalgal mat was observed at the sediment surface in many sediment cores. Partial failure of the microalgal mat was observed at high shear velocity, suggesting that the mat may fail and surface sediment erode at shear velocities comparable to or greater than those calculated from in situ flow measurements. However, this study took place during neap tide, and it is likely that peak bottom velocities during spring tides are high enough to periodically “clear” under-farm sediment of recent deposits.
Chapter
Many different physical processes contribute to mixing in the ocean. Mixing plays a significant role in shaping the mean state of the ocean and its response to a changing climate. This chapter provides a review of some recent work on the processes driving mixing in the ocean, on techniques for parameterizing the various mixing processes in climate models, and on the role of ocean mixing in the climate system. For the latter, this chapter illustrates how ocean mixing shapes the contemporary mean climate state by focusing on key ocean features influencing the climate (such as the meridional overturning circulation and heat transport, ocean heat and carbon uptake, ocean ventilation, and overflows from marginal seas), how ocean mixing participates in shaping the transient climate change (including anthropogenic ocean heat and carbon uptake, sea level rise and changes in nutrient fluxes that impact marine ecosystems), how ocean mixing is projected to change under future climate change, and how tides and related mixing differed for paleoclimates. Improving our collective understanding of the dynamics of mixing processes and their interactions with the large-scale state of the ocean will lead to greater confidence in projections of how the climate system will evolve under climate change and to a better understanding of the feedbacks that will act to regulate this evolution.
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In this study, we employed a 3-D and two-way nested Regional Ocean Modeling System (ROMS) to address several important outstanding issues regarding tidal energy development in the Gulf of Maine. We investigated the impact of projected sea-level rise (SLR) on the energy resources of the region, and examined how tidal dynamics will be influenced by energy extraction and/or SLR. Further, we assessed whether the effect of SLR on the generation of tides in the ocean (hence at the boundary of the region) is significant in these assessments. We find that the impact of SLR exceeds the impact due to energy extraction in the Gulf of Maine - even when considering very large energy extraction, of order 3.0 GW, in the Minas Passage. Although results showed that energy extraction does not significantly increase the amplitude of the tides in the far-field, a drastic change in the Bay of Fundy (e.g. full blockage) can lead to considerably higher amplitudes of tides (around 35 cm, or 12%) in the western Gulf of Maine. As a result of 1 m SLR, the theoretical tidal energy resources in some areas, including the Bay of Fundy can increase noticeably while any significant change in extracted energy highly depends on the turbine technology.
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Nanomechanical systems are useful to inspect some fundamental aspects of physics such as the relations between the elastic, thermal and electromagnetic properties of solid-state objects. As many other nanometer scale systems, they are interestingly subjected to strong nonlinearities that can guide the emergence of ubiquitous phenomena - like synchronization and chaos – or be exploited for manipulating and processing information. Such nanomechanical systems can be put in interaction with an optical cavity or coupled to an electrostatic-actuator. These two approaches are embedded in the wide topic of electro-optomechanics. This work takes advantage of photonic crystal versatility to investigate the nonlinear optical and mechanical dynamics of such electro- or optomechanical systems under coherent modulation.The first experiments use a nanophotonic platform combining a suspended InP membrane and an underneath integrated silicon waveguide. The membrane is etched with a 2D photonic crystal embedding several evanescently coupled defect cavities. These latter constitute a photonic molecule whose electromagnetic eigenmodes can be driven with a laser, via the waveguide, thus enabling a sensitive access to the mechanical noise spectrum of the membrane. Using a coherent modulation of the input laser field, we show how the input modulation sidebands are transferred to the mechanical frequency domain via the optomechanical interactions. The presence of thermo-optic nonlinearities further leads to a desymmetrization of the noise spectrum features. The experiment is described theoretically via Floquet theory. Relying on thermo-optic bistability, a bistable photonic mode is finally used to amplify a small signal by vibrational resonance.In a second part, we study two mechanically coupled electro-optomechanical photonic crystal nanocavities. Here the system is probed via an optomechanical scheme and driven with an integrated electro-capacitive actuation to drive the system's mechanical normal modes. Under low-power drive, the system can be robustly studied and calibrated using simple model of coupled damping harmonic oscillators. The use of higher power excitation reveals the strong intrinsic nonlinearities of the system which can be modeled by two driven coupled Duffing oscillators. The use of coherent modulation of the input force now reveals interesting period-doubling cascade route to chaos dynamics. The simultaneous excitation of both normal modes in their nonlinear regime makes them couple such that synchronization can be studied. As chaotic system can be used to generate chaos, this bichromatic synchronized chaotic dynamics could be exploited in novel multispectral data encryption protocols.This work open the way toward the exploration of large optomechanical arrays, in which collective dynamics could be studied.
Article
Until recently, high-resolution global modeling of tides has been done separately from high-resolution global modeling of the atmospherically-forced oceanic general circulation. Here we review the emerging class of high-resolution global models that are simultaneously forced by both atmospheric fields and the astronomical tidal potential. Such models simulate barotropic (surface) tides, internal tides, near-inertial motions, the eddying general oceanic circulation, and a partially resolved internal gravity wave (IGW) continuum spectrum (Garrett-Munk spectrum) simultaneously. We review the technical aspects of such global models and their myriad applications, for example, in satellite oceanography, operational oceanography, boundary forcing of regional models, tidal-cryosphere interactions, and assessment of future coastal flooding hazards in a changing climate with altered tides.
Spring tides generally occur a day or two after full and new moon, a delay usually called “the age of the tide”. This phenomenon is explained qualitatively by the phase change with frequency of an expansion of the tides in terms of the damped normal modes of the oceans. A rough quantitative interpretation indicates a lower bound of about 25 for the Q of normal modes at frequencies close to semi-diurnal. It appears that such modes are not well matched to the tidal potential. Various assumptions, such as that of linearity, are discussed.
Article
Nineteen years of hourly tide readings at Honolulu, Hawaii, and Newlyn, England, are analysed without astronomical prejudice as to what frequencies are present, and what are not, thus allowing for background noise. The method consists of generating various complex input functions c i , ( t ) for the same time interval as the recorded tide £( t ), and of determining the associated lag weights w in the convolutions ζ ^ ( t ) = ∑ i ∑ S ⁡ w i s c i ( t − τ s ) + ∑ i j ∑ s s ′ ⁡ w i j s s ′ c i ( t − τ s ) c j ( t − τ s ′ ) + . . . by the condition ((£—£)2) = minimum. The two expansions represent linear and bilinear processes; the Fourier transforms of w for any chosen i (or ij ) are the linear (or bilinear) admittances. Input functions are the (time variable) spherical harmonics of the gravitational potential and of radiant flux on the Earth’s surface; these functions are numerically generated hour by hour, directly from the Kepler-Newton laws and the known orbital constants of Moon and Sun, without time-harmonic expansions (unlike the harmonic method of Kelvin-Darwin-Doodson). The radiative input is required to predict non-gravitational tides, and it allows for the essential distinction that the Earth is opaque to radiation and transparent to gravitation.
Article
The surface-wave response of a harbour to a prescribed, incident wave is calculated on the hypotheses of shallow-water theory, an ideal fluid, and a narrow mouth, M. An equivalent electrical circuit is constructed, in which the incidentwave displacement in M appears as the input voltage and the flow through M appears as the input current. This circuit contains a radiation impedance, ZM, which comprises resistive and inductive terms, and a harbour impedance, ZH, which comprises an infinite sequence of parallel combinations of inductance and capacitance that bear a one-to-one correspondence with the natural modes of the closed harbour, together with a single capacitor, which corresponds to the degenerate mode of uniform displacement and dominates the response of the harbour as a Helmholtz resonator. Variational approximations to ZH and ZM are developed. The equivalent circuit exhibits parallel resonance at the resonant frequencies of the closed harbour, ωn, and series resonance at a second set of frequencies, $\tilde{\omega}_n$, where $\tilde{\omega}_n\downarrow \omega_n > 0$ and $\tilde{\omega}_0\downarrow 0$ as M [rightward arrow] 0; $\tilde{\omega}_0$ corresponds to the Helmholtz mode. A narrow canal between the coastline and the harbour is represented by a four-terminal network between ZM and ZH. It is shown that narrowing the harbour mouth and/or increasing the length of the canal does not affect the mean response of the harbour to a broad-band, random input except in the Helmholtz mode, but that it does increase significantly the response in that mode, which may dominate tsunami response. The general results are applied to circular and rectangular harbours. The numerical calculation of ZH for an arbitrarily shaped harbour is discussed.
Article
The tides of coastal embayments derive their energy from the ocean tides rather than from the direct action of lunar and solar gravitational forces. They are considered to be part of co-oscilating systems in which the period is determined by the tide in the outer sea, while the detailed character of the motion depends on the size and form of the enclosed basin (Defant, 1925; Doodson and Warburg, 1941). In narrow basins of simple form in which the influence of the earth's rotation is small, the motions resemble standing waves. Ideally, such waves are characterized by the simultaneous rise and fall of level on either side of a nodal line at which no change in elevation takes place. The elevation at high water increases with distance from the nodal line and slack water coincides with high and low water. The properties of tides due to standing waves may be deduced by assuming the motion to result from a primary progressive wave moving up the channel which undergoes complete reflection at a barrier. Mathematically, this situation may be treated as the interference of two identical progressive waves moving in opposite directions and so related that both waves are in phase at the barrier. This treatment of standing waves assumes the presence of total reflection, the absence of damping and the absence of effects of the earth's rotation. Since these conditions are not realized in natural tidal basins, the standing wave concept leads to oversimplification. In coastal embayments the most striking departure from the expectations of the standing wave concept is the discrepancy between times of high water and slack water, which may be great near the mouths of the larger bays and sounds. High water does not occur simultaneously within such enclosures but is earlier near the sea. Commonly, the nodal line is represented merely by a region in which the tidal range is small. These are effects which can be explained if damping of the primary and reflected waves by frictional or other effects is taken into account. According to these concepts, the problem of tidal behavior in embayments is to determine numerically the properties of the primary and reflected waves so as to account for the observed relations of amplitude and stream velocity of the actual tide and to correlate these numerical properties with the geographical form of the embayment. In the present paper an attempt is made to treat the tidal behavior in such a way that the observed changes in elevation and motion of the water along the path of the wave may be used to determine the distribution of phase of the primary and reflected waves along the channel and to measure the damping. The relations between the several aspects of a wave as it advances along a channel of uniform depth and width have been developed theoretically so as to show the times of high water and slack water, the range of the tide, and the phase relations of the primary and reflected waves along the channel for any degree of damping. By expressing the relationship of the several aspects of a reflected wave in a form in which the wave period is taken as the unit of time and distance is given in terms of the related phase changes, it is possible to eliminate the purely geographical dimensions and to obtain a wholly general description of the tide which may be used to indicate how any given channel distorts the behavior of the wave as it advances. In the case of irregular channels, in order to justify the application of relations deduced for uniform channels, in which the change in phase of the primary and reflected waves and their damping is proportional to the distance traveled and in which the velocity of the waves is constant, it is necessary to make the following assumptions: 1. That the effect of irregularities in cross section is to alter the velocity of the primary and reflected waves; i.e., to distort the geographical distribution of phase differences. 2.That damping is proportional to the phase change in the waves rather than to the distance traveled. 3. That the damping coeffcient, as defined, is constant along the length of the channel.
Tidal Dynamics in Estuaries, Estuary and Coastline Hydrodynamics (edit
• A T Ippen
• D R F Harleman
• AT Ippen