Dynamics and Modelling Ocean Waves
Abstract
This book addresses both fundamental and applied aspects of ocean waves
including the use of wave observations made from satellites. More
specifically it describes the WAM model, its scientific basis, its
actual implementation, and its many applications. The three sections of
the volume describe the basic statistical theory and the relevant
physical processes; the numerical model and its global and regional
applications; and satellite observations, their interpretation and use
in data assimilation.
... There are many operational-scale models of this kind which include coupling between long and short waves in order to predict storm surge and wave statistics including ADCIRC+SWAN [10], ADCIRC+STWAVE [8,11], AdH+STWAVE [41], ADCIRC+WAVEWATCHIII [44], and SCHISM-WWMIII [52]. Spectral wave models are expensive and in particular the computation of the source terms within the models can take a large portion of the computing load [50,42,34,1,45,30,32,52]. ...
... The source terms within the context of the WAE are both complex and highly empirical due to the complex nature of the physics it is trying to approximate and is still an active area of research [34,1]. Since the latter half of the 20th century, the general format of the source terms for the WAE has remained relatively unchanged, and is often written as a sum of wind input ( ), nonlinear interaction ( ), and dissipation( ) [32], though the specific parameterizations of these are always evolving. ...
... Beginning in the 1980s and continuing through the 1990s, many operational models based on this third generation paradigm were developed. Some popular examples of third generation wind wave models that are still widely used operationally are SWAN, WAVEWATCH III, WWM III and WAM [6,55,51,34]. Third generation models are different from first and second generation models in that they explicitly approximate the full nonlinear interaction in . Third generation models for the most part are still the common form of wind wave model. ...
A study is conducted that focuses on the trade-off between run time and accuracy of using reduced order source terms in a coupled wave-circulation model. In the study, ADCIRC+SWAN is used to model Hurricane Ike and Hurricane Ida. Water levels from the coupled model are compared to gauge data and significant wave height, peak period, and mean wave direction are compared to buoys. Results show potential for efficacy of reduced order source terms in order to eliminate computational cost while sacrificing minimal accuracy with respect to field measurements.
... The performance of WAM cycle 4 (Komen et al. 1994, hereafter WAM4) set up in terms of integrated parameters in the BoB is proved in many studies (Kumar et al., 2013;Anand et al., 2015). The performance of the other 3G models such as SWAN and WW3 in BoB can be found in Umesh et al. (2017), Umesh and Swain (2018), Umesh et al. (2019). ...
... The optimal package setting is found by carrying out statistical analysis. Their findings suggested that wind input due to Komen et al. (1994) and white capping dissipation due to Janssen (Janssen, 1991(Janssen, , 1992 in combination with Climate Forecast System Analysis (CFSR) wind forcing in the optimal one for Marmara sea. Recently, Umesh and Behera (2020) employed WW3 in Indian seas (ARB and BoB) and studied the integrated parameters during 2003 ad 2004. ...
... STP1 refers to the original WAM4. STP1 comprises of wind input due to Janssen (Janssen, 1989(Janssen, , 1991 and white capping dissipation from Komen-Janssen dissipation model (Komen et al., 1994;Janssen, 1989Janssen, , 1991. Janssen's wind model used quasilinear theory to see the effect of wind-generated gravity waves on ocean/atmosphere interactions. ...
... This research focuses specifically on spectral wind wave models which are defined through the Wave Action Balance Equation (WAE). These spectral wind wave models work by estimating the transport of wave action distributed among wind waves of various frequencies and directions as defined through the WAE [2,3,4,5,6]. The WAE presents challenges for numerical discretization techniques because it is a first order transient hyperbolic equation whose domain lies in 4 dimensions (2 in space, frequency, direction) with a non-divergent free velocity field and possibly nonlinear source/sink terms. ...
... The WAE presents challenges for numerical discretization techniques because it is a first order transient hyperbolic equation whose domain lies in 4 dimensions (2 in space, frequency, direction) with a non-divergent free velocity field and possibly nonlinear source/sink terms. Numerical spectral wind wave models have been in operation since the 1970s and are used daily as a tool in many fields including engineering, shipping, and meteorology [7,8,2]. They are also important tools for both improving our understanding of ocean processes and for predicting the impacts of severe weather events. ...
... Currently, there are many well-known spectral wind wave models used in practice such as ECWAM [7,9] which is supported by the European Centre for Medium-Range Weather Forecasts (ECMWF), Simulating WAves Nearshore (SWAN) [10] which is supported by Delft University of Technology, and WAVEWATCH III [8] which is supported by the United States National Oceanic and Atmospheric Administration (NOAA). A brief summary of the methods employed in contemporary numerical spectral follows but we note that there are many great historical reviews on numerical spectral wind wave models see e.g, [11,12,2,13,3,5,4,14]. ...
Several potential FEM discretizations of the Wave Action Balance Equation are discussed. The methods, which include streamline upwind Petrov-Galerkin (SUPG), least squares, and discontinuous Galerkin, are implemented using the open source finite element library FEniCSx for simplified 2-D cases. Open source finite element libraries, such as FEniCSx, typically only support geometries up to dimension of 3. The Wave Action Balance Equation is 4 dimensions in space so this presents difficulties. A method to use a FEM library, such as FEniCSx, to solve problems in domains with dimension larger than 4 using the product basis is discussed. A new spectral wind wave model, WAVEx, is formulated and implemented using the new finite element library FEniCSx. WAVEx is designed to allow for construction of multiple FEM discretizations with relatively small modifications in the Python code base. An example implementation is then demonstrated with WAVEx using continuous finite elements and SUPG stabilization in geographic/spectral space. For propagation in time, a generalized one step implicit finite difference method is used. When source terms are active, the second order operator splitting scheme known as Strang splitting is used. In the splitting scheme, propagation is solved using the aforementioned implicit method and the nonlinear source terms are treated explicitly using second order Runge-Kutta. Several test cases which are part of the Office for Naval Research Test Bed (ONR Test Bed) are demonstrated both with and without 3rd generation source terms and results are compared to analytic solutions, observations, and SWAN output.
... MIKE 21 SW model ( DHI, 2009a ) is a 3 rd generation spectral wave model suited for the propagation of waves in the oceanic scale and in nearshore areas. The governing equation of the model is based on the principle of conservation of the wave action-balance ( Komen et al., 1994 ) which reads in Cartesian coordinates: ...
... where N( x, y, σ, θ, t) is the wave action density, c x , c y are the propagation velocities in the spatial domain, c σ is the propagation velocity in the frequency domain, c θ is the propagation velocity in the directional domain, S denotes source and sink terms (e.g. generation due to wind, whitecapping dissipation, non-linear wave interactions, depthinduced breaking) and σ is the wave intrinsic angular frequency. All the aforementioned transfer velocities are computed according to the linear wave theory ( Komen et al., 1994 ). The hydrodynamic model MIKE21 HD ( DHI, 2009b ) is based on the solution of the depth-integrated shallow water equations, expressed by the continuity and momentum JID: OCEANO [mNS;January 24, 2024;17:49 ] equations in the Cartesian space: ...
... To assess the impact by Moskstraumen on the wave field, we used the WAM third-generation spectral wave model (Komen et al. 1994). In WAM, the sea state is modeled by solving the wave action evolution equation, i.e., a spectral representation of N 5 N(s, u; x, t) with a nonzero right hand side of (5), which in deep water takes the form (Komen et al. 1994) ...
... To assess the impact by Moskstraumen on the wave field, we used the WAM third-generation spectral wave model (Komen et al. 1994). In WAM, the sea state is modeled by solving the wave action evolution equation, i.e., a spectral representation of N 5 N(s, u; x, t) with a nonzero right hand side of (5), which in deep water takes the form (Komen et al. 1994) ...
Accurate estimates of extreme waves are central for maritime activities, and stochastic wave models are the best option available for practical applications. However, the way currents influence the statistics of space–time extremes in spectral wave models has not been properly assessed. Here we demonstrate impacts of the wave modulation caused by one of the world’s strongest open ocean tidal currents, which reaches speeds of at least 3 m s ⁻¹ . For a bimodal swell and wind sea state, we find that most intense interactions occur when the wind sea opposes the tidal current, with an increase in significant wave height and spectral steepness up to 45% and 167%, respectively. The steepness modulation strengthens the second-order Stokes contribution for the normalized extreme crests, which increases between 5% and 14% during opposing wind sea and current. The normalized extreme wave heights have a strong dependence on the narrow-bandedness parameter, which is sensitive to the variance distribution in the bimodal spectrum, and we find an increase up to 12% with currents opposing the wind sea. In another case of swell opposing a tidal jet, we find the spectral steepness to exceed the increase predicted by a simplified modulation model. We find support in single-point observations that using tidal currents as forcing in wave models improves the representation of the expected maximum waves, but that action must be taken to close the gap of measurements in strong currents.
Significance Statement
The purpose of this study is to investigate how a very strong tidal current affects the surface wave field, and how it changes the stochastic extreme waves formulated for a space–time domain. Our results suggest that the expected maximum waves become more realistic when tidal currents are added as forcing in wave models. Here, the expected extremes exceed traditional model estimates, i.e., without current forcing, by more than 10%. These differences have implications for maritime operations, both in terms of planning of marine structures and for navigational purposes. However, there is a significant lack of observations in environments with such strong currents, which are needed to further verify our results.
... A validated MIKE 21 spectral wave model [45] was developed using the same domain as the hydrodynamic model outlined in Section 2.1.1 (Figure 2). This fully spectral formulation is based on the wave action conservation equation as described in Komen et al. [46] and Young [47], where the directional-frequency wave action spectrum is the dependent variable. The discretization in the geographical and spectral spaces is performed using a cell-centered finite volume method [45]. ...
... This fully spectral model can simulate both swell and wind-generated waves. The quadruplet-wave interaction is described by the Discrete Interaction Approximate (DIA) [46]. White capping-driven energy dissipation is based on the formulation of Hasselmann [48] and Bidlot et al. [49], where the final dissipation coefficients used in the model, C dis (Cdis) and δ (DELTAdis), are 3.5 and 0.5, respectively. ...
Offshore anthropogenic activities such as the installation of Offshore Renewable Energy (ORE) developments and sediment extraction for marine aggregates have been shown to disrupt current flow, wave propagation, and sediment transport pathways, leading to potential environmental instability. Due to the complexity of the interconnected sediment transport pathways in the south-western Irish Sea combined with an increase in planned anthropogenic activities, the assessment of this risk is imperative for the development of a robust marine spatial plan. Subsequently, this study uses two-dimensional morphological modelling to build upon previous studies to assess the dependency of Arklow Bank’s local sediment transport regime on external sediment sources. Additionally, scenario modelling is used to identify vulnerable areas of this offshore linear sand bank to wind and wave-forcing and to examine the nature of this impact. A sediment budget is estimated for Arklow Bank, whereby seven source and nine sink pathways are identified. New evidence to support the exchange of sediment between offshore sand banks and offshore independent sand wave fields is also provided. The areas of the bank most vulnerable to changes in external sediment sources and the addition of wind- and wave-induced flow are analogous. These high vulnerability zones (HVZs) align with regions of residual cross-flow under pure current conditions. The restriction of sediment sources off the southern extent of Arklow Bank impacts erosion and accretion patterns in the mid- and northern sections of the bank after just one lunar month of simulation. Where tidal current is the primary driver of sand bank morphodynamics, wind- and wave-induced flow is shown to temporarily alter sediment distribution patterns. Wind and wave-induced flow can both accelerate and decelerate the east-west fluctuation of the upper slopes of the bank, yet the nature of this impact is inconsistent due to the misalignment of the directionality of these two forces. The methods and new knowledge derived from this study are directly applicable to tidally-dominated environments outside the Irish Sea.
... Part of the energy is also scattered across directions, conferring a distinctive two dimensional (directional) nature to the wave energy spectrum [2]. Wave growth ceases when waves become faster than the wind, a condition which normally occurs when the wave age, i.e., the ratio of wave phase velocity (C P ) to wind speed (U ), exceeds 1.25 [3]. ...
... In this regard, similar magnitudes of kurtosis were reported in laboratory observations of highly nonlinear mechanically and wind-generated water waves [2,4,6]. Comparison with theoretical estimates from equations (2,3) indicates that bound wave nonlinearity cannot capture strongly non-Gaussian statistics, while quasi-resonance interactions between free waves can detected them to a certain extent (see inset in Fig. 3). As the sea state developed into more mature conditions, the kurtosis decreased exponentially, approaching Gaussian statistics already for C P /U ≈ 1. Theoretical estimates (2,3) are consistent with observations under these circumstances, substantiating the weak nonlinear properties of the sea state for well developed sea states. ...
We report unique direct observations of surface waves from a stereo camera system aboard the South African icebreaker S.A. Agulhas II during an expedition across the Southern Ocean in the austral winter. Records include water surface elevation across a range of wave conditions, spanning from early stages of wave growth to full development. We give experimental evidence of rogue seas, i.e., sea states characterizided by heavy tails of the probability density function, well beyond the expectation based on bound mode theory. These conditions emerge during wave growth, where strong wind forcing and high nonlinearity drive wave dynamics. Quasi-resonance wave-wave interactions, which are known to sustain the generation of large amplitude rogue waves, capture this behaviour. Wave statistics return to normality as the wind forcing ceases and waves switch to a full developed condition.
... A variety of wave models were developed with their own approximations, and a wide range of applications have been carried out based on such models. To date, the phaseaveraged approach has been advanced to the third-generation wind wave models, eg., WAM, WAVEWATCHIII, SWAN, etc., which are widely employed to forecast/hindcast the evolution of spectra of wind waves and swells [9,10,57,68]. On the other hand, the phase-resolving models are developed to simulate the waves propagation and their interactions with bathymetry and structures with the free surface of each individual wave being resolved. ...
This paper presents a new numerical model based on the highly nonlinear potential flow theory for simulating the propagation of water waves in variable depth. A new set of equations for estimating the surface vertical velocity is derived based on the boundary integral equation considering the water depth variability. A successive approximation scheme is also proposed in this study for calculating the surface vertical velocity. With the usage of Fast Fourier Transform, the model can be efficiently used for simulating highly nonlinear water waves on large spatiotemporal scale in a phase-resolving approach. The new model is comprehensively verified and validated through simulating a variety of nonlinear wave phenomenon including free propagating solitary wave, wave transformations over submerged bar, Bragg reflection over undulating bars, nonlinear evolution of Peregrine breather, obliquely propagating uniform waves and extreme waves in crossing random seas. Good agreements are achieved between the numerical simulations and laboratory measurements, indicating that the new model is sufficiently accurate. A discussion is presented on the accuracy and efficiency of the present model, which is compared with the Higher-Order Spectral method. The results show that the present model can be significantly more efficient at the same level of accuracy. It is suggested that the new model developed in the paper can be reliably used to simulate the nonlinear evolution of ocean waves in phase-resolving approach to shed light on the dynamics of nonlinear wave phenomenon taking place on a large spatiotemporal scale, which may be computationally expensive by using other existing methods.
... The fundamental concept underpinning spectral wave modeling is the energy balance equation. This states that the evolution of the wave spectrum is the sum of three source terms describing the input of energy from the wind, the nonlinear transfer of energy within the wave variance spectrum, and the dissipation of energy from wave breaking or shallow water processes (Komen et al., 1994). Wave models compute an explicit representation of all three source terms and the evolution of the wave spectrum, without a priori assumptions about the spectral shape. ...
The impact of surface wave assimilation on hurricane track and intensity forecasts has been investigated using a fully coupled air-ocean-wave tropical cyclone data assimilation and forecast modeling system. A new 3DVAR wave assimilation method in the Navy Coupled Ocean Data Assimilation system (NCODA) maps the 1D wave energy spectra from buoys to 2D directional wave energy spectra using the maximum likelihood method (MLM) and corrects the wave model forecast component directional wave energy spectra. The Coupled Ocean/Atmosphere Mesoscale Prediction System for Tropical Cyclone Prediction (COAMPS-TC) is used to conduct three Hurricane Harvey (2017) air-ocean-wave coupled data assimilation and forecasting experiments with and without the wave data assimilation. Hurricane Harvey traversed through the Western Gulf of Mexico from 24 August to 1 September, 2017 and made landfall in the Texas and Louisiana coast. Validation of track, maximum wind speed, significant wave height, and mean absolute wave periods show wave assimilation of the 1D wave energy spectra from 13 National Data Buoy Center (NDBC) buoys reduced the forecast errors of these parameters compared to experiments without the wave assimilation. In spite of this positive outcome, the wave assimilation is unable to reduce Harvey’s 0-120 h forecast mean wave direction errors and correlation compared to the NDBC buoy time series
... Their values demonstrate a slight tendency to decrease with an increasing incidence angle. Thus, we can see that the wind errors always remain within the range of typical wind scatterometer errors of ±2 m/s and ±20° [45], proving the feasibility of the semicircle observation scheme for wind retrieval over the sea surface. ...
The rapid development of aircraft and unmanned aerial vehicles (UAV) increases their use, including in polar areas, which are characterized by their remoteness and rather harsh conditions. The dominant trends in airborne radar development are expanding their functionality and increasing the altitude of their applicability. Our study focuses on the functionality enhancement of airborne high-altitude conical scanning radars currently used for circular clouds and precipitation observations as well as for sea wind measurements. Recently, we showed how a semicircular observation scheme, instead of a circular one, can double the maximum applicable altitude of sea wind measurements made with such radars. Here we apply this approach to show how an airborne high-altitude conical scanning radar’s functionality can also be expanded for sea water/ice discrimination within a semicircular observation scheme, again doubling the maximum discrimination altitude compared to circular observations. The discrimination is performed in scatterometer mode using the minimum statistical distance of the measured normalized radar cross sections (NRCSs) to the geophysical model functions (GMFs) of the sea water and ice underlying surfaces. However, as no sea ice GMF is available for the considered horizontal transmit and receive polarization at the Ku band, we instead used a substitute sea ice GMF having the same azimuth isotropic property setting for its NRCSs as the averaged value of the measured azimuth NRCSs within the semicircular observations scheme. Our analysis found that incidence angles of 30°, 45°, and 60° are well suited to our sea water/ice discrimination method, and that incidence angles higher than 30° are preferable as they provide a higher difference in the statistical distance of the measured NRCSs to the sea ice and water GMFs, whereas an incidence angle of 30° provides the highest applicable altitude for sea water/ice discrimination and wind retrieval. We also demonstrated the ability of the sea water/ice discrimination procedure’s implementation for any airborne wind scatterometer or multimode radar operated in scatterometer mode over freezing seas to avoid entirely erroneous sea wind measurement results when a sea ice surface is observed. The obtained results can also be used for enhancing aircraft and UAV radars and for developing new remote sensing systems. Doi: 10.28991/ESJ-2024-08-02-07 Full Text: PDF
... Waves are one of the primary dynamic elements in the ocean. Komen [1] provide a comprehensive text on the dynamics and modeling of ocean waves, offering insights into the physics governing wave movement and the techniques used to model wave behavior. Donelan [2] delve into the nature of directional wave spectra, which characterize the distribution of wave energy across different directions and frequencies. ...
Coastal construction heavily depends on accurately estimating design wave parameters. This paper presents a technique for calculating ocean engineering design wave heights that addresses the challenges of inadequate wind speed and measured wave data in the field using High Performance Computing (HPC). The proposed method combines the Simulating WAves Nearshore (SWAN) wave model driven by wind with two different wind field models: the NCEP/NCAR reanalysis wind field and the Jelesnianski typhoon model wind field. By combining these models, the study reduces the underestimation of wind speed and inaccurate depiction of typhoon-related details. The method's effectiveness is demonstrated by applying it to calculate the design wave elements of the deep-sea breeding platform in Dongluo Island, Fujian. The study results show that the platform can experience a maximum wave height of 9.42 m during a 50-year recurrence period. The research shows that the platform's southwest corner is the most vulnerable location. This new calculation method is a significant improvement in ocean engineering design since it overcomes the limitations that come with the lack of wind speed and measured waves. By utilizing multiple wind field models, the calculated wave heights' accuracy and reliability is considerably enhanced. The application of this method to the breeding platform in Dongluo Island has yielded valuable insights for designing resilient structures in similar oceanic environments. This study demonstrates the important application of computational numerical simulations in the field of ocean engineering, providing high-precision predictive capabilities for structural design and risk assessment.
... Some examples of third-generation numerical models used to generate wave hindcasts are the WAM model (WAMDI Group, 1988;Bidlot et al., 2007), WAVEWATCH III model (hereinafter abbreviated as WW3) (WW3DG, 2019) and SWAN model (Booij et al., 1999). These wave models provide different parameterizations for several source terms (Tolman and Chalikov, 1996;Rogers et al., 2012) of wind-induced wave processes such as wave generation, propagation, and energy dissipation (Komen et al., 1994;Ardhuin et al., 2010;Leckler et al., 2013;Zieger et al., 2015). Surface wind fields retrieved from atmospheric reanalyses are always used as forcing input data of spectral wave models to generate wave historical reconstructions at global scales (Chawla et al., 2013;Perez et al., 2017;Sharmar and Markina, 2020). ...
... In this study, we use the configuration of the GCOAST coupled modelling framework (Bonaduce et al. 2020), which integrates contributions from the Nucleus for European Modelling of the Ocean (NEMO, Madec, 2016), and the spectral wave model WAM (ECMWF, 2019;Janssen 1989;Günther et al. 1992;Komen et al. 1994;Warszawski et al. 2014). The GCOAST model domain covers the Baltic Sea, the Danish GEBCO 2020) where Bathymetry is shown as a color bar. ...
... Такие спектры рассчитываются современными моделями прогноза волнового волненияKomen et al., 1994) и измеряются некоторыми дистанционными методами (радары синтезированной апертуры, сканирующие системы типа SWIM (англ. Surface Waves Investigation and Monitoring), CFOSAT (англ. ...
... The sublittoral zone is also largely congruent with the surf platform where deep-water waves are transformed (e.g. wave shoaling) and dissipated by friction at the lake bed and breaking [103]. Thereby, the wave energy interacts with the submerged macrophytes (e.g. ...
Wrack lines are a key formation along shorelines that provide organic matter and bring ecological diversity to the local environment. Although wrack line formation has been extensively studied along marine beaches and estuaries, in contrast, knowledge about the environmental variables that promote wrack line formation within inland lakes is widely lacking. In one of the first studies to focus on wrack line formation on lakesides, we analysed the dimensions, volume, elevation and particulate composition of 36 wrack lines across 20 shore sections of a large, oligotrophic Alpine lake with natural water level fluctuations (Lake Constance-Obersee). Using multivariate partial least squares (PLS) regression, we identified the key environmental variables that drive wrack accumulation in lakeside areas. Our results demonstrate that wrack line volume increased with (1) the width of the eulittoral zone as an indicator of the swash conditions (up-rush vs. down-wash), (2) high exposure to wind waves as indicated by the total effective fetch, (3) high exposure to ship waves (catamaran ferry), and (4) the width of the sublittoral zone as an indicator of the availability of source material ( Chara spp.) and of the wave energy dissipation rate of the incoming deep water waves. Sediment texture played only a minor role. Wide eulittoral zones and high ship wave exposure favoured high proportions of lake-borne components ( Chara remains, mollusc shells), while the reverse was true for land-based components. Anthropogenic wastes were only present in small proportions. We discuss four main factor groups influencing the amount of wrack in marine beaches and on lakeshores considering similarities (waves, breakers, swash, dissipation, relief) and differences (tides vs. annual water level fluctuations) of the two systems, and point out research gaps. We demonstrate that wrack line formation is also important in large inland lakes and can be analysed using basic ideas from relevant marine studies.
... In this module, the waves are described using the density spectrum ( , ), where represents the relative angular frequency ( = 2 ) and represents the direction of wave propagation. The equation governs the behavior of these waves is the wave action balance equation, which can be formulated in either cartesian or spherical coordinates (Eq. 1) [25]. ...
Coastal areas are usually heavily exploited. Numerous anthropogenic constructions are developed along the coastal areas for recreational, economic and/or cultural purposes. They influence the coastal hydrodynamics. Therefore, identifying the source of coastline transformation is essential for controlling these modifications and develop a sustainable coastal area. Simultaneous deployment of numerical modeling and RS imageries is a suitable approach for understanding hydrodynamic processes in coastal areas. In this study, the hydrodynamic condition of the Beris Port area located in the Makran region, north of the Gulf of Oman, has been analyzed using MIKE-21 software package, RS, and GIS techniques. Our results reveal the accretion of 20.97 ha adjacent to the breakwater since 1988. We also found that the shore near the port is heavily accumulated by sediment, while this is not the case for those shore far from the port. According to our results significant wave height is considerably low inside the port, even during the high season of summer, which is due to the construction of the port and the bay shape of the coast. The current speed, inside the port, is also low (0.01 m/s). The current adjacent to the port is in the opposite direction to the main current direction of the region, causing nearshore accretion. Therefore, it is believed that the accretion problem is due to the poor design of the breakwaters' layout. Thus, a new alignment for the breakwater is suggested, taking into account the hydrodynamics and morphodynamics of the area.
... see equations (2.31) and (2.32) in Komen et al (1996) page 83, with z α given by Charnok's relation with constant close toα = 0.0144 ...
The goal of this note is to provide an explanation for the saturation of the drag coefficient in strong wind conditions. The hydrodynamic model under consideration takes into account the important effects of airborne droplets of water in a thin layer above the water surface that effectively behave as a different fluid between the water and the air. Above this layer the model is coupled with a log-wind profile for the strong winds blowing above the sea. The main underlying mechanism governing the behavior of the drag coefficient is the Kelvin Helmholtz instability for capillary waves on the water surface and the continuity of shear stress along the intermediate interface.
... More specifically, the SWAN model algorithm is based on the wave action density N(σ, θ), which is the relation of the spectral energy density E(σ, θ) to the representative wave frequency σ [17]. The model relies on the spectral action balance [18,19] to describe the evolution of the sea state, which can be expressed by Equation (2) ...
This study estimates wave energy for the Moroccan Atlantic coast using SWAN, a third-generation wave model, covering a period of 30 years, from 1991 to 2020. The model is forced by the wind from the ERA-5 reanalysis dataset and uses boundary conditions generated by the WAVEWATCH III model. The significant wave height and period are used to obtain wave energy, which is analyzed at a regional scale. The mean wave energy density within the domain is assessed to be about 20 kW/m. Five specific locations are evaluated along the coast in order to determine the most energetic ones. The most energetic area of the Moroccan Atlantic coast is located at the center, between the cities of Agadir and Essaouira. Finally, the performance of six different wave energy converters is assessed through their power matrix for each of the five locations.
... Analisa arus dan gelombang perairan menggunakan model numerik untuk menyederhanakan perhitungan komplek yang sulit dilakukan dengan perhitungan numerik biasa (Abbott et al., 1978;Matt Folley, 2016). Penggunaan perhitungan numerik formulasi fully spectral untuk analisa model (Azhar et al., 2011;Johnson, 2006;Kirezci et al., 2021;Ondara & Wisha, 2016;Ris et al., 1995) didasarkan pada persamaan gelombang dimana spektrum directional frequency wave action sebagai dependent variabel (Komen et al., 1994;Young, 1999). Penelitian ini bertujuan untuk menganalisa kondisi arus, pasang surut dan gelombang eksisting sehingga data tersebut dapat digunakan sebagai data masukan untuk revitalisasi dermaga PPI Ulee Lheue. ...
Salah satu potensi wilayah perairan Banda Aceh adalah di bidang perikanan, baik itu perikanan tangkap ataupun perikanan budidaya. Dermaga perikanan di wilayah pesisir Kota Banda Aceh adalah dermaga yang terletak di Pelabuhan pendaratan Ikan (PPI) Ulee Lheue. Kondisi arus dan gelombang menyulitkan proses bongkar muat dan banyaknya kapal yang rusak pada saat bersandar merupakan permasalah yang terjadi di perairan sekitar dermaga tersebut. Penelitian ini bertujuan untuk mengetahui kondisi morfologi, arus dan gelombang di perairan tersebut sehingga hasil dari penelitian ini dapat menjadi masukan dalam melakukan revitalisasi dan peengembangan kawasan tersebut. Penelitian dilakukan dengan melakukan simulasi dan pemodelan hidrodinamika dengan menggunakan data batimetri, pasang surut, arah dan kecepatan angin serta morfologi garis pantai. Hasil menunjukkan bahwa tinggi gelombang maksimum di perairan dermaga perikanan Ulee Lheue 0,33 meter, energi gelombang 46,6 w/m dan periode maksimum 3,68 detik. Arah arus permukaan disekitar pesisir pantai di sekitar dermaga terlihat menyusuri bentuk morfologi pantai
... Numerous efforts have been made to develop parametric and numerical models for the large-scale hurricane wind and wave fields. For efficient engineering applications such as rapid hurricane risk assessment, the parametric models are preferred over the time-consuming weather models such as weather research and forecasting (WRF) model for hurricane winds (Skamarock et al. 2019) and wave model (WAM)/steady state spectral wave for deep-water/shallow-water waves (Komen et al. 1994;Massey et al. 2011). In the parametric hurricane wind models (e.g. ...
Long-span bridges with floating towers have recently drawn great attention from the engineering community. Due to their sensitivity to the aerodynamic and hydrodynamic loads during extreme storms, accurate and efficient simulation tools for hurricane winds and waves are needed for improved understanding of the complex dynamics of the fully coupled wind–wave–structure interaction system. Conventional simulation schemes usually generate winds and waves separately, and hence cannot capture the intense wind–wave interactions under hurricanes. In this study, a physics-statistics-based hybrid simulation scheme of nonstationary hurricane wind and wave fields is presented, where the winds and waves are coupled in both large and small scales. To simulate the large-scale winds and waves, a height-resolving hurricane wind model is coupled with a parametric hurricane wave model through a dependence between sea surface roughness and surface wind speed. In the small-scale simulations, the nonstationary wind fluctuations are statistically obtained by a Hilbert-wavelet-based scheme in which the target parameters (e.g. fluctuation intensity) are estimated based on the local sea state, while the nonstationary sea surface elevations are physically acquired by solving the governing equation of the nonlinear wave evolution under the action of winds. The simulation fidelity of the proposed physics-statistics-based hybrid scheme is demonstrated by generating the coupled nonstationary wind and wave fields approaching to a hypothetical long-span bridge with floating towers under a hurricane event.
... in which E(σ, θ) represents energy density spectrum, and A and B depend the on wave frequency and direction, as well as wind speed and direction. More detailed description can be referred to in the documents [34][35][36][37][38][39]. Note that the radiation stress tensors S xx , S xy , S yx , and S yy of Equations (7) and (8) can be written as: ...
Coastal evolutions are expected to have a significant impact on storm tides, disproportionately aggravating coastal flooding. In this study, we utilize a nested storm tide model to provide an integrated investigation of storm tide responses to changes in coastline and bathymetry along the Zhejiang coasts. We selected coastline and bathymetry data from 1980 and 2016, as well as data from three typical typhoon events (i.e., Winnie, Haikui, and Chan-hom) for simulating the storm surge processes. The results indicate that changes in the coastline and bathymetry from 1980 to 2016 have resulted in an increase in storm tides in the northern part and a decrease in the central part of Zhejiang. Specifically, storm tides in Hangzhou Bay have increased significantly, with an average increase of about 0.3 m in the maximum storm tides primarily attributed to coastline changes. On the contrary, in smaller basins like Sanmen Bay, while reclamation itself has reduced peak storm surges, rapid siltation has consequently exacerbated the storm surge. By decomposing storm tides into astronomical tides and storm surges, we discovered that the change in tidal levels was twice as significant as the surge change. Moreover, the nonlinear tide–surge interaction was nearly four times that of the pure surge, significantly contributing to storm surge variation. Alterations in the momentum balance reveal that the water depth-induced bottom friction and wind stress increase contributes to the local enlargement of storm tides at the bay head, while the coastline changes exaggerate nearshore storm tides through an increase in the advection term.
... In addition to WW3, there are two other third-generation models that have been developed to further our understanding of wave dynamics. The first is WAM (Komen et al., 1996), which is considered the first thirdgeneration model, and the second is SWAN (Booij et al., 1999), which focuses on the physics of waves in the coastal zone. ...
Accurate wave predictions are crucial for many marine-related activities, including offshore operations, navigation, and marine renewable energy. To improve the forecast performance, this study presents a data assimilation system that utilizes the WAVEWATCH III wave model and the local Ensemble Optimal Interpolation scheme to assimilate significant wave heights data from HY-2B altimeter in the China Seas. The effects of assimilation are analyzed in both coastal and offshore regions at different distances from assimilated satellite data points during a forecast period. The results show that systematic bias in wave forecasting for both offshore and nearshore locations can be effectively reduced through the use of data assimilation, with localization employed to minimize the influence of random errors. Nearshore forecasting benefits from assimilation to a greater extent than offshore forecasting, with a more enduring improvement observed. Additionally, the decline in forecast improvement with increasing distance from assimilated data highlights the necessity of assimilating a greater quantity of observational satellite data. Furthermore, careful consideration should be given to the size of the ensemble when using a specific localization radius, as the improvement in skill may stagnate with larger ensembles. Finally, assimilating additional nearshore satellite data does not negatively impact the predictive precision.
... Hasselmann, 1962;S. Hasselmann et al., 1985;Komen et al., 1994) were developed. Third-generation wave models are phase-averaged Abstract Extreme significant wave height estimates, and their probability of exceedance, are fundamental offshore and coastal engineering design parameters. ...
Extreme significant wave height estimates, and their probability of exceedance, are fundamental offshore and coastal engineering design parameters. These estimates are characterised by uncertainty due to an incomplete understanding of the atmosphere‐ocean energy and momentum exchanges during intense storms. This particularly affects extreme wave statistics of ocean regions exposed to large and frequent synoptic disturbances such as Extra‐Tropical Cyclones (ETCs). In this work, we assessed the performance of global phase‐averaged spectral wave models in representing the 1 in 100‐year sea state generated by a Southern Ocean ETC in April 2021. We collected in‐situ and remote sensing observations, from the storm generation region to its decaying phase and the impact on South‐East Australian coastlines. We compared the observations with a suite of reanalysis and hindcast global wave model datasets. While comparing well for wind speed up to 20 m/s, the models presented differences in solving the air‐sea momentum exchange between the atmosphere and the ocean for wind speed velocities between 20 and 35 m/s, which are a distinctive characteristic of ETCs. Despite marked differences in the storm generation region, the models converged to a similar representation of the swell systems impacting the South‐East Australian coastlines, as demonstrated by a comparison with deep‐water buoy observations close to the coastlines. Furthermore, we found that the energy of the ERA5 reanalysis, which assimilates satellite wave height measurements is quickly dispersed and, as such, of little advantage in representing the 9.9 m significant wave heights that impacted the South‐East Australian coastlines on April 10 th 2021.
... where d/dt denotes material derivative and S the source term . In third generation spectral wave models, the spectrum can describe multi-modal sea states and the source term contains parameterizations of the physical processes that include energy input by winds, nonlinear energy transfer among frequency components, and dissipation through wave breaking and bottom friction (e.g., Tolman, 2008;Komen et al., 1994;Zijlema, 2010). These models owe their success to their low computational costs and proven accuracy for typical ocean conditions due in part to the extensive and continuing efforts on parameterization of the physics involved (e.g., . ...
... The significant wave height required to force OVA14 (cf. Table 1) was provided by the 0.1° resolution ocean-wave WAM model (ECMWF-IFS), based on the work by Komen et al. (1996). Though no validation of the WAM model is performed in this study, this same model was used by Ovadnevaite et al. (2014) for the formulation of OVA14. ...
This study contributes to the communal effort to improve understanding of sea spray generation and transport. For the first time, laboratory‐derived sea spray generation functions (SSGFs) are parameterized in the Meso‐NH mesoscale atmospheric model and are field tested. Formulated from the MATE19 laboratory experiments (Bruch et al., 2021) the two SSGFs are driven by the upwind component of the wave‐slope variance (herein B21A), or both and the wind friction velocity cubed (herein B21B). In this first attempt to incorporate the SSGFs in Meso‐NH, the simulations are run without a wave model, and the wave‐wind SSGFs are assumed wind‐dependent. Model evaluation is achieved with a new set of sea spray and meteorological measurements acquired over the 0.1–22.75 μm radius range and U 10 1–20 m s ‐1 wind speeds onboard R/V Atalante during the 25 day SUMOS field campaign in the Bay of Biscay. The B21B SSGF offers particularly good sensitivity to a wide range of environmental conditions over the size range, with an average overestimation by a factor 1.5 compared with measurements, well below the deviations reported elsewhere. B21A also performs well for larger droplets at wind speeds above 15 m s ‐1 . Associated with airflow separation and wave breaking, wave‐slope variance allows to represent multiple wave scales and to scale sea spray generation in the laboratory and the field. Using Meso‐NH simulations we find that sea spray may be transported inland and to altitudes well above the marine atmospheric boundary layer.
... WaveWatch III ® ( [50][51][52], hereafter, WW3) is a third-generation wave model developed at NOAA/NCEP in the spirit of the WAM model [53][54][55]. WW3 is a widely used spectral model for wave hindcast and forecast in ocean engineering and Earth sciences. In WW3, the Wave Action Equation (WAE) is solved using a splitting method to treat in different steps spatial propagation, intra-spectral propagation, and source term integration [56][57][58]. ...
Knowledge of wave climate is essential for efficient management of the world’s coastal areas. Senegal is a relevant case, given its high coastal vulnerability to energetic wave conditions. This study investigates wave climates along the coastal zone of Senegal based on a new high-resolution hindcast covering the period 1980–2021. This study evaluates the average, seasonal, and extreme values for the significant wave heights (Hs), periods (Tm02/Tp), and mean directions (DIR). In boreal winter, the wave climate is dominated by swells coming from the North-Atlantic lows. In contrast, in boreal summer, the Southern Coast (from Dakar to Casamance) is exposed to swells generated in the South Atlantic Ocean. Throughout their refraction around the Dakar Peninsula, NW swells rotate by ~100° from NW to SW, while their Hs is roughly halved when reaching the Southern Coast of Senegal. Over the studied period, trends in Hs are weak (~0.6 cm.decade−1) on the Northern Coast and double on the Southern Coast (~1.2 cm.decade−1), mostly due to an increase during boreal summer (2 cm.decade−1). The wave periods show weak trends (~0.05 s.decade−1), and DIRs show weak counterclockwise rotation (−1°.decade−1). These trends are explained by the main climate modes of the Atlantic Ocean (NAO/EA during winter, SAM during summer) and are important for future research and long-term monitoring of the Senegalese Coast.
The Earth is no longer the only known celestial body containing one or more liquid phases. The Cassini spacecraft has discovered seas of hydrocarbons at the surface of Titan, while a series of corroborating evidences argue in favor of the existence of an aqueous ocean beneath the icy crust of several moons. Capillarity embraces a family of physical processes occurring at the free surface of a liquid. These phenomena depend on the liquid properties and on the local planetary conditions. Capillarity may have important direct or indirect implications on the geoscientific and astrobiological points of view. In this paper, we discuss capillarity physics among solar system objects and expected consequences for planetary science.
Accurate modelling of air-sea processes is essential for reliable forecasts of Mediterranean tropical-like cyclones (also known as “Medicanes”). Medicanes occasionally develop in the Mediterranean causing extreme weather conditions with catastrophic potential due to excessive precipitation, windstorms, and coastal flooding. In this work, we investigate how the complexity of ocean-wave-atmosphere coupling and model initialization affect the simulated track and intensity of the Medicane Ianos (2020). Results indicate that the model's initial conditions and the cyclone's development stage are the main drivers of track position errors, while ocean and wave feedback have a significant impact on the intensity and evolution of the cyclone. Compared with an atmosphere-only simulation, an atmosphere-ocean coupled system reproduces the cyclone's SST cooling effect (up to 3.7 °C), in agreement also with the satellite observations thus, reducing the cyclone intensity, as estimated by the minimum MSLP, the 10-m wind speed and the surface enthalpy flux. Adding a wave model to the coupled system, further increases the magnitude of ocean cooling (by about 1.2 °C), due to increased sea surface roughness leading to increased wind stress and enhanced upper ocean mixing. Overall, surface waves are shown to have competing effects on cyclone intensity i.e., negative feedback via increasing the surface momentum flux and positive feedback via increasing the enthalpy flux, the latter being more sensitive to surface roughness rather than to SST modifications brought by the wave coupled system. The turbulent air-sea fluxes under high winds, appear to be very sensitive to sea-state patterns resolved by the coupled models, highlighting the need to improve forecasting systems for extreme weather events in the Mediterranean.
The generation and propagation mechanism of strong nonlinear waves in the South China Sea is an essential research area. In this study, the third-generation wave model WAVEWATCH III is employed to simulate wave fields under extreme sea states. The model, integrating the ST6 source term, is validated against observed data, demonstrating its credibility. The spatial distribution of the occurrence probability of strong nonlinear waves during typhoons is shown, and the waves in the straits and the northeastern part of the South China Sea show strong nonlinear characteristics. The high-order spectral model HOS-ocean is employed to simulate the random wave surface series beneath five different platform areas. The waves during the typhoon exhibit strong nonlinear characteristics, and freak waves exist. The space-varying probability model is established to describe the short-term probability distribution of nonlinear wave series. The exceedance probability distributions of the wave surface beneath different platform areas are compared and analyzed. The results show that with an increase in the platform area, the probability of a strong nonlinear wave beneath the platform increases.
The global rise in energy consumption necessitates evaluating alternative energy sources, including marine energy. Modeling the transient nature of oceans remains a persistent challenge in harnessing marine energy. Using digital tools, we simulated various wave sizes to gain insights into wave behavior. Our study focuses on analyzing wave energy along Morocco's Atlantic coast. Using the ECMWF ERA dataset, we compared wave properties in five cities from 2005 to 2010: Tangier, Dakhla, Casablanca, El Jadida, and Essaouira. Results revealed significant wave power potential, particularly in Casablanca, El Jadida, and Essaouira. These Atlantic sites showed an average maximum power of up to 40 kW/m, with Essaouira having an annual average power of 13 kW/m. In summary, marine energy offers promising opportunities to meet global energy needs. Our study highlights the potential for wave power plants along Morocco's Atlantic coast, with specific locations showing strong wave power potential.
This study investigates ocean wave dynamics in the Atlantic Ocean through a comprehensive derivation process integrating fluid dynamics principles and statistical analysis techniques. Starting from the fundamental wave equations, we progress through the derivation of the Laplace transform, spectral wave height equation, inverse Fourier transform, cumulative distribution function, and probability distribution function. The final equation synthesizes these steps to estimate the probability of extreme wave events. This research enhances our understanding of wave behavior and its implications for coastal engineering and climate studies.
The nonlinear Schrödinger equation is widely used as an approximate model for the evolution in time of the water wave envelope. In the context of simulating ocean waves, initial conditions are typically generated from a measured power spectrum using the random-phase approximation, and periodized on an interval of length L. It is known that most realistic ocean waves power spectra do not exhibit modulation instability, but the most severe ones do; it is thus a natural question to ask whether the periodized random-phase approximation has the correct stability properties. In this work, we specify a random-phase approximation scaling, so that, in the limit of L→∞,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L\rightarrow \infty ,$$\end{document} the stability properties of the periodized problem are identical to those of the continuous power spectrum on the infinite line. Moreover, it is seen through concrete examples that using a too short computational domain can completely suppress the modulation instability.
This introductory chapter discusses wave characteristics and related terminologies in general. We first view waves as a motion of a spatial pattern (a snapshot) of an entity on the time axis and as a temporal oscillation on the spatial axis. This spatiotemporal behavior leads to the concept of phase velocity, which characterizes the medium that the wave propagates through. In the second half of the chapter, we discuss some mathematical aspects of wave dynamics. We derive wave equations from the spatiotemporal characteristics and discuss their solutions in general.
We present a global wind wave climate model ensemble composed of eight spectral wave model simulations forced by 3-hourly surface wind speed and daily sea ice concentration from eight different CMIP6 GCMs. The spectral wave model uses ST6 physics parametrizations and a global three-grid structure for efficient Arctic and Antarctic wave modeling. The ensemble performance is evaluated against a reference global multi-mission satellite altimeter database and the recent ECMWF IFS Cy46r1 ERA5 wave hindcast, ERA5H. For each ensemble member three 30-year slices, one historical, and two future emission scenarios (SSP1-2.6 and SSP5-8.5) are available, and cover two distinct periods: 1985–2014 and 2071–2100. Two models extend to 140 years (1961–2100) of continuous wind wave climate simulations. The present ensemble outperforms a previous CMIP5-forced wind wave climate ensemble, showing improved performance across all ocean regions. This dataset is a valuable resource for future wind wave climate research and can find practical applications in offshore and coastal engineering projects, providing crucial insights into the uncertainties connected to wind wave climate future projections.
The behavior and predictability of rip currents (strong, wave‐driven offshore‐directed surfzone currents) have been studied for decades. However, few studies have examined the effects of rip channel morphology on the rip generation or have compared morphodynamic models with observations. Here, simulations conducted with the numerical morphodynamic model MIKE21 reproduce observed trends in flows and bathymetric evolution for two channels dredged across a nearshore sandbar and terrace on an ocean beach near Duck, NC, USA. Channel dimensions, wave conditions, and flows differed between the two cases. In one case, a strong rip current was driven by moderate height, near‐normally incident waves over an approximately 1‐m deep channel with relatively little bathymetric evolution. In the other case, no rip was generated by the large, near‐normally incident waves over the shallower (∼0.5 m) channel, and the channel migrated in the direction of the mean flow and eventually filled in. The model simulated the flow directions, the generation (or not) of rip currents, and the morphological evolution of the channels reasonably well. Model simulations were then conducted for different combinations of the two channel geometries and two wave conditions to examine the relative importance of the waves and morphology to the rip current evolution. The different bathymetries were the dominant factor controlling the flow, whereas both the initial morphology and wave conditions were important for channel evolution. In addition, channel dimensions affected the spatial distribution of rip current forcings and the relative importance of terms.
Preliminary results of the derivation of a new phase-resolving (deterministic) spatio-temporal nonlinear model of water wave evolution in nondeep waters with constant bathymetry are presented in this paper. The model is the first of its kind to include a nonlinear dispersion relation and cubic (fourwave) interactions. Simulations show the importance of nonlinear dispersion for bound wave components which, if not properly accounted for, result in inaccurate transfer of wave energy. We also investigate the relative importance of cubic nonlinearity, as compared to a quadratic (three-wave interactions) one, and show that it is non-negligible. The model provides the first step before the incorporation of these extensions into a phase-averaged (stochastic) formulation, which can then be used as a more accurate nonlinear source term for wave forecasting models.
Nearshore is dynamic and constantly affected by the environmental conditions of the sea, on the other hand, it plays a great role in economic-social management issues. The shoreline is also a part of the nearshore that is constantly affected by tide, waves, currents and human activities. Therefore, it is expected that this section will always be accompanied by changes. The first step of any nearshore development and construction is to know the hydrodynamic conditions of the area. In this study, an attempt has been made to investigate the sensitivity of the shoreline of Bandar Lengeh County by considering the height and energy of nearshore waves. Wave height and energy data have been estimated by running the MIKE 21 spectral wave numerical model for a period of 12 months. The results have been obtained with good accuracy compared to ECMWF data. The correlation coefficient and the RMSE are equal to 0.95 and 0.239. The modeling results show that the maximum average height and energy of waves in the shoreline are 0.22 m and 0.21 kW/m, respectively, in the last months of spring and the beginning of summer. Using the fuzzy-gamma logic and considering the gamma coefficient as 0.9, shoreline sensitivity to variables has been estimated and finally divided into three classes High, moderate, and low. 20% of the shoreline is in the high class, and 23% and 57% of the shoreline are in the moderate and low class, respectively.
Lateral changes in the group velocity of waves propagating in oceanic or coastal waters cause a deflection in their propagation path. Such refractive effects can be computed given knowledge of the ambient current field and/or the bathymetry. We present an open-source module for solving the wave ray equations by means of numerical integration in Python v3. The solver is implemented for waves on variable currents and arbitrary depths following the Wentzel–Kramers–Brillouin (WKB) approximation. The ray tracing module is implemented in a class structure, and the output is verified against analytical solutions and tested for numerical convergence. The solver is accompanied by a set of ancillary functions such as retrieval of ambient conditions using OPeNDAP, transformation of geographical coordinates, and structuring of data using community standards. A number of use examples are also provided.
The problem of shoaling on coastal structures is the result of an event that occurs as part of the natural cycle. In cases where shoaling cannot be detected or prevented, various economic and operational problems may arise and may cause disruptions. In this study, the complex coastal dynamic impact of shoaling on three sequential fishery coastal structures located within the borders of Rize province in the Eastern Black Sea region of Türkiye was examined in terms of bathymetric changes and sediment transport under the influence of the incident wave climate. The effects of these structures on each other were also investigated. With this aim, bathymetric measurements were carried out to examine the impact of waves on seabed erosion and deposition. A serious shoaling problem was identified at one of the harbor launches under investigation, where approximately 13,200 m3 of deposition occurs annually in a relatively small harbor launch area. Such physical problems are thought to be the result of shoaling, the selection of sites that are not viable for fishery-related coastal structures, or the wrong positioning of the breakwater.
The global wave model WAVEWATCH III®; works well in open water. To simulate the propagation and attenuation of waves through ice-covered water, existing simulations have considered the influence of sea ice by adding the sea ice concentration in the wind wave module; however, they simply suppose that the wind cannot penetrate the ice layer and ignore the possibility of wind forcing waves below the ice cover. To improve the simulation performance of wind wave modules in the marginal ice zone (MIZ), this study proposes a parameterization scheme by directly including the sea ice thickness. Instead of scaling the wind input with the fraction of open water, this new scheme allows partial wind input in ice-covered areas based on the ice thickness. Compared with observations in the Barents Sea in 2016, the new scheme appears to improve the modeled waves in the high-frequency band. Sensitivity experiments with and without wind wave modules show that wind waves can play an important role in areas with low sea ice concentration in the MIZ.
Optimisation of energy efficiency and operational performance as well as assessment of safety levels and emissions of marine operations require detailed information about the acting wave system. It is possible - with an analogy to classical wave buoys - to estimate the directional wave spectrum by processing sensor measurements of wave-induced responses (e.g., motions and structural responses) from a ship. Compared to other sources of wave data (e.g., buoys, satellites, third-generation wave models), estimation concepts using the ship itself as a buoy provide the wave spectrum at the exact spatio-temporal point, potentially increasing accuracy and with minimal associated cost. This paper gives an overview of the technology, discusses associated uncertainties, and highlights new developments made for estimating waves via measured ship responses.
Data from the 1996 ASGAMAGE experiment, performed in the southern North Sea at research platform Meetpost Noordwijk (MPN), are analysed for the parameters affecting the momentum flux. The stress turns out to be quadratically related to the 10-m wind speed and linearly to the wind speed at a wavelength related level. The Charnock parameter (dimensionless roughness length) shows a pronounced correlation with wave age. This implies, due to a coupling between wave age and the steepness of the waves, a connection between the stress and the steepness. We find that our North Sea results are consistent withopen ocean observations. For a given wind speed the mean stress at MPN turns out to be higher because the wave age there is in general lower. We define and give an expression for a drag coefficient at a wavelength related level that can be calculated straightforwardly from the wave age and then reduced to a standard level.
Ocean wave swell generated in the vicinity of Campbell Island in the Southern Ocean is tracked along Great Circle paths across the Pacific Ocean. Data from a wave buoy at Campbell Island provides data on the directional spectrum in the generation region. The swell is measured at locations along a series of 19 Great Circle paths across the Pacific using Sentinel-1 SAR and CFOSAT satellite data. The WAVEWATCH III spectral wave model is used as a diagnostic tool to investigate the physical processes active in the swell propagation and decay. The results indicate that present day spectral wave models over-estimate the decay rate of swell. Although these models contain source terms to represent swell decay and negative wind input, these terms still largely remain tuning parameters. The data indicates that further research is required to adequately represent the observed magnitudes of the swell decay. In addition, the data show that currents have only a small impact on the observed swell decay and that islands can have a major impact. Such island impacts are poorly represented by spectral wave models.
To reduce life threats and financial losses under hurricane weather and traffic conditions, stakeholders need to make a sequence of decisions (e.g., enforcing traffic control and/or broadcasting travel advisory) with the presence of various uncertainties, which could be formulated as a Markov decision process (MDP). To effectively solve the MDP for optimal operation of hurricane-impacted transportation networks, a risk-informed decision-support framework is proposed consisting of both a decision-making environment and tool. The decision-making environment involves essentially three coupled modules of hurricane hazard, transportation infrastructure, and traffic flow, where the uncertainties from natural environment, built environment, and human behavior are examined. Specifically, multiple correlated hazards for each specific storm are capsulated in the hurricane hazard module, representative hurricane-vulnerable infrastructure components and associated moving vehicles are evaluated in the transportation infrastructure module, and network-level traffic relations are addressed in the traffic flow module. In view of the complexity and intractability of a hurricane-transportation infrastructure-traffic system through full model representation, the efficient low-dimensional modeling approaches including both physics-based analytical and data-driven surrogate models are utilized in all these three simulation modules. Considering an explicit probabilistic model for the decision-making environment (and hence state transition function) is not available, the operation optimization (involving competing objectives of traffic safety and mobility) is accomplished through a deep reinforcement learning-based decision-making tool that learns to act optimally (involving both traffic control and travel advisory actions) by directly interacting with the environment. A hypothetical case study is conducted to verify the applicability and effectiveness of the proposed framework as a testbed for optimal operation of hurricane-impacted transportation networks.
The instability of Stokes waves, steady propagating waves on the surface of an ideal fluid of infinite depth, is a fundamental problem in the field of nonlinear science. The dominant instability of these waves depends on their steepness. For small amplitude waves, it is well known that the Benjamin-Feir or modulational instability dominates the dynamics of a wave train. We demonstrate that for steeper waves, an instability caused by disturbances localized at the wave crest vastly surpasses the growth rate of the modulational instability. These dominant localized disturbances are either coperiodic with the Stokes wave or have twice its period. In either case, the nonlinear evolution of the instability leads to the formation of plunging breakers. This phenomenon explains why long propagating ocean swell consists of small-amplitude waves.
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