Environmental Fluid Mechanics

Vegetation present in the water streams, on the banks and in the floodplain areas largely affects the river hydraulics. Indeed, river vegetation significantly influences hydrodynamics, sediment transport, bedforms, and pollutant transport. Environmental management of rivers requires an understanding of the various processes and predictive capabilities of models. In the past, many studies were conducted, especially in laboratory settings, in order to quantify flow resistance due to vegetation. It is only recently that the effects of vegetation on sediment transport came to the attention of researchers. In particular, both suspended and bedload transport were considered. This paper reviews recent works conducted on the effect of vegetation on incipient sediment motion and bedload transport. With regard to the incipient sediment motion, methods based on critical velocity, turbulence, vegetation drag, and velocity in the bed roughness boundary layer have been discussed. For bedload transport, methods based on bed shear stress, turbulent kinetic energy, a revisiting of classical formulas for estimating bedload transport in non-vegetated channels, and estimation from erosion around a single vegetation stem are analyzed. Finally, indications on further research and new development are provided.

A two-dimensional, vertically integrated, non-linear numerical model was applied to investigate the Urias coastal lagoon’s (URCOL) tide-driven currents, bed load sediment transport, and seabed morphodynamics. The coastal body of water, located on the eastern side of the Gulf of California, includes the Mazatlán harbour, the most important port on the Pacific Mexican coast due to the relevant activities like the heavy vessel traffic. URCOL also includes an extensive aquaculture infrastructure at the lagoon head. The tidal hydrodynamic modelling revealed the mixed character of tides predominantly semidiurnal in the lagoon. The numerical computation at the harbour entrance showed an ebb-dominant tidal distortion. The distribution patterns of the erosion and accretion rates are consistent with the convergent and divergent character of the vectors of sediment transport rates. The sediment accretion has been predicted mainly in the middle part of the channel, right where the channel starts curving, changing the alignment of the lagoon. The tidal hydrodynamics, sharp topographic gradient, and geometric features of the lagoon seem to determine the location of accretion and erosion areas.

Because of the interaction between the flow and piers, the velocity of coherent turbulent flow around tandem double round-ended piers becomes complicated, proposing a threat to the navigation in the bridge area. This paper numerically investigates the flow velocity performance around tandem double round-ended piers by performing a flow field model and moving ship model. Flow velocity performance was analyzed under different inflow velocities in the four flow modes: single mode, attachment mode, transitional vortex detachment mode (TVDM), and independent vortex detachment mode. The yaw moment was employed to verify the performance from the perspective of the force on the ship. In each mode, the flow velocity in x\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x$$\end{document} axis (vx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${v}_{x}$$\end{document}) and y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$y$$\end{document} axis (vy\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${v}_{y}$$\end{document}) behind the downstream pier are similar, the difference mainly occurs between the two piers. In TVDM, the spacing ratio (L/D = 6) is close to the critical spacing ratio (L/D)c which is significantly affected by the inflow velocity. Under high inflow velocity, vx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${v}_{x}$$\end{document} and vy\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${v}_{y}$$\end{document} are greater, KP and critical spacing ratio are smaller, and the formation of the Karman vortex street is closer to the pier. Verification of flow velocity performance by yaw moment has high reliability. The extreme values of yaw moment mostly appear in the sections where vy\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${v}_{y}$$\end{document} increases and vx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${v}_{x}$$\end{document} appears to be negative. The research on the flow velocity around the piers in various modes provides a reference in studying on turbulence width and improving navigation safety in the bridge area.

The formation of a layered structure in the form of vertically separated density steps (staircases) in stably stratified fluids has been reported in many laboratory and oceanic studies as well as in the terrestrial atmospheric boundary layer (ABL) to a lesser extent, with attribution to different dynamical mechanisms. This paper presents observations of layered structures in fog-laden marine ABL, where both fog and density steps appear almost simultaneously following a turbulent mixing event under nocturnal conditions. The observations were made during the C-FOG (2018) field campaign aboard a research vessel using rawinsonde launches, aided by a suite of supporting onboard instruments. This is a case of great practical interest because of the impediment by fog-laden staircases to optical and near-infrared wave propagation in the ABL due to enhanced beam jitter by density steps and beam attenuation by fog. A new mechanism is proposed to explain the genesis of density layering, wherein steps appear when fluid parcels with significant buoyancy differences (Δb\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta b$$\end{document}) osculate in regions of weak turbulence (local length and velocity scales, LH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L}_{H}$$\end{document} and uH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${u}_{H}$$\end{document}, respectively) devoid of adequate inertial forces (∼uH2/LH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim {u}_{H}^{2}/{L}_{H}$$\end{document}) to cause fluid parcels to stir past each other. This is expressed in terms of a local bulk Richardson number criterion Ri=ΔbLH/uH2>Ric\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Ri= {\Delta b{L}_{H}/{u}_{H}^{2}>Ri}_{c}$$\end{document}, where Ric\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Ri}_{c}$$\end{document} is a critical value. A simple laboratory experiment with an idealized (three layer) density stratification and a known turbulence source (oscillating grid) was performed to demonstrate the proposed mechanism, and through a combination of measurements and modeling it was found Ric\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Ri}_{c}$$\end{document}≈\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\approx$$\end{document} 1.5. The proposed criterion was consistent with C-FOG field observations as well as representative previous layering observations in the atmosphere and ocean due to localized turbulence mixing events caused by Kelvin–Helmholtz billowing.

This investigation was inspired by the work of Dorbolo et al. (Phys Rev E 93(3):15, 2016), which was the first to study, at a laboratory scale, the phenomenon observed in the natural world of floating disks of ice rotating. They conclude that, in controlled conditions, ice disks are able to induce their own rotation. Whilst their work successfully exposes multiple aspects of the kinematics of such disks, and the buoyancy-driven flow generated beneath them as they melt, the mechanism by which rotation is triggered remains unsubstantiated. We therefore return in this work to the study of floating ice disks, focusing specifically on the importance of experimental technique in obtaining reliable measurements of disk behaviour. Our investigation reveals that the motion of ice disks placed on a nominally quiescent body of fresh water is unpredictable, with some disks remaining motionless, and others rotating clockwise or anticlockwise. For those in motion, the average rate of rotation observed was less than half of that recorded by Dorbolo et al., a discrepancy possibly explained by residual background motions in the nominally quiescent surrounding body of water. However, given our observation that non-melting disks of high-density polyethylene (HDPE) cooled to the same temperature as the ice (comparable HDPE and ice disks differing by only ∼4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim 4$$\end{document}% in mass) consistently rotated at rates less than those made of ice, it is hypothesised that, within the confines of the freshwater environment, the motion of the turbulent meltwater plume that forms beneath an ice disk amplifies the effect of residual background motions. From our observations, it is concluded that residual motions are an underlying physical trigger for disk rotation.

In disposal operations of hypersaline solutions, the use of local environmental regulations is vital to minimize the impact on marine ecosystems. Based on data from environmental protection agencies’ regulatory standards, an environmental impact assessment of off-shore activities was performed. The operation characteristics and environmental conditions of disposal on the Brazilian coast in offshore operations were defined to determine the local salinity increment. The brine dispersion modeling was performed on the in-house developed MFSim platform. The applied methodology consists of solving the equations of continuity, Navier-Stokes and a scalar balance based on the LES approach. Thereby, the applied methodology was validated considering the inclined jet phenomenon. The results showed good agreement with experimental data. Furthermore, critical disposal scenarios were simulated, considering variations in sea current, disposal flow rate, and brine density. The results show the environmental impact of 26 scenarios that were used as input data for applying the Kriging metamodel. Applying the computational model and the Kriging metamodel makes it possible to determine the operational parameters for safe discharge conditions from the environmental point of view with lower computational resources.

A method is introduced to cluster instantaneous vortices using a density-based spatial clustering technique to better distinguish overlapping secondary circulation from different mechanisms. Applying the method to large eddy simulation results of a tight open channel bend, two secondary circulation sub-cells are distinguished: the inner bank cell and the center cell. The identification of these structures using instantaneous vortices shows a connection between channel bend mean secondary flow and instantaneous coherent structures, which is further solidified by the agreement of mean bend circulation and circulation calculated using instantaneous vortices. The inner bank sub-cell exhibits high maximum circulation early in the bend followed by a rapid decline, a pattern which is characteristic of tight bends. The center sub-cell exhibits slower development and retains its circulation longer, which is characteristic of milder bends. The locations of the sub-cells within the channel cross section lead to different opportunities for vorticity generation in each sub-cell, which explains their different development patterns. Article Highlights A method is introduced to identify secondary circulation structures using clusters of instantaneous vortices. Distinct sub-cells are identified in the secondary circulation of a tight open channel bend: one at the inner bank and one in the center. The inner bank sub-cell’s development behavior resembles that of tight bends, while the center sub-cell’s resembles mild bends.

Bridge pier is a common feature in hydraulic structure. Its impact to the river usually occurs in group form rather than single pier, so this challenging piers-group influence towards river hydraulics and turbulence needs to be explored. In this paper, the measurements were conducted using an Acoustic doppler velocimeter (ADV) to study velocities in three dimensions (longitudinal, transversal, and vertical). Based on the experimental data, we have observed reversed depth-averaged velocity vector after each pier in the group of three-pier. The analysis has been conducted on the contribution of each bursting event to Reynolds shear stress (RSS) generation, in order to identify the critical events and turbulence structures around the piers. In the upstream near-wake flow in the bed-wall layer, strong sweep and ejection events have been observed; while at downstream, sweeps were more dominant. The pattern of burst changed in the outer layer of flow, where ejections were more dominant. Furthermore, the contribution fractional ratio to RSS variation at hole size H = 0 indicates that sweeps and ejections were significantly generated at the near wake-flow in upstream.

In this paper, we project future changes in the hydrodynamics of Lake Tanganyika under a high emission scenario using the three-dimensional (3D) version of the Second-generation Louvain-la-Neuve Ice-ocean Model (SLIM 3D) forced by a high-resolution regional climate model. We demonstrate the advantages of 3D simulation compared to 1D vertical models. The model captures the seasonal variability in the lake, with seasonal deep mixing and surfacing of the thermocline. In a simulation of current conditions, the thermocline in the south of the lake moves upward from a depth of 75 m until it reaches the lake surface during August and September. We compare the current conditions with an end-of-the-century simulation under a pessimistic emission scenario (RCP 8.5) showing that surface water temperature increases on average by 3 ± 0.5 °C. Because deeper water warms less, the stratification increases in the upper 150 m of the water column. This temperature-induced stratification reduces mixing and prevents the outcropping of the thermocline, eventually shutting down the ventilation of deep water in the south basin. Our results highlight the extreme changes likely faced by Lake Tanganyika if global greenhouse gas emissions are not curbed.

The dense and complex root network of mangroves strongly affect the hydrodynamics of swamp systems, governed by their unique characteristics varying with the species. The present study investigates the flow hydrodynamics within a heterogeneous mangrove swamp system, constructed in a laboratory flume using natural mangrove plants in the emergent condition. The laboratory observations made in this study are the first of its kind to analyze the flow structure and turbulent characteristics within a heterogeneous mangrove system. Mangrove plants of two different species were used for experimentation. The study incorporated spatial heterogeneity through plant arrangement, geometry of the plants as well as by the use of different species types inside the swamp, which was not considered in previous studies where vegetation was simulated with artificial plant elements. Flow structure and turbulent characteristics were assessed at different locations along the patch. Turbulent dissipation estimated at dense locations are more than that contributed by the solid volume of mangroves, thus highlighting the contribution of mangrove geometry in turbulent dissipation. Estimated turbulent kinetic energy values indicates that wake generated turbulence are with a smaller length scale and not get carried further forward. Vertically averaged values of location specific drag coefficients were estimated for the two species separately, applying the concept of solid volume fractions and using layer schematization approach and is very ideal in case of the mangrove plants which are having varying frontal area and spreaded areal roots.

Air pollution caused by particle resuspension is a growing public health problem in many cities. Pollen and anthropogenic pollutants, such as heavy metal particles and micro-plastics debris, settle onto urban ground surfaces. Prolonged urban heat waves are propitious for heavy and continuous deposition. Particles in the submillimeter size range eventually resuspend by urban winds within seconds, may be inhaled, cause allergic reactions and escape the city’s boundaries. Here, the resuspension and subsequent dispersion of generic particles ranging from 10 to 100 $$\upmu$$ μ m in size are simulated. The city area “Bayerischer Bahnhof” in Leipzig, Germany, has been chosen as a practical example. To track the resuspended particles, a Lagrangian model is used. Taking advantage of graphics processing unit, turbulent flow simulations at different wind speeds are performed in almost real time. The results show that particle resuspension starts, when the inlet wind speed beyond the canopy, that is at a height of 40 m, exceeds 7 m/s. At wind speed beyond 14 m/s, resuspension occurs in almost all city parts. At moderate wind speed, high-risk areas are identified. The effect of green infrastructures on both the flow field and particle resuspension is also investigated.

In this study, repeated lock-exchange experiments under well-controlled conditions were carried out to evaluate the uncertainty of the macro-propagation and entrainment process and the statistical variation/correlation of the current parameters. The results show that the lobe and cleft structures grow in amplitude while short in wavelength as current propagates, which enlarges the uncertainty of the gravity current propagation. A larger density difference inhibits the split process of the lobe and cleft structures and reduces the fluctuation degree of the current front edge. The macroscopic propagation parameters of the gravity current for the repeated experiment all meet the normal distribution, confirmed by the Shapiro–Wilk test. The mapping relationship between the dimensionless current front velocity and the front height forms a “circle-shaped” mode, while the corresponding relationship between the dimensionless current front velocity and the front height performs wedge-shaped. The evolution trend of the variation coefficient of the mixing layer area is that the two quasi-stationary periods are connected by a sharp decline. The variability of the former quasi-stationary period is stronger than the latter one, and the variation strength of the two quasi-stationary periods is both positively correlated with the initial density difference. The uncertainty at the early stage of the entrainment process is dominated due to the evolution of the mixing layer. However, the lobe and cleft structure provide another uncertainty source of the entrainment coefficient at the later stage. In addition, the uncertainty of the current propagation brought by image resolution is far less than that formed by the evolution of the gravity current itself.

In this study, repeated lock-exchange experiments under well-controlled conditions were carried out to evaluate the uncertainty of the macro-propagation and entrainment process and the statistical variation/correlation of the current parameters. The results show that the lobe and cleft structures grow in amplitude while short in wavelength as current propagates, which enlarges the uncertainty of the gravity current propagation. A larger density diference inhibits the split process of the lobe and cleft structures and reduces the fuctuation degree of the current front edge. The macroscopic propagation parameters of the gravity current for the repeated experiment all meet the normal distribution, confrmed by the Shapiro–Wilk test. The mapping relationship between the dimensionless current front velocity and the front height forms a “circle-shaped” mode, while the corresponding relationship between the dimensionless current front velocity and the front height performs wedge-shaped. The evolution trend of the variation coefcient of the mixing layer area is that the two quasi-stationary periods are connected by a sharp decline. The variability of the former quasi-stationary period is stronger than the latter one, and the variation strength of the two quasi-stationary periods is both positively correlated with the initial density difference. The uncertainty at the early stage of the entrainment process is dominated due to the evolution of the mixing layer. However, the lobe and cleft structure provide another uncertainty source of the entrainment coefcient at the later stage. In addition, the uncertainty of the current propagation brought by image resolution is far less than that formed by the evolution of the gravity current itself.

The Australian Aboriginals built fish traps and weirs over a long period of time, and there is a wide variety of structures. Herein this study focuses on rock fish traps constructed in inland waterways. A common shape was a horseshoe design convex in shape and opened downstream. In this study, some basic physical modelling of rock fish trap models was conducted under controlled flow conditions. A generic horseshoe element shape was selected, with a range of porosity, consistent with the rock fish trap construction. Flow conditions were tested from low partial submergence to complete submergence, corresponding to large flood events. The results give some seminal insights into the hydrodynamics of these fish traps and provide some physically-based understanding of their operation and purpose.

Wind-driven shear stresses drive saltation and dust emissions over sand dunes. However, the complex topography of coastal dunes and practical difficulties in measuring shear stresses in the presence of blowing sand make a detailed view of this important information difficult to obtain. We combine computational fluid dynamics with field instrumentation and high resolution topographic data to investigate the shear stresses resulting from on-shore winds on the ground surface for a flat sloping beach area, nebkha foredune, and transverse dune at Oceano Dunes, CA. This approach allows for paired simulations over measured and modified topographies using the same boundary condition. Shear values from scenarios that account for the effects of vegetation and aerodynamic form separately are presented. Using available dust emissions data, an accounting of the emissions from the surface was performed. Sparse vegetation on the nebkha in the foredune was found to play a significant role in modulating the shear on the surface and initial boundary layer modification of the onshore wind profile.

Two recently reported models, the Virtual Variance Sources (VVS) model and the Volumetric Particle Approach (VPA), both predicting the second moment of passive scalar concentration fluctuations in the atmosphere caused by a localized source of gas, are comparatively studied. Both models operate within the framework of a Lagrangian Stochastic Particle Model. Meteorological and tracer data from project Sagebrush phase 1 experiment are used to examine the models for real meteorological data for a localized ground source scenario under the same conditions and parametrizations, including dissipation timescale parametrization. As a reference, the simple scaling model of Chatwin and Sullivan (CS) was also applied. Both the VVS model and the VPA reasonably predict the concentration variance. Notably, the CS model yields comparable results to its more sophisticated counterparts. In addition to comparison to statistics of high frequency concentration measurements, important applicative aspects of the models were studied. The VPA is found to exhibit better statistical convergence demanding less particles, and relatively low sensitivity to dissipation timescale.

The hydrodynamics of flow passing through heterogeneous vegetation configurations is always complex and it becomes difficult to capture the flow structures through experimental studies. This computational study investigated the flow structures around the circular and square-shaped vegetation patches arranged in linear as well as staggered patterns for the vertically layered configuration of vegetation. Reynolds-averaged Navier–Stokes (RANS) techniques and Reynolds stress model were used to compute the flow patterns. Experimental data of layered vegetation were used to validate the numerical model. The simulated mean stream–wise velocities have shown close agreement with the experimental results. The outcomes of this study in the form of flow characteristics spatial variation highlighted that the computing position (region of investigation) can be a significant parameter while observing the flow features of vegetated open channels. The lateral exchange of momentum between the vegetation patches and free stream regions, as well as the vertical exchange of momentum between the vegetation structure and the overlying flow layers caused flow separation and significant spatial variations in the flow structures. It was observed that the circular patch configuration, especially for linear patch arrangement, of vertically layered vegetation can cause significant flow resistance resulting in maximum velocity reduction while experiencing reduced turbulence in sheltering zones behind the patches. The vortex streets as well as the sheltering zone behind the patches in case of circular configuration were more prominent and lasted for a longer distance as compared to the square patch configuration. The exposed sheltering zones behind the vegetation patches suggest a positive flow response towards aquatic ecosystems and the deposition of sediments.

Salt fingers, which can occur in a fluid with stable temperature stratification and unstable salinity stratification, have larger fluxes when the ratio of the contributions of temperature and salinity to the density gradient (i.e., the density ratio) is close to one. This study investigated whether differential diffusion—or the preferential transport of temperature in a weakly turbulent, strongly stratified flow—can decrease an initially large density ratio enough to strengthen salt fingers. Laboratory experiments were conducted in which a stratification favorable for salt fingers was stirred with oscillating arrays of vertical rods. The density ratio decreased slightly when its initial value was large, as expected in differential diffusion, and it increased when its initial value was small, as expected for salt fingers. The mixing efficiency was less than 4%, and in two of the runs with low initial density ratio, it started negative. A one-dimensional eddy diffusion model in which the overall eddy diffusivities simply sum the contributions of salt fingers and mechanically generated turbulence described the evolution well and predicted an equilibrium state once the two eddy diffusivities became equal.

The paper presents internal-flow hydraulics for stratified flows generated in laboratory-scale channels with different geometries, forcing conditions and two-layer flow regimes. Analytical model formulations are presented for the internal-flow head function of quadratic-type channels. While the study focuses on maximal two-layer exchange, where two hydraulic transitions of critical flow are required for the bi-directional stratified flow to be fully controlled, for the channel geometries where only one critical-flow hydraulic transition is present, the two-layer exchange is considered to be sub-maximal, i.e. partially controlled, or frictionally determined without this hydraulic transition. In particular, for the latter case, it is shown that dominant frictional shear and interfacial mixing processes, driving buoyancy flux between the counter-flowing layers, may be a reason that maximal two-layer exchange conditions are not achieved for these specific channel-sill geometries. This interfacial mixing is largely associated with internal dynamics of stably stratified, two-layer, bi-directional flows along the channel by externally imposed barotropic net-exchange flow components, which can restrict or wholly block one of the counter-flowing layers. A novel buoyancy-flux transfer model is therefore incorporated into the internal-flow hydraulic model to provide partially-controlled or frictionally-determined conditions for the uni- and bi-directional stratified flows generated. Previous and new experimental investigations are used to justify the extended internal-flow hydraulic model solutions proposed in the present study, including (1) buoyancy-driven exchange across a descending barrier within a rectangular channel-basin configuration, (2) dense gravity flows along an upsloping and constricted triangular channel, and (3) externally forced two-layer exchange (i) across a submerged sill obstruction with a rectangular cross-section and (ii) through an elongated sill-channel with a trapezoidal cross-section. As these previous laboratory studies were often motivated by the observations for stratified flows in incompletely blocked river estuaries, across fjordic sills and through sea straits, the hydraulic modelling results are discussed in the context of applicability to these natural stratified-flow environments.

The main objective of conducting numerical simulations of flows in rivers with vegetation is to investigate the complex flow dynamics involved in non-equilibrium conditions. In such cases, it is inappropriate to apply the drag coefficient CD, which is typically derived based on uniform flows involving groups of infinitely long cylinders. This paper presents a method for evaluating the drag forces acting on emergent obstacles for non-uniform open-channel flows. This method is devised based on two sets of experiments: on flows with small-diameter cylinders, focusing on the water surface profiles through the group; and on flows with large-diameter cylinders, focusing on the local pressure distribution and local water surface profile around a target cylinder. In addition to the conventional drag force expression that includes CD, two new terms are proposed to account for the effects of water surface variation and pressure gradient in non-uniform open-channel flow on the drag. The first of these terms, which introduces the use of the Froude number to account for the effect of water surface variation, is derived theoretically and evaluated against past and present experimental results under uniform-flow conditions. On the other hand, the second of these terms, which includes the representative length of the separation zone to evaluate the effect of pressure gradient, is confirmed to be a necessity through numerical calculation of the longitudinal water surface profile in emergent cylinders. The incorporation of these two terms using a simple unified expression can help improve the accuracy of numerical simulations for practical problems of flows with emergent obstacles.

Shear instabilities of stratified fluids are a classical topic with a broad literature. The classic instability takes the form of Kelvin-Helmholtz billows that initially develop in two dimensions, one of which is the vertical. Spanwise instability develops later as part of the transition to a three-dimensionalized state. We simulate mode-2 internal waves on the laboratory scale in a rotating frame of reference that, in the absence of rotation, form spanwise aligned billows on the wave flanks. Rotation breaks the symmetry of the classical shear instability because the wave amplitude decays away from the focussing wall (i.e. the waves generated are internal Kelvin waves). We document the development of the wave and the shear instabilities as the Rossby number is varied, finding that (i) even weak rotation (high Rossby number) leads to a significant modification of the billow three-dimensionalization, (ii) strong rotation (low Rossby number) leads to a strong near wall focussing of turbulence transition that is clearly evident in the second invariant of the velocity gradient, Q, of turbulence theory. For low rotation rates, or intermediate to high Rossby numbers, we identify novel instabilities with billow cores aligned in the along-tank direction, rather than the typical spanwise direction.

The hydrodynamics of coral reefs strongly influences their biological functioning, impacting processes such as nutrient availability and uptake, recruitment success and bleaching. For example, coral reefs located in oligotrophic regions depend on upwelling for nutrient supply. Coral reefs at Sodwana Bay, located on the east coast of South Africa, are an example of high latitude marginal reefs. These reefs are subjected to complex hydrodynamic forcings due to the interaction between the strong Agulhas current and the highly variable topography of the region. In this study, we explore the reef scale hydrodynamics resulting from the bathymetry for two steady current scenarios at Two-Mile Reef (TMR) using a combination of field data and numerical simulations. The influence of tides or waves was not considered for this study as well as reef-scale roughness. Tilt current meters with onboard temperature sensors were deployed at selected locations within TMR. We used field observations to identify the dominant flow conditions on the reef for numerical simulations that focused on the hydrodynamics driven by mean currents. During the field campaign, southerly currents were the predominant flow feature with occasional flow reversals to the north. Northerly currents were associated with greater variability towards the southern end of TMR. Numerical simulations showed that Jesser Point was central to the development of flow features for both the northerly and southerly current scenarios. High current variability in the south of TMR during reverse currents is related to the formation of Kelvin-Helmholtz type shear instabilities along the outer edge of an eddy formed north of Jesser Point. Furthermore, downward vertical velocities were computed along the offshore shelf at TMR during southerly currents. Current reversals caused a change in vertical velocities to an upward direction due to the orientation of the bathymetry relative to flow directions. Highlights A predominant southerly current was measured at Two-Mile Reef with occasional reversals towards the north. Field observations indicated that northerly currents are spatially varied along Two-Mile Reef. Simulation of reverse currents show the formation of a separated flow due to interaction with Jesser Point with Kelvin–Helmholtz type shear instabilities along the seaward edge.

Cold pulses generated by the fission of internal solitary waves over gentle slopes are an important source of nutrients and relief from excess heat to benthic ecosystems. This numerical study investigates the effect of stratification form on pulses produced by fission of internal solitary waves propagating over a smooth, gentle, linear topographic slope in 2D simulations. Three stratification types are investigated, namely (i) thin tanh (homogeneous upper and lower layers separated by a thin pycnocline), (ii) surface stratification (linearly stratified layer overlaying a homogeneous lower layer) and (iii) broad tanh (continuous density gradient throughout the water column). Incident wave amplitude was varied. In the thin tanh stratification, good agreement is seen with past studies, whilst the dynamics observed in the surface stratification are very similar to those in the thin tanh stratification. However, in the broad tanh stratification, due to the different form of incident waves, the fission dynamics differ, but produce pulses similar in form to those produced by fission in the other stratifications. Pulse amplitude, wavelength and propagation velocity are found to strongly depend on incident wave amplitude, and each degenerate linearly as the pulse propagates upslope.

Entrainment characteristics of a pure jet and buoyant jets in a stably-stratified ambient are compared with the help of laboratory experiments employing simultaneous particle image velocimetry and planar laser induced fluorescence techniques. For the buoyant jet, two cases of background stratification are considered, N = 0.4 s-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-1}$$\end{document} and 0.6 s-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-1}$$\end{document}, where N is the buoyancy frequency. Evolution of volume flux, Q, momentum flux, M, buoyancy flux, F, characteristic velocity, wm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$w_m$$\end{document}, width, dm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_m$$\end{document}, and buoyancy, bm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b_m$$\end{document} with axial distance is quantified that helps in understanding the mean flow characteristics. Subsequently, two different methods are used for computing the entrainment coefficient, α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}; namely the standard entrainment hypothesis based on the mass conservation equation and energy-consistent entrainment relation proposed by van Reeuwijk and Craske (J Fluid Mech 782:333–355, 2015). It is observed that entrainment coefficient is constant for the pure jet (αpj≈\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _{pj}\approx$$\end{document} 0.1) up until the point where the upper horizontal boundary starts to influence the flow. The entrainment coefficient for buoyant jets, αbj\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _{bj}$$\end{document}, is not constant and varies with axial location before starting to detrain near the neutral layer. Near the source, αbj≈\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _{bj}\approx$$\end{document} 0.12 for both the values of N, while away from the source, N = 0.6 s-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-1}$$\end{document} exhibits a higher value of αbj≈\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _{bj}\approx$$\end{document} 0.15 in comparison to αbj≈\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _{bj}\approx$$\end{document} 0.13 for N = 0.4 s-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-1}$$\end{document}. During detrainment near the neutral layer, αbj≈\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _{bj}\approx$$\end{document} – 0.2 for N = 0.4 s-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{s}}^{-1}$$\end{document} and αbj≈\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _{bj}\approx$$\end{document} – 0.3 for N = 0.6 s-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{s}}^{-1}$$\end{document}. Importantly, close to the source, α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document} from standard entrainment hypothesis and energy-consistent relation are in reasonable match for pure jet and buoyant jets. However, far away from the source, the energy-consistent relation is ineffective in quantifying the entrainment coefficient in the pure jet and detrainment in buoyant jets. We propose ways in which the energy-consistent relation could be reconciled with standard entrainment hypothesis in the far-field region. Article Highlights Entrainment coefficient stays invariant for jets till the finite size of the domain in the axial direction disrupts this feature. Entrainment coefficient for buoyant jets evolving in a stratified ambient varies with axial distance followed by detrainment beyond the neutral layer. The existing entrainment relation performs reasonably well in the momentum dominated region but performs poorly when the finite size of the domain affects the flow for pure jet and when the flow is buoyancy dominated for the case of buoyant jets.

We present large-eddy simulations (LES) of riverine flow in a study reach in the Sacramento River, California. The riverbed bathymetry was surveyed in high-resolution using a multibeam echosounder to construct the computational model of the study area, while the topographies were defined using aerial photographs taken by an Unmanned Aircraft System (UAS). In a series of field campaigns, we measured the flow field of the river river across multiple transects throughout the field site using an acoustic Doppler current profiler (ADCP) and estimated using large-scale particle velocimetry of the videos taken during the operation UAS. We used the measured data of the river flow field to evaluate the accuracy of the LES-computed hydrodynamics. The propagation of uncertainties in the LES results due to the variations in the riverbed’s effective roughness height and the river’s inflow discharge was studied and showed that both parameters redistributed the flow distribution laterally and vertically in the velocity profile. For the uncertainty quantification (UQ) analyses, the polynomial chaos expansion (PCE) method was used to develop a surrogate model, which was randomly sampled sufficiently by the Monte Carlo Sampling (MCS) method to generate confidence intervals for the LES-computed velocity field. Also, Sobol indices derived from the PCE coefficients were calculated to help understand the relative influence of different input parameters on the global uncertainty of the results. The UQ analysis showed that uncertainties of LES results in the shallow near bank regions of the river were mainly related to the roughness, while the variation of inflow discharge leads to uncertainty in the LES results throughout the river, indiscriminately.

We investigate the effects of anisotropic permeability and changing boundary conditions upon the onset of penetrative convection in a porous medium of Darcy type and of Brinkman type. Attention is focussed on the critical eigenfunctions which show how many convection cells will be found in the porous layer. The number of cells is shown to depend critically upon the ratio of vertical to horizontal permeability, upon the Brinkman coefficient, and upon the upper boundary condition for the velocity which may be of Dirichlet type or constant pressure. The critical Rayleigh numbers and wave numbers are determined, and it is shown how an unconditional threshold for nonlinear stability may be derived. Highlights Shows how number of convection cells depends upon the temperature of the upper layer and the anisotropy of the permeability Shows how number of convection ceels depends upon the temperature of the upper layer and the Brinkman coefficient Shows how number of convection cells patters depends upon the upper boundary condition on the velocity or the ambient pressure

An analysis of forces for flow around an elliptic cylinder at low Reynolds number has been presented in this work. The finite-volume based open source code OpenFOAM is used for the numerical simulations. pimpleFoam solver is used to solve Navier- Stokes equations for incompressible flow. The combined effects of aspect ratios (AR = 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0), domain sizes (\(D_s\) = 30\(D_h\), 40\(D_h\), 50\(D_h\) and 60\(D_h\)) and Reynolds numbers (Re = 40, 100) on flow fields and various aerodynamic parameters are presented. Here, \(D_h\) represents characteristic length, which is two times the semi-major axis. It is found that at \(Re = 40\), the value of \(C_{D,avg}\) decreases with the increase of aspect ratio. While, at \(Re = 100\), the value of \(C_{D,avg}\) first decreases up to \(AR = 0.5\) and then increases for all domain sizes. The contribution of the pressure and viscous force in the flow is studied in detail for both the Reynolds number. The contribution of pressure in lift force at \(Re = 40\) is found to be one to two times higher than that of viscous force. Whereas, at \(Re = 100\) the contribution of viscous force in producing lift force is insignificant. The value of Strouhal number at \(Re = 100\) is non-decreasing for increase in aspect ratio at a given value of domain size.

Water flow in porous media is strongly controlled by the microscale structure of the pore space. Therefore, understanding the dynamics at pore scale is fundamental to better estimate and describe the hydraulic properties and phenomena associated to water flow which are observed in a macroscale such as field or laboratory experiments. Pore geometry plays a key role since its variations cause modifications in hydraulic behaviour at the macroscale. In this study, we develop a new analytical model which represents the pore space of a medium as a bundle of tortuous sinusoidal capillary tubes with periodic pore throats and a fractal pore-size distribution. This model is compared with a previous model of straight constrictive capillary tubes in order to analyze the effect of pore geometry on hydraulic properties under partially saturated conditions. The comparison of the constitutive models shows that macroscopic hydraulic properties, porosity and permeability, present the strongest differences due to changes in the pore geometry. Nonetheless, no variations are observed in the relative hydraulic properties, effective saturation and relative permeability. The new model has been tested with experimental data consisting on sets of porosity-permeability, water content-pressure head, conductivity-pressure head, and hysteretic water content-pressure values. In all cases, the model is able to satisfactorily reproduce the data. This new analytical model presents an improvement over the previous model since the smoother variation of the pore radii allows a more realistic representation of the porous medium.

Large-eddy simulation is implemented to investigate the behavior of a low-frequency turbulent flow around an inline array of blocks. Three different types of blocks such as a cubic block, vertical rectangle block and horizontal rectangle block were used. Since the peak of the power spectra of the velocity fluctuation is appeared for a low frequency in all the cases, a low-frequency turbulent flow is generated around the blocks. The peak frequency of the power spectra of the streamwise velocity fluctuation at the lateral side of the blocks are in good agreement with the peak frequency of the power spectra of the spanwise velocity fluctuation between the blocks. It indicates that the low-frequency turbulent flow at both the lateral sides of the blocks strongly affects the turbulent flow within the spaces between the blocks. In addition, the spanwise flow from the high-momentum fluid to the low-momentum fluid is observed near the front face of the block when a pair of the large-scale structure of the high-momentum and low-momentum fluid is appeared near the bottom surface at the both sides of the blocks.

The simulation of shallow flows over obstacles is an important problem in environmental fluid dynamics, including exchange flows over seabed sills, atmospheric flows past steep mountains and water flows over river bedforms. A common mathematical treatment consists in using vertically-averaged models instead of vertically-resolved ones by introducing a suitable shallow water approximation. The dispersionless Saint Venant equations are a useful tool, albeit accuracy is not enough in many circumstances. The next approach consists in resorting to the Serre–Green–Naghdi theory, which is well known to produce good solutions for long non-breaking waves. However, a common feature of flows over obstacles is the generation of breaking waves at its lee side, which are important to model, given their role in the mixing and transport of passive scalars downstream of the terrain barrier. The Serre–Green–Naghdi theory fails to model these flows, producing unrealistic trains of undular waves. A widely used practice consist in resorting to a patching approach in a numerical setting where the solutions of Serre–Green–Naghdi and Saint Venant equations are assembled once wave breaking is detected by case-dependent empirical parameters. In this work an alternative method to dealt with wave breaking over obstacles within the Boussinesq-type approximation is proposed. The exact depth-averaged equations for flows over uneven beds are developed and presented as function of the vertical acceleration and non-uniformity of velocity with elevation. By introducing a suitable kinematic field, a new high-order phase resolving system of non-hydrostatic equations is presented, containing the usual dispersive corrections of Serre–Green–Naghdi theory plus high-order corrections for velocity profile modeling. It is found that the new theory allows the simulation of both breaking and non-breaking waves in shallow flows over obstacles without introducing any case-dependent calibration parameter. The new shallow water approximation is thus an alternative method to deal with wave breaking in Boussinesq type models.

The present study develops a safety survey system for measuring natural river discharge. Monitoring of rivers is very important for river environment conservation and flood prevention. The new system is a drone-type float with a Global Positioning System (GPS) receiver, which can safely and quickly monitor a river. This float flies to the target point on a free surface according to the operator’s control. After which, it runs freely downstream, detecting the time-series of self-position with a centimeter-order accuracy using the real-time kinetic GPS method. It also measures the local water depth using an ultrasonic sensor during the drifting downstream. The same works are repeatedly conducted on all survey lines to evaluate the discharge through a target cross-section. The data correction formula considering the wind effects is introduced to improve the measurement accuracy. We performed field tests in natural rivers and obtained reliable results for practical application. The present system can evaluate the discharge in a 250 m width large-scale river without using an observation bridge or a rubber boat.

Downbursts are strong downdrafts that originate from thunderstorm clouds and create vigorous radial outflows upon hitting the ground. This study is part of the comprehensive experimental research on downburst outflows produced as large-scale impinging jets in the WindEEE Dome simulator at Western University, Canada. The 2800 tests carried out form the largest database of experimental measurements on downburst winds developed thus far, which is made available to the public in its whole and described in detail in a complementary study. Therefore, the current manuscript merely focuses on the data post-processing outcomes and interpretation of results from a selected subset of measurements. Impinging jets are here simulated as transient phenomena in which velocity time series are characterized by a sudden ramp-up of velocity, followed by the velocity peak, a short statistically stationary region, and the final velocity slowdown, as it is expected to occur in the actual downbursts. A dominant velocity peak that was systematically observed in all velocity records is associated with the radial advection of the primary vortex in the outflow. Depending on the radial distance from the downdraft, the primary vortex was sometimes preceded by a secondary, much smaller, vortex close to the surface. Vertical profiles of mean velocity and turbulence intensity are for the first time characterized through the extent of a downburst-like event in the spatiotemporal domain. Particularly, these profiles rapidly change in relation to the passage of the primary vortex and consequent variation of the surface layer thickness. This study lays out a foundation for an experimental model of non-stationary downburst outflows to come.

Understanding the developing mechanism of an outer bank cell is benefit for making full use of its important function to protect the concave bank from erosion in alluvial river bends. This study employs a bend flume experiment and a 3D renormalized group with κ-ϵ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa -\epsilon$$\end{document} closure numerical model to investigate outer bank cells. Results obtained from the physical experiment and numerical simulations elucidate that (1) outer bank cell does not develop at the same time as the occurrence of center region cells, but it often yields later; (2) in sharply curved bends, outer bank cells are originated from the mutual effect of the centrifugal force created by channel bends and the pressure differences due to transverse water surface slopes; (3) a parameter β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta$$\end{document} was derived and also testified effectively for quantitatively evaluating the occurrence of an outer bank cell and influence of flow parameters on the development of outer bank cells in sharply curved open channel bends.

The present study provides a simplified closed-form solution for the deposition flux of atmospheric Particulate Matter on electrical insulators. Due to the lack of experimental data on deposition over this type of solid bodies, the mathematical model is closed by means of a 4D regression procedure on obstacle-scale numerical data. This dataset is obtained with the Lagrangian Stochastic Model SPRAY-WEB (Università del Piemonte Orientale et al., 2021). The code was already validated on Particulate Matter dispersion and deposition on solid obstacles (Amicarelli et al. in Environ Fluid Mech 21(2): 433–463, 2021) and is here applied to a XP-70 porcelain-disk electrical insulator. A published tutorial is associated with this numerical dataset (SPRAY-WEB, 2021). The verification metrics on the performance of the closed-form solution show that the errors lie below the guideline thresholds for air-quality numerical simulations (Chang and Hanna in Meteorol Atmos Phys 87:167–196, 2004) and are limited by a Maximum Gross Error of ca.24% for an external verification. Although they cannot be used to close any mathematical model or to represent any specific event, the long-term averaged deposition fluxes of Zhang et al. (IEEE Trans Dielectr Electr Insulat 21(4):1901–1909, 2014. 10.1109/TDEI.2014.004343) are associated with the same insulator used for this study. With respect to the full-scale experiment mentioned above, the present solution provides an overestimation of 13%. The closed-form solution can be used for instantaneous preliminary estimates or be integrated within air-quality numerical codes for fast assessments of contamination maps for electrical insulators. Such applications aim to quantify the insulator functional damage (i.e., flashovers, short-circuits). The closed-form solution can be also generalized any time new data are available.

The principle theme of this study is to introduce a novel countermeasure to reduce the energy of the overflowing floodwater by utilization of a water cushion. For this purpose, laboratory experiments including “LW” cases (levee with water cushion) and “OL” cases (only levee) were conducted to elucidate the role of a water cushion in the flow structure variation after a levee is overflowed and to reduce energy. A moat (a deep and wide trench) with varying non-dimensional length (Lm* = Lm/hL; Lm is the length of the moat where hL is the levee height) and depth (Dm* = Dm/hL; Dm is the moat depth) acting as a water cushion was provided at the toe of a levee with varied landward slopes (SL). The energy reductions in the LW and OL systems were found to be very close to each other at lower overflow water depths, while it was 25% greater in the LW system than in the OL system at higher overflow water depths. Changes in the landward slope (SL) of the levee, non-dimensional length (Lm*), and depth (Dm*) of moat significantly changed the flow structure and created six different flow structures. However, 1–6%, 1–3%, and 1–5% differences in energy reduction rate were observed by varying SL, Lm*, and Dm*, respectively, in LW cases. All flow structures contributed greatly to energy reduction, but the energy reduction rate was maximum in flow structure named as T-2. Flow structures named as T-2 and T-6 are preferable due to increased water depth inside the moat and presence of submerged hydraulic jump which can be achieved during landward slopes SL = 1:1, 1:2 and by decreasing Lm* Dm*, of moat during Landward slope SL = 1:3.

Hydraulic jumps are commonly employed as energy dissipators to guarantee long-term operation of hydraulic structures. A comprehensive and in-depth understanding of their main features is therefore fundamental. In this context, the current study focused on hydraulic jumps with low Froude numbers, i.e. Fr 1 = 2.1 and 2.4, at relatively high Reynolds number: Re ~2 × 10 ⁵ . Experimental tests employed a combination of dual-tip phase-detection probes and ultra-high-speed video camera to provide a comprehensive characterisation of the main air-water flow properties of the hydraulic jump, including surface flow features, void fraction, bubble count rate and interfacial velocities. The current research also focused on the transverse distributions of air-water flow properties, i.e. across the channel width, with the results revealing lower values of void fraction and bubble count rate next to the sidewalls compared to the channel centreline data. Such a spatial variability in the transverse direction questions whether data near the side walls may be truly representative of the behaviour in the bulk of the flow, raising the issue of sidewall effects in image-based techniques. Overall, these findings provide new information to both researchers and practitioners for a better understanding of the physical processes inside the hydraulic jump with low Froude numbers, leading to an optimised design of hydraulic structures. Article Highlights Experimental investigation of air-water flow properties in hydraulic jumps with low Froude numbers Detailed description of the main air-water surface features on the breaking roller Transversal distribution of the air-water flow properties across the channel width and comparison between centreline and sidewall.

The sudden increase in air temperature associated with strong gusty winds of northerly direction is a phenomenon occasionally observed during the cold season in the central region of Rio Grande do Sul (RS) state, located in extreme southern Brazil. This geophysical flow, which is known as Vento Norte (VNOR; Portuguese for “North Wind”), promotes temperature variations that depart significantly from the local cold-season climatology. In this study, eleven years of surface meteorological observations collected at seven weather stations distributed over central RS are employed to investigate the regional extension of the effects of the VNOR windstorm. The analysis revealed that the sharp increase in temperature and in wind magnitude caused by VNOR is observed over a rather wide region of central RS. However, it is in the vicinities of the city of Santa Maria, located just south of an abrupt drop in terrain elevation, that the most intense VNOR effects are observed suggesting a downslope enhancement of the windstorm. A detailed investigation of the meteorological data also showed that the duration of the VNOR windstorm is well correlated with the magnitude of the maximum wind gusts, with the most intense VNOR events also lasting longer. VNOR events occur more frequently in the period between the morning (0700 LST) and early afternoon (1400 LST). The onset of the windstorm is detected predominantly during overnight and morning hours, with 70% of VNOR cases initiating between 0000 and 1000 LST. Regarding the VNOR demise, 66% of the windstorms dissipate between early afternoon and early evening hours (1200–1900 LST). Results from this study are applicable in the areas of atmospheric diffusion and local weather forecasting.

Based on the mechanism of landslide dam failure caused by overtopping, a simplified mathematical model for simulating dam breach overtopping flow processes was proposed in our previous work. The model is composed of five main modules including hydrodynamic, sediment transport and erosion, headward erosion, breach lateral evolution, and breach side slope stability. However, the breach lateral evolution module is still based on the assumption existing in most available models that breach lateral spreading is linearly related to the undercutting, i.e., the lateral erosion rate is twice as much as the vertical undercutting rate in the process of dam breaking. This assumption is obviously lack of theoretical basis. Through a theoretical analysis of sediment initial motion on the river channel slope, a lateral erosion formula was deduced in this paper. Then the lateral enlargement model was developed to update the breach evolution module in the previously established simulation model. To verify the effectiveness of the modification, A case study was conducted in the same overtopping failure event of Baige landslide dam, which was located at the border of Tibet Autonomous Region and Sichuan province in China, took place on November 3, 2018. A good model performance was achieved with predicted flood volume, peak discharge and occurrence time within 10% margin of error compared with field monitoring data. Furthermore, a comparing with the previous model was carried out and the results obtained by the modified model applying the new lateral enlargement formula proposed in this study indicate that the predicting accuracy of the model can be improved significantly for the simulation of landslide dam overtopping failure.

The authors of the discussed paper presented an interesting study of the lateral gravity currents for the different flow conditions. The authors showed the three-dimensional (3D) turbulent structures at the channel junction. The discussed paper utilized the transient Reynolds-Averaged Navier–Stokes (RANS) equations to visualize the 3D turbulent structures. The present discussion paper shows that the choice of the transient RANS is not appropriate for investigating the 3D turbulent structures at the channel junction. The current discussion paper compares the performance of the transient RANS model and eddy-resolving Detached eddy simulation model in predicting the characteristics 3D turbulent structures at the junction. The comparisons show that the transient RANS model is unable to capture the breakdown of the sheet-shaped turbulent structure due to Kelvin–Helmholtz instability when the flow from the lateral channel separates at the sharp downstream junction corner.

Buoyant turbulent plumes are often categorized by their geometry and described as either round plumes, issuing from a point source, or line/planar plumes, issuing from an elongated source. As line plumes rise above their source they get thicker (normal to the source axis) and, far from the source, they will no longer be planar but more resemble a round plume. However, the vast majority of experimental measurements of line plumes focus on the near source region, where they are still planar and the flow is two-dimensional. Further, these experiments constrain the ends of the plume with barriers to prevent entrainment through the ends of the plume and maintain a twodimensional flow. Herein, results are presented from a series of experiments that were conducted to measure the transition of an unconstrained line plume into a round plume. A model is presented that allows the calculation of the entrainment into a plume of arbitrary cross sectional shape in terms of the hydraulic radius of the plume defined as the cross-sectional area divided by the perimeter over which entrainment is occurring. This formulation, along with a smooth transition function that changes both the geometry and entrainment coefficient, is used to make predictions of the front position over time for a line plume in a filling box. The model was run for different values of the nozzle width to box height ratio and transition height to nozzle width ratio. Results of the model were compared to the experimental front position measurements and show that an unconstrained line plume will transition to a round plume at a height equal to approximately three times the source width. This is consistent with the idea that the line plume will transition when its thickness is similar in magnitude to its nozzle width.

Mixing layers and associated large-scale turbulent structures are some of the most common features of turbulent shallow water flow. Due to their quasi-two-dimensional nature, large-scale structures are also referred to as two-dimensional coherent structures (2DCS). The presence of these structures instigates several complications in the flow, such as scouring of the bed material, affecting the maneuverability of water vessels, and causing the formation of pollutant trapping zones inside recirculating flows; thus, impacting the stability of hydraulic structures, inducing drowning hazards, and affecting aquatic environments in the vicinity. Like all turbulence phenomena, it is challenging to predict shallow water turbulence directly with sufficient accuracy due to its highly random nature. This work proposes a semi-coupled model that aims to predict the spatial distribution of 2DCS in an open channel flow domain. The proposed model solves the 2D unsteady full momentum equations, and the computed outputs are analyzed to predict the possible locations of 2DCS in the flow. The model parameters are calibrated with experimental observations. The model results are then compared with CFD simulations of the Shallow Water model and standard turbulence models (k-Ɛ, k-ω, and LES (Large Eddy Simulation)), performed in OpenFOAM. A good agreement is observed between the results. The proposed model is approximately five times faster in predicting large-scale turbulent structures than standard CFD simulations. Results also demonstrate the superiority of LES models in resolving large-scale turbulence.

The action of wave dominated flow on river bank leads to retreatment of the bankline thereby causing intense erosion issues. The understanding of the bank erosion process mechanisms is of great importance in the context of protecting or controlling the progressive growth of bankline which imposes a direct threat on near bank fertile agricultural land and habitats. The present study emphasizes on acquiring improved understanding on the bank erosion processes related to wave action that severely impact the bank erosion rate. Turbulent fluctuations of the near bank flow were observed to be modulated due to the interplay between eroded bank wall and stream flow under the influence of wave following and against the current. The fluctuating turbulent velocity field was measured using micro acoustic Doppler velocimeter (ADV) at regions close to the bank wall during the different stages of the erosion progress. Streamwise turbulence intensity was found to be relatively large upto a particular undercut depth during the erosion progression. The integral time and length scales and Taylor microscales were determined for different temporal stages using autocorrelation function. Results depict that wave current combined flow in conjunction with rough wall surface formed by the erosion process amplifies the turbulent kinetic energy and turbulent dissipation rate at vicinity of the wall. The velocity fluctuations show large intermittency as evaluated from Gaussian pdf for wave current combined flows. This may affect the near wall turbulence structures which is a causative factor for enhancement of erosion rate as compared to current only flow. Article highlights Modulation of turbulence scales under wave current combined flow. Interaction between wave current combined flow and roughness formed in bank wall due to erosion. Turbulent structures and its effects on progressive bank erosion process.

This study applies the models describing the effect of a neutrally stratified high-Reynolds-number boundary layer on peak wind estimation. A neutrally stratified atmosphere was simulated by ideal large-eddy simulations. The peak factor (PF) model successfully predicted the dependence of the PF on the duration and the evaluation time based on a spectral model containing k-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k^{-1}$$\end{document} slopes at low frequencies. Time-dependent wind peak emergence was evaluated considering the amplitude modulation (AM) concept. For a large part of the atmospheric surface layer, the deviation of the time-dependent mean wind speed played a key role in peak modulation. The effect of a small-scale fluctuation cycle on peak modulation was found to be pronounced, specifically near the surface. It was possible to construct a predictive indicator of a peak event arrival based on the existing predictive model by AM.

The flow and descent of dense water masses formed in shallow regions of the ocean is an important leg in the global overturning circulation. The dense overflow waters tend to flow along the continental slopes as geostrophically balanced gravity plumes, but may be steered downslope by canyons and ridges cross-cutting the slopes. In that process, entrainment and mixing will be greatly enhanced. Ilicak et al. (Ocean Model 38:71–84, 2011) propose a parameterization to include the effects of corrugations in large scale models by increasing the vertical mixing locally. We re-visit the problem using the terrain-following Bergen Ocean Model and a DOME-inspired idealized topography. It is shown that the applied corrugations can move the core of the plume 800 m down the slope, while enhanced mixing raises the center of gravity by only 1–200 m. The overall effect of a corrugation is hence to lower the center of gravity, suggesting that the parameterization proposed by Ilicak et al. (Ocean Model 38:71–84) will act in the wrong vertical direction, if used on its own. A comparison of two bottom drag parameterizations, show that a parameterization consistent with a no-slip boundary condition is needed to correctly represent Ekman drainage, and that the Ekman drainage contribution to plume descent is comparable to that of the corrugation. Ridges are more effective in steering dense water downward than canyons, and we compare the dynamics between the two settings to explain the difference.

In this paper, details, and results of three-dimensional numerical modeling of flow around the semi-conical piers vertically mounted on the bed in a channel, are presented. For flow simulation, 3-D Navier–Stokes equations are solved numerically using the finite volume method and large eddy simulation. In this study, the semi-conical piers with different side slope angles (α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}) are tested, and the flow around them is compared with the cylindrical reference pier. Flow structures, vortex shedding behind piers, horseshoe vortices, instantaneous and time-averaged flow structures are presented and discussed. Numerical model results show that the semi-conical piers are eventuated remarkable reduction (up to 25%) in downward flow velocity in the upstream side of the piers, and much more reduction (up to 46%) in bed shear stresses in comparison with the cylindrical pier. Moreover, the model results showed some decrease in vortex shedding frequency for the semi-conical piers compared to the cylindrical pier.

We examine katabatic flow driven by a non-uniformly cooled slope surface but unaffected by Coriolis acceleration. A general formulation is given, valid for non-uniform surface buoyancy distributions over a down-slope length scale L≫δ0, where δ0=ν/(Nsinα)1/2 is the slope-normal Prandtl depth, for a kinematic viscosity ν, buoyancy frequency N and slope angle α. We demonstrate that the similarity solution of Shapiro and Fedorovich (J Fluid Mech 571:149–175, 2007) can remain quantitatively relevant local to the end of a non-uniformly cooled region. The usefulness of the steady similarity solution is determined by a spatial eigenvalue problem on the L length scale. Broadly speaking, there are also two modes of temporal instability; stationary down-slope aligned vortices and down-slope propagating waves. By considering the limiting inviscid stability problem, we show that the origin of the vortex mode is spatial oscillation of the buoyancy profile normal to the slope. This leads to vortex growth in a region displaced from the slope surface, at a point of buoyancy inflection, just as the propagating modes owe their existence to an inflectional velocity. Non-uniform katabatic flows that detrain fluid to the ambient are shown to further destabilise the vortex mode whereas entraining flows lead to weaker vortex growth rates. Rayleigh waves dominate in general, but the vortex modes become more significant at small slope angles and we quantify their relative growth rates.

The study presents a systematic assessment of 2D RANS-VOF simulation of positive surge wave propagation in open channels using three widely used turbulence models: standard k-ε, RNG k-ε and the k-ω SST. The numerical simulation results are validated on the basis of rigorous comparison with data obtained from existing physical model studies and in-house experiments. The study finds that the standard k-ε model fails to simulate the free surface features of the surge wave precisely. The RNG k-ε and the k-ω SST models show better performance in this regard. The standard k-ε model is also unable to replicate the physical trends of the measured velocity data. While the overall agreement between the velocity characteristics estimated by the RNG k-ε model and experimental data is satisfactory, the model exhibits weakness while capturing the recirculation zone beneath the breaking surge having Froude number 1.6. The k-ω SST model simulates the pertinent velocity characteristics and the relevant flow structures with better accuracy in comparison to the RNG k-ε model for both undular and breaking surges. The non-hydrostatic pressure field is well approximated by both the RNG k-ε and the k-ω SST models. A comparison of the free surface levels computed by SGN models reveals that the limitation of the depth averaged non-hydrostatic models in capturing the breaking of waves may be overcome by the proposed RANS-VOF approach. Comparison with 2D LES results obtained from existing studies on positive surge modelling indicates that the proposed 2D RANS-VOF model is capable of producing results almost at par with the LES models.

The mechanical energy balance and energy loss have attracted significant attention in the literature. The general form of the energy equation has been previously presented; however, in most applications the simplified 1-D form without considering the details of turbulent flows has been applied. In this study, a form of the total mechanical energy balance equation for 3-D turbulent flows in open-channels is investigated in which all turbulence parameters involving the effects of the secondary currents can be evaluated by using equalizations that have not previously been applied to the total mechanical energy equation and RANS turbulence models. Based on the equalizations, the existing correlations in the total energy equation are replaced with a combination of mean flow variables and known turbulence parameters from turbulent flow numerical simulations. Therefore, the details of the total mechanical energy balance for 3-D turbulent flows in open-channels with different geometries can be analyzed using the proposed methodology. Then, an explicit relationship for the energy loss, usually determined empirically, is derived from the developed energy equation. In order to investigate the utilization of the analytical relationships, 3-D numerical simulations are performed using OpenFOAM to solve the Navier–Stokes equations with the RSM turbulence model. By applying the analytical relationship and the simulation results, the mechanical energy losses are obtained and compared with the energy losses from the previous energy equations, the effect of the various parameters on the total mechanical energy balance is studied, the role of wall resistance in the mechanical energy is investigated and efforts are made to identify the parameters affecting the local and friction losses of turbulent flows in the irregular open-channels. Finally, a deeper understanding of the details of the energy transformation process and the mechanical energy loss of the complex flows is achieved.