MK
M. Kumar
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1
Three-Dimensional Sediment Dynamics in Well-Mixed Estuaries
Importance of the Internally Generated Overtide, Spatial Settling Lag, and Gravitational Circulation
To investigate the dominant sediment transport and trapping mechanisms, a semi-analytical three-dimensional model is developed resolving the dynamic effects of salt intrusion on sediment in well-mixed estuaries in morphodynamic equilibrium. As a study case, a schematized estuary with a converging width and a channel-shoal structure representative for the Delaware estuary is considered. When neglecting Coriolis effects, sediment downstream of the estuarine turbidity maximum (ETM) is imported into the estuary through the deeper channel and exported over the shoals. Within the ETM region, sediment is transported seaward through the deeper channel and transported landward over the shoals. The largest contribution to the cross-sectionally integrated seaward residual sediment transport is attributed to the advection of tidally averaged sediment concentrations by river-induced flow and tidal return flow. This contribution is mainly balanced by the residual landward sediment transport due to temporal correlations between the suspended sediment concentrations and velocities at the M2 tidal frequency. The M2 sediment concentration mainly results from spatial settling lag effects and asymmetric bed shear stresses due to interactions of M2 bottom velocities and the internally generated M4 tidal velocities, as well as the salinity-induced residual currents. Residual advection of tidally averaged sediment concentrations also plays an important role in the landward sediment transport. Including Coriolis effects hardly changes the cross-sectionally integrated sediment balance, but results in a landward (seaward) sediment transport on the right (left) side of the estuary looking seaward, consistent with observations from literature. The sediment transport/trapping mechanisms change significantly when varying the settling velocity and river discharge.
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To investigate the dominant sediment transport and trapping mechanisms, a semi-analytical three-dimensional model is developed resolving the dynamic effects of salt intrusion on sediment in well-mixed estuaries in morphodynamic equilibrium. As a study case, a schematized estuary with a converging width and a channel-shoal structure representative for the Delaware estuary is considered. When neglecting Coriolis effects, sediment downstream of the estuarine turbidity maximum (ETM) is imported into the estuary through the deeper channel and exported over the shoals. Within the ETM region, sediment is transported seaward through the deeper channel and transported landward over the shoals. The largest contribution to the cross-sectionally integrated seaward residual sediment transport is attributed to the advection of tidally averaged sediment concentrations by river-induced flow and tidal return flow. This contribution is mainly balanced by the residual landward sediment transport due to temporal correlations between the suspended sediment concentrations and velocities at the M2 tidal frequency. The M2 sediment concentration mainly results from spatial settling lag effects and asymmetric bed shear stresses due to interactions of M2 bottom velocities and the internally generated M4 tidal velocities, as well as the salinity-induced residual currents. Residual advection of tidally averaged sediment concentrations also plays an important role in the landward sediment transport. Including Coriolis effects hardly changes the cross-sectionally integrated sediment balance, but results in a landward (seaward) sediment transport on the right (left) side of the estuary looking seaward, consistent with observations from literature. The sediment transport/trapping mechanisms change significantly when varying the settling velocity and river discharge.
Three-dimensional model for estuarine turbidity maxima in tidally dominated estuaries
An idealized modeling approach
We develop a three-dimensional idealized model that is specifically aimed at gaining insight in the physical mechanisms resulting in the formation of estuarine turbidity maxima in tidally dominated estuaries. First, the three-dimensional equations for water motion and suspended sediment concentration together with the so-called morphodynamic equilibrium condition, are scaled. Next, surface elevation, velocity and sediment concentration are expanded in a small parameter ϵ=A¯M2 /H, where A¯M2 is the mean amplitude of the M2 tide and H is the mean water depth at the seaward side. This results in a system of equations at each order in this small parameter. This ordering allows solving for the vertical structure of the velocity and suspended sediment concentration, independently of the horizontal dimension. After obtaining these vertical structures, the horizontal dependencies of the physical variables follow from solving a two-dimensional elliptic partial differential equation for the surface elevation. The availability of fine sediments in the estuary follows from a two-dimensional elliptic partial differential equation which results from requiring the system to be in morphodynamic equilibrium, and prescribing the total amount of easily erodible sediments available in the estuary. These elliptic equations for the surface elevation and sediment availability are solved numerically using the finite element method with cubic polynomials as basis functions. As a first application, the model is applied to the Ems estuary using a simplified geometry and bathymetric profiles characteristic for the years 1980 and 2005. The availability of fine sediments and location of maximum concentration are investigated for different lateral depth profiles. In the first experiment, a uniform lateral depth is considered. In this case, both the sediment availability and suspended sediment concentration are, as expected, uniform in the lateral direction. In 1980, the sediment is mainly trapped near the entrance, while in 2005, the sediment is mostly trapped in the freshwater zone. In the next experiment, the lateral bathymetry is varied parabolically while keeping the mean depth unchanged. In this case, the fine sediment is mainly found at the shallow sides, but the maximum sediment concentration is found in the deeper channel where the bed shear stress is much larger than on the shoals. As a final experiment, a more realistic (but smoothed) geometry and bathymetry for the Ems estuary are considered, showing the possibilities of applying the newly developed model to complex geometries and bathymetries.
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We develop a three-dimensional idealized model that is specifically aimed at gaining insight in the physical mechanisms resulting in the formation of estuarine turbidity maxima in tidally dominated estuaries. First, the three-dimensional equations for water motion and suspended sediment concentration together with the so-called morphodynamic equilibrium condition, are scaled. Next, surface elevation, velocity and sediment concentration are expanded in a small parameter ϵ=A¯M2 /H, where A¯M2 is the mean amplitude of the M2 tide and H is the mean water depth at the seaward side. This results in a system of equations at each order in this small parameter. This ordering allows solving for the vertical structure of the velocity and suspended sediment concentration, independently of the horizontal dimension. After obtaining these vertical structures, the horizontal dependencies of the physical variables follow from solving a two-dimensional elliptic partial differential equation for the surface elevation. The availability of fine sediments in the estuary follows from a two-dimensional elliptic partial differential equation which results from requiring the system to be in morphodynamic equilibrium, and prescribing the total amount of easily erodible sediments available in the estuary. These elliptic equations for the surface elevation and sediment availability are solved numerically using the finite element method with cubic polynomials as basis functions. As a first application, the model is applied to the Ems estuary using a simplified geometry and bathymetric profiles characteristic for the years 1980 and 2005. The availability of fine sediments and location of maximum concentration are investigated for different lateral depth profiles. In the first experiment, a uniform lateral depth is considered. In this case, both the sediment availability and suspended sediment concentration are, as expected, uniform in the lateral direction. In 1980, the sediment is mainly trapped near the entrance, while in 2005, the sediment is mostly trapped in the freshwater zone. In the next experiment, the lateral bathymetry is varied parabolically while keeping the mean depth unchanged. In this case, the fine sediment is mainly found at the shallow sides, but the maximum sediment concentration is found in the deeper channel where the bed shear stress is much larger than on the shoals. As a final experiment, a more realistic (but smoothed) geometry and bathymetry for the Ems estuary are considered, showing the possibilities of applying the newly developed model to complex geometries and bathymetries.
Three-dimensional salt dynamics in well-mixed estuaries
Influence of estuarine convergence, coriolis, and bathymetry
A semianalytical three-dimensional model is set up to dynamically calculate the coupled water motion and salinity for idealized well-mixed estuaries and prognostically investigate the influence of each physical mechanism on the residual salt transport. As a study case, a schematized estuary with an exponentially converging width and a channel–shoal structure is considered. The temporal correlation between horizontal tidal velocities and tidal salinities is the dominant process for the landward residual salt transport. The residual salt transport induced by residual circulation is locally significant, but the induced salt transport integrated over the cross section is small. The impacts of the estuarine geometry, Coriolis force, and bathymetry on the salt dynamics are studied using three dedicated experiments, in which the impact of each of these factors is studied separately. To assess the impact of width convergence, a convergent estuary without bathymetric variations or Coriolis force is considered. In this experiment, the temporal correlation between tidal velocities and salinities is the only landward salt transport process. In the second experiment, Coriolis effects are included. This results in a significant residual salt transport cell due to the advection of the tidally averaged salinity by residual circulation, with salt imported into the estuary from the left side and exported on the right (looking seaward). In the last experiment, a lateral channel–shoal structure is included while the Coriolis effects are excluded. This results in a significant landward salt transport through the deeper channel and a seaward salt transport over the shoals due to the advection of the tidally averaged salinity by residual circulation.
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A semianalytical three-dimensional model is set up to dynamically calculate the coupled water motion and salinity for idealized well-mixed estuaries and prognostically investigate the influence of each physical mechanism on the residual salt transport. As a study case, a schematized estuary with an exponentially converging width and a channel–shoal structure is considered. The temporal correlation between horizontal tidal velocities and tidal salinities is the dominant process for the landward residual salt transport. The residual salt transport induced by residual circulation is locally significant, but the induced salt transport integrated over the cross section is small. The impacts of the estuarine geometry, Coriolis force, and bathymetry on the salt dynamics are studied using three dedicated experiments, in which the impact of each of these factors is studied separately. To assess the impact of width convergence, a convergent estuary without bathymetric variations or Coriolis force is considered. In this experiment, the temporal correlation between tidal velocities and salinities is the only landward salt transport process. In the second experiment, Coriolis effects are included. This results in a significant residual salt transport cell due to the advection of the tidally averaged salinity by residual circulation, with salt imported into the estuary from the left side and exported on the right (looking seaward). In the last experiment, a lateral channel–shoal structure is included while the Coriolis effects are excluded. This results in a significant landward salt transport through the deeper channel and a seaward salt transport over the shoals due to the advection of the tidally averaged salinity by residual circulation.
Response of large-scale coastal basins to wind forcing
Influence of topography
Journal article
(2016)
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Wen L. Chen, Pieter C. Roos, Henk Schuttelaars, Mohit Kumar, Tjerk Zitman, SJMH Hulscher
Because wind is one of the main forcings in storm surge, we present an idealised process-based model to study the influence of topographic variations on the frequency response of large-scale coastal basins subject to time-periodic wind forcing. Coastal basins are represented by a semi-enclosed rectangular inner region forced by wind. It is connected to an outer region (represented as an infinitely long channel) without wind forcing, which allows waves to freely propagate outward. The model solves the three-dimensional linearised shallow water equations on the f plane, forced by a spatially uniform wind field that has an arbitrary angle with respect to the along-basin direction. Turbulence is represented using a spatially uniform vertical eddy viscosity, combined with a partial slip condition at the bed. The surface elevation amplitudes, and hence the vertical profiles of the velocity, are obtained using the finite element method (FEM), extended to account for the connection to the outer region. The results are then evaluated in terms of the elevation amplitude averaged over the basin’s landward end, as a function of the wind forcing frequency. In general, the results point out that adding topographic elements in the inner region (such as a topographic step, a linearly sloping bed or a parabolic cross-basin profile), causes the resonance peaks to shift in the frequency domain, through their effect on local wave speed. The Coriolis effect causes the resonance peaks associated with cross-basin modes (which without rotation only appear in the response to cross-basin wind) to emerge also in the response to along-basin wind and vice versa.
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Because wind is one of the main forcings in storm surge, we present an idealised process-based model to study the influence of topographic variations on the frequency response of large-scale coastal basins subject to time-periodic wind forcing. Coastal basins are represented by a semi-enclosed rectangular inner region forced by wind. It is connected to an outer region (represented as an infinitely long channel) without wind forcing, which allows waves to freely propagate outward. The model solves the three-dimensional linearised shallow water equations on the f plane, forced by a spatially uniform wind field that has an arbitrary angle with respect to the along-basin direction. Turbulence is represented using a spatially uniform vertical eddy viscosity, combined with a partial slip condition at the bed. The surface elevation amplitudes, and hence the vertical profiles of the velocity, are obtained using the finite element method (FEM), extended to account for the connection to the outer region. The results are then evaluated in terms of the elevation amplitude averaged over the basin’s landward end, as a function of the wind forcing frequency. In general, the results point out that adding topographic elements in the inner region (such as a topographic step, a linearly sloping bed or a parabolic cross-basin profile), causes the resonance peaks to shift in the frequency domain, through their effect on local wave speed. The Coriolis effect causes the resonance peaks associated with cross-basin modes (which without rotation only appear in the response to cross-basin wind) to emerge also in the response to along-basin wind and vice versa.
Along-channel and cross-channel sediment transport in tidal estuaries is usually driven by tides, density gradients, Coriolis’s force, wind stress, channel curvature and bathymetric variations. Since the water motion is influenced by density-induced gravitational circulation which in turn affects the salinity distribution, the coupled water motion and salinity has a potentially strong effect on the residual sediment transport, and thus the trapping of fine sediment. To better understand the dynamical effects of water motion and salinity on sediment transport, the salinity field has to be computed consistently. In this work, the water density is assumed to be a function of salinity only, thus ignoring the influence of temperature and assuming the sediment concentration to be low. To obtain the coupled water motion and salinity, the three-dimensional shallow water equations and the salinity equation are solved simultaneously using a perturbation method together with an iterative finite element method (Kumar et al., 2016; Wei et al, in preparation), resulting in a consistent water motion and salinity field. This information is then used to calculate the sediment concentrations, so that the influence of the salt dynamics on sediment transport is prognostically calculated. Owing to the adopted perturbation method, the contribution of various physical processes to residual sediment transport can be studied separately, which allows for a full investigation on individual contribution of each process to longitudinal/lateral transport of salinity and sediment. Moreover, as wind is another important forcing of estuarine circulation (Chen et al., 2009, de Jonge and van Beusekom 1995, Ridderinkhof et al., 2000), the influence of wind stress on estuarine sediment transport will be studied. The present work will bring insights into sediment transport and trapping mechanisms in real estuaries, for example, the Delaware estuary.
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Along-channel and cross-channel sediment transport in tidal estuaries is usually driven by tides, density gradients, Coriolis’s force, wind stress, channel curvature and bathymetric variations. Since the water motion is influenced by density-induced gravitational circulation which in turn affects the salinity distribution, the coupled water motion and salinity has a potentially strong effect on the residual sediment transport, and thus the trapping of fine sediment. To better understand the dynamical effects of water motion and salinity on sediment transport, the salinity field has to be computed consistently. In this work, the water density is assumed to be a function of salinity only, thus ignoring the influence of temperature and assuming the sediment concentration to be low. To obtain the coupled water motion and salinity, the three-dimensional shallow water equations and the salinity equation are solved simultaneously using a perturbation method together with an iterative finite element method (Kumar et al., 2016; Wei et al, in preparation), resulting in a consistent water motion and salinity field. This information is then used to calculate the sediment concentrations, so that the influence of the salt dynamics on sediment transport is prognostically calculated. Owing to the adopted perturbation method, the contribution of various physical processes to residual sediment transport can be studied separately, which allows for a full investigation on individual contribution of each process to longitudinal/lateral transport of salinity and sediment. Moreover, as wind is another important forcing of estuarine circulation (Chen et al., 2009, de Jonge and van Beusekom 1995, Ridderinkhof et al., 2000), the influence of wind stress on estuarine sediment transport will be studied. The present work will bring insights into sediment transport and trapping mechanisms in real estuaries, for example, the Delaware estuary.