Existence and stability of morphodynamic equilibria in double inlet systems

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The Effect of Tidal Asymmetry and Temporal Settling Lag on Sediment Trapping in Tidal Estuaries

Over decades and centuries, the mean depth of estuaries changes due to sea-level rise, land subsidence, infilling, and dredging projects. These processes produce changes in relative roughness (friction) and mixing, resulting in fundamental changes in the characteristics of the horizontal (velocity) and vertical tides (sea surface elevation) and the dynamics of sediment trapping. To investigate such changes, a 2DV model is developed. The model equations consist of the width-averaged shallow water equations and a sediment balance equation. Together with the condition of morphodynamic equilibrium, these equations are solved analytically by making a regular expansion of the various physical variables in a small parameter. Using these analytic solutions, we are able to gain insight into the fundamental physical processes resulting in sediment trapping in an estuary by studying various forcings separately. As a case study, we consider the Ems estuary. Between 1980 and 2005, successive deepening of the Ems estuary has significantly altered the tidal and sediment dynamics. The tidal range and the surface sediment concentration has increased and the position of the turbidity zone has shifted into the freshwater zone. The model is used to determine the causes of these historical changes. It is found that the increase of the tidal amplitude toward the end of the embayment is the combined effect of the deepening of the estuary and a 37% and 50% reduction in the vertical eddy viscosity and stress parameter, respectively. The physical mechanism resulting in the trapping of sediment, the number of trapping regions, and their sensitivity to grain size are explained by careful analysis of the various contributions of the residual sediment transport. It is found that sediment is trapped in the estuary by a delicate balance between the M 2 transport and the residual transport for fine sediment (\emphws=0.2 mm s −1) and the residual, M 2 and M 4 transports for coarser sediment (\emphws=2 mm s − 1). The upstream movement of the estuarine turbidity maximum into the freshwater zone in 2005 is mainly the result of changes in tidal asymmetry. Moreover, the difference between the sediment distribution for different grain sizes in the same year can be attributed to changes in the temporal settling lag

The Effect of Tidal Asymmetry and Temporal Settling Lag on Sediment Trapping in Tidal Estuaries

Over decades and centuries, the mean depth of estuaries changes due to sea-level rise, land subsidence, infilling, and dredging projects. These processes produce changes in relative roughness (friction) and mixing, resulting in fundamental changes in the characteristics of the horizontal (velocity) and vertical tides (sea surface elevation) and the dynamics of sediment trapping. To investigate such changes, a 2DV model is developed. The model equations consist of the width-averaged shallow water equations and a sediment balance equation. Together with the condition of morphodynamic equilibrium, these equations are solved analytically by making a regular expansion of the various physical variables in a small parameter. Using these analytic solutions, we are able to gain insight into the fundamental physical processes resulting in sediment trapping in an estuary by studying various forcings separately. As a case study, we consider the Ems estuary. Between 1980 and 2005, successive deepening of the Ems estuary has significantly altered the tidal and sediment dynamics. The tidal range and the surface sediment concentration has increased and the position of the turbidity zone has shifted into the freshwater zone. The model is used to determine the causes of these historical changes. It is found that the increase of the tidal amplitude toward the end of the embayment is the combined effect of the deepening of the estuary and a 37% and 50% reduction in the vertical eddy viscosity and stress parameter, respectively. The physical mechanism resulting in the trapping of sediment, the number of trapping regions, and their sensitivity to grain size are explained by careful analysis of the various contributions of the residual sediment transport. It is found that sediment is trapped in the estuary by a delicate balance between the M 2 transport and the residual transport for fine sediment (\emphws=0.2 mm s −1) and the residual, M 2 and M 4 transports for coarser sediment (\emphws=2 mm s − 1). The upstream movement of the estuarine turbidity maximum into the freshwater zone in 2005 is mainly the result of changes in tidal asymmetry. Moreover, the difference between the sediment distribution for different grain sizes in the same year can be attributed to changes in the temporal settling lag

Morphodynamic equilibria in short tidal basins using a 2DH exploratory model

A depth-averaged (2DH) exploratory model is developed to identify morphodynamic equilibria in short mesotidal inlet systems with arbitrary planform geometries. The water motion is forced by an M (2) tidal constituent at the seaward entrance and is described by the depth-averaged shallow water equations, whereas the depth-integrated suspended sediment concentration follows from a diffusion equation, taking into account local inertia, horizontal eddy diffusion and topographically induced diffusive effects, erosion, and deposition. Based on a scaling analysis, it follows that the fine sandy bed evolution is dominated by the depth-integrated diffusive sediment transport. The depth-integrated advective contributions are one order smaller and therefore neglected. This observation also allows for the neglect of the advective terms in the governing equations. The associated morphodynamic equilibria are directly identified based on a continuation approach. By means of the exploratory model, the morphodynamic equilibria are studied in basins with a planform geometry characterized by width variations as a function of the distance to the seaward boundary. The model results show that in the case of a sufficient degree of widening in the landward direction, the equilibrium bed level exhibits significant lateral structures, characterized by shallow zones and deeper channels. The first channel bifurcation, as observed in many short tidal inlet systems, is forced by the planform geometry of the basin, and the associated physical mechanisms are explained. Furthermore, two mechanisms inducing asymmetric morphodynamic equilibria are investigated, of which the effect of an asymmetric basin planform seems to be dominant over that of the Coriolis force

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

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

Salt dynamics in well-mixed estuaries: importance of advection by tides

Understanding salt dynamics is important to adequately model salt intrusion, baroclinic forcing, and sediment transport. In this paper, the importance of the residual salt transport due to tidal advection in well-mixed tidal estuaries is studied. The water motion is resolved in a consistent way with a width-averaged analytical model, coupled to an advection–diffusion equation describing the salt dynamics. The residual salt balance obtained from the coupled model shows that the seaward salt transport driven by river discharge is balanced by the landward salt transport due to tidal advection and horizontal diffusion. It is found that the tidal advection behaves as a diffusion process, and this contribution is named tidal advective diffusion. The horizontal diffusion parameterizes processes not explicitly resolved in the model and is called the prescribed diffusion. The tidal advective diffusion results from the correlation between the tidal velocity and salinity and can be explicitly calculated with the dominant semidiurnal water motion. The sensitivity analysis shows that tidal advective diffusivity increases with increasing bed roughness and decreasing vertical eddy viscosity. Furthermore, tidal advective diffusivity reaches its maximum for moderate water depth and moderate convergence length. The relative importance of tidal advective diffusion is investigated using the residual salt balance, with the prescribed diffusion coefficient obtained from the measured salinity field. The tidal advective diffusion dominates the residual salt transport in the Scheldt estuary, and other processes significantly contribute to the residual salt transport in the Delaware estuary and the Columbia estuary