Henk M. Schuttelaars

Lateral entrapment of sediment in tidal estuaries: An idealized model study

Two physical mechanisms leading to lateral accumulation of sediment in tidally dominated estuaries are investigated, involving Coriolis forcing and lateral density gradients. An idealized model is used that consists of the three?dimensional shallow water equations and sediment mass balance. Conditions are assumed to be uniform in the along?estuary direction. A semidiurnal tidal discharge and tidally averaged density gradients are prescribed. The erosional sediment flux at the bed depends both on the bed shear stress and on the amount of sediment available in mud reaches for resuspension. The distribution of mud reaches over the bed is selected such that sediment transport is in morphodynamic equilibrium, that is, tidally averaged erosion and deposition of sediment at the bed balance. Analytical solutions are obtained by using perturbation analysis. Results suggest that in most estuaries lateral density gradients induce more sediment transport than Coriolis forcing. When frictional forces are small (Ekman number E 0.02), the lateral density gradient mechanism dominates and entraps sediment in areas with fresher water. Results also show that the lateral sediment transport induced by the semidiurnal tidal flow is significant when frictional forces are small (E ? 0.02). Model predictions are in good agreement with observations from the James River estuary.

Residual sediment fluxes in weakly-to-periodically stratified estuaries and tidal inlets

In this idealized numerical modeling study, the composition of residual sediment fluxes in energetic (e.g., weakly or periodically stratified) tidal estuaries is investigated by means of one-dimensional water column models, with some focus on the sediment availability. Scaling of the underlying dynamic equations shows dependence of the results on the Simpson number (relative strength of horizontal density gradient) and the Rouse number (relative settling velocity) as well as impacts of the Unsteadiness number (relative tidal frequency). Here, the parameter space given by the Simpson and Rouse numbers is mainly investigated. A simple analytical model based on the assumption of stationarity shows that for small Simpson and Rouse numbers sediment flux is down estuary and vice versa for large Simpson and Rouse numbers. A fully dynamic water column model coupled to a second-moment turbulence closure model allows to decompose the sediment flux profiles into contributions from the transport flux (product of subtidal velocity and sediment concentration profiles) and the fluctuation flux profiles (tidal covariance between current velocity and sediment concentration). Three different types of bottom sediment pools are distinguished to vary the sediment availability, by defining a time scale for complete sediment erosion. For short erosion times scales, the transport sediment flux may dominate, but for larger erosion time scales the fluctuation sediment flux largely dominates the tidal sediment flux. When quarter-diurnal components are added to the tidal forcing, up-estuary sediment fluxes are strongly increased for stronger and shorter flood tides and vice versa. The theoretical results are compared to field observations in a tidally energetic inlet.

Analysis of Tidal Straining as Driver for Estuarine Circulation in Well-Mixed Estuaries

Tidal straining, which can mathematically be described as the covariance between eddy viscosity and vertical shear of the along-channel velocity component, has been acknowledged as one of the major drivers for estuarine circulation in channelized tidally energetic estuaries. In this paper, the authors investigate the role of lateral circulation for generating this covariance. Five numerical experiments are carried out, starting with a reference scenario including the full physics and four scenarios in which specific key physical processes are neglected. These processes are longitudinal internal pressure gradient forcing, lateral internal pressure gradient forcing, lateral advection, and the neglect of temporal variation of eddy viscosity. The results for the viscosity–shear covariance are correlated across different experiments to quantify the change due to neglect of these key processes. It is found that the lateral advection of vertical shear of the along-channel velocity component and its interaction with the tidally asymmetric eddy viscosity (which is also modified by the lateral circulation) is the major driving force for estuarine circulation in well-mixed tidal estuaries.

Morphodynamic evolution of double‐barred beaches

The linear and nonlinear morphological behavior of double-barred coastal systems under the forcing of obliquely incident waves is studied using a nonlinear numerical model. The linearly most unstable bed forms consist of crescentic patterns (rip channels), whose spacing depends on the magnitude of the longshore current velocity. Using the nonlinear model, six morphodynamic experiments have been performed with various initial bed perturbations in order to assess, among others, the influence of the initial bed perturbation on the morphodynamic evolution. The nonlinear experiments have been pursued well into the nonlinear regime, showing that after a phase of initial exponential growth, a highly dynamic behavior is observed and no equilibrium state is reached. The spacings predicted with the linear stability analysis are observed during the exponential phase of the nonlinear experiments. In the dynamic phase, however, four to seven modes significantly contribute to the resulting bed features. In this final stage, the apparent wavelength of 1000 m of the resulting bed forms on the inner bar is quite insensitive to the initial bed perturbation. On the outer bar it seems that the longer the wavelength of the initial bed perturbation, the longer the wavelength of the final bed forms in the dynamic phase and the larger the migration celerity. In general, the bed forms can be characterized as crescentic or undulating bed patterns. Good correspondence between simulated and observed spacings, shapes and migration celerities are found.

Seasonal variability in M2 and M4 tidal constituents and its implications for the coastal residual sediment transport

We use an observational data set of tidal gauges in the North Sea to investigate the annual cycle of the M2 and M4 amplitudes and phases. The sea surface elevation amplitude of the M2 can vary by 8–10% and the M4 amplitude by 12–30% over the course of the year, with larger amplitudes in summer. The annual phase variations are in the range of 3–15?. The reason for these variations is the thermal structure of the North Sea: a well-developed thermocline in summer and well-mixed water column during winter. The interaction of the M2 and M4 tides is one of the main drivers of the residual sediment transport. Using an analytical model, the seasonal variability in residual sediment transport is estimated. This transport can vary by 10–50% over the course of the year. These variations are mainly related to the seasonal variability of the M2 and M4 amplitudes.

Numerical analysis of stratification and destratification processes in a tidally energetic inlet with an ebb tidal delta

Stratification and destratification processes in a tidally energetic, weakly stratified inlet in the Wadden Sea (south eastern North Sea) are investigated in this modeling study. Observations of current velocity and vertical density structure show strain-induced periodic stratification for the southern shoal of the tidal channel. In contrast to this, in the nearby central region of the channel, increased stratification is already observed directly after full flood. To investigate the processes leading to this different behavior, a nested model system using GETM is set up and successfully validated against field data. The simulated density development along a cross section that includes both stations shows that cross-channel stratification is strongly increasing during flood, such that available potential energy is released in the deeper part of the channel during flood. An analysis of the potential energy anomaly budget confirms that the early onset of vertical stratification during flood at the deeper station is mainly controlled by the stratifying cross-channel straining of the density field. In contrast to this, in the shallow part of the channel, the relatively weak cross-channel straining is balanced by along-channel straining and vertical mixing. An idealized analytical model confirms the following hypothesis: The laterally convergent flood current advecting laterally stratified water masses from the shallow and wide ebb tidal delta to the deep and narrow tidal channel has the tendency to substantially increase cross-channel density gradients in the tidal channel. This process leads to stratification during flood.

Morphodynamic instabilities of planar beaches: Sensitivity to parameter values and process formulations

The initial growth of bed perturbations on planar sloping beaches under the forcing of obliquely incident, breaking waves is investigated using a state?of?the?art numerical model. This allows for a systematic investigation of the sensitivity of the spatial structures of the bed perturbations and their growth and migration rates to different model formulations and parameterizations. If the sediment is only transported in the direction of the net current velocity and sediment stirring is taken proportional to the wave height squared, growing up?current oriented crescentic bars are found with a preferred spacing of 800 m and a down?current migration rate of 10 m d?1. Varying the angle of wave incidence, drag coefficient and bed slope results in qualitatively similar growing bed forms. Using an Engelund and Hansen transport formula, very oblique down?current oriented bars are obtained that grow in time. No preferred wavelength, however, is found. Using the Bailard transport formula results in growing, up?current oriented bars with a preferred spacing smaller than 300 m for wave angles smaller than 7°. When using either the Engelund and Hansen or Bailard sediment transport formulation, it is essential to take the transport in the direction of the wave orbital velocity into account in order to have growing bed perturbations.

Impact of the depth-to-width ratio of periodically stratified tidal channels on the estuarine circulation

The dependency of the estuarine circulation on the depth-to-width ratio of a periodically, weakly stratified tidal estuary is systematically investigated here for the first time. Currents, salinity, and other properties are simulated by means of the General Estuarine Transport Model (GETM) in cross-sectional slice mode, applying a symmetric Gaussian-shaped depth profile. The width is varied over four orders of magnitude. The individual along-channel circulation contributions from tidal straining, gravitation, advection, etc., are calculated and the impact of the depth-to-width ratio on their intensity is presented and elucidated. It is found that the estuarine circulation exhibits a distinct maximum in medium-wide channels (intermediate depth-towidth ratio depending on various parameters), which is caused by a maximum of the tidal straining contribution. This maximum is related to a strong tidal asymmetry of eddy viscosity and shear created by secondary strain-induced periodic stratification (2SIPS): in medium channels, transverse circulation generated by lateral density gradients due to laterally differential longitudinal advection induces stable stratification at the end of the flood phase, which is further increased during ebb by longitudinal straining (SIPS). Thus, eddy viscosity is low and shear is strong in the entire ebb phase. During flood, SIPS decreases the stratification so that eddy viscosity is high and shear is weak. The circulation resulting from this viscosity–shear correlation, the tidal straining circulation, is oriented like the classical, gravitational circulation, with riverine outflow at the surface and oceanic inflow close to the bottom. In medium channels, it is about 5 times as strong as in wide (quasi onedimensional) channels, in which 2SIPS is negligible.

Impact of estuarine convergence on residual circulation in tidally energetic estuaries and inlets

Estuarine convergence (landward reduction of width and/or depth) is known to have the potential to significantly enhance estuarine circulation, a result theoretically derived under the assumption of constant eddy viscosity. Recent studies of longitudinally uniform energetic tidal channels indicate that tidal straining, a process driven by tidally varying eddy viscosity, is a major driver of estuarine circulation. The combined effect of estuarine convergence and tidal straining is investigated, for the first time, in this paper. The present idealized numerical study shows that estuarine convergence is reducing or even reversing tidal straining circulation in such a way that estuarine circulation can be weakened. This is a counterintuitive hydrodynamic effect of estuarine convergence, which may reduce (rather than increase) up-estuary particulate matter transport in estuaries and tidal inlets.

Sensitivity of tidal motion in well-mixed estuaries to cross-sectional shape, deepening, and sea level rise

For well-mixed estuaries, key physical mechanisms are identified and quantified that cause changes in characteristics of the semi-diurnal sea surface elevation and lateral velocity due to modifications of the lateral bottom profile, channel deepening, and sea level rise. This is done by decomposing solutions of a new analytical model into components relating to different physical processes. The default geometry and parameter values are representative for the Ems estuary, with a converging width and a reflective landward boundary. The default Gaussian lateral bottom profile is modified to obtain profiles with the same cross-sectional area, but with a different skewness or steepness. Results show that a steeper lateral bottom profile leads to amplification of the sea surface elevation. The width convergence is shown to influence the resonance characteristics. Channel deepening and sea level rise result in amplification of the sea surface elevation until a resonance peak is reached. When flooding is incorporated, the amount of sea level rise at which maximum tidal amplification occurs is found to be about two times lower. When using a symmetric Gaussian bottom profile, the lateral tidal flow is determined by Coriolis deflection of longitudinal flow and lateral density gradients caused by differential salt advection. However, an additional lateral tidal flow component incorporating the effect of continuity related to sea level variations and longitudinal gradients in longitudinal flow is shown to become increasingly important for skewed lateral bottom profiles. Furthermore, the lateral flow due to the lateral density gradient is enhanced for bottom profiles with increased steepness.