Huib E. de Swart

The generation of offshore tidal sand banks and sand waves

A simple morphological model is considered which describes the interaction between a tidal flow and an erodible bed in a shallow sea. The basic state of this model describes a spatially uniform tide over a flat bottom where the flow vector is represented as a tidal ellipse. The linear stability of this solution is analysed with respect to bed form perturbations. Results are presented for both a uni-directional and circular tide. In the former case the wave-length and the orientation of the fastest growing bed mode agree well with those of tidal sand banks. However, this model only predicts the growth of large-scale sand ridges. With a simplified numerical model we tentatively show that the effects of secondary currents on the sediment transport trigger the formation of instabilities at an essentially smaller scale, viz, sand waves. Another limitation of a model with uni-directional tides is that no selective modes found are the first to become unstable if the model parameters are varied. In the case of a circular tide, critical model parameters are found below which the basic state is stable. We conclude that this provides a starting point for the development of a weakly non-linear analysis, which will yield information on the amplitude behaviour of marginally growing bed forms.

Residual currents induced by asymmetric tidal mixing in weakly stratified narrow estuaries

Abstract Residual currents induced by asymmetric tidal mixing were examined for weakly stratified, narrow estuaries using analytical and numerical models. The analytical model is an extension of the work of R. K. McCarthy, with the addition of tidal variations of the vertical eddy viscosity in the longitudinal momentum equation. The longitudinal distribution of residual flows driven by asymmetric tidal mixing is determined by the tidal current amplitude and by asymmetries in tidal mixing between flood and ebb. In a long channel, the magnitude of the residual flow induced by asymmetric tidal mixing is maximum at the estuary mouth and decreases upstream following the longitudinal distribution of tidal current amplitude. Larger asymmetry in tidal mixing between flood and ebb produces stronger residual currents. For typical tidal asymmetry, mixing is stronger during flood than during ebb and results in two-layer residual currents with seaward flow near the surface and landward flow near the bottom. For revers...

Mechanisms of along-channel sediment transport in the North Passage of the Yangtze Estuary and their response to large-scale interventions

The effects of large-scale interventions in the North Passage of the Yangtze Estuary (the Deep Waterway Project, DWP) on the along-channel flow structure, suspended sediment distribution and its transport along the main channel of this passage are investigated. The focus is explaining the changes in net sediment transport in terms of physical mechanisms. For this, data of flow and suspended sediment concentration (SSC), which were collected simultaneously at several locations and at different depths along the main channel of the North Passage prior to and after the engineering works, were harmonically analyzed to assess the relative importance of the transport components related to residual (time-mean) flow and various tidal pumping mechanisms. Expressions for main residual flow components were derived using theoretical principles. The SSC revealed that the estuarine turbidity maximum (ETM) was intensified due to the interventions, especially in wet seasons, and an upstream shift and extension of the ETM zone occurred. The amplitude of the M2 tidal current considerably increased, and the residual flow structure was significantly altered by engineering works. Prior to the DWP, the residual flow structure was that of a gravitational circulation in both seasons, while after the DWP, there was seaward flow throughout the channel during the wet season. The analysis of net sediment transport reveals that during wet seasons and prior to the DWP, the sediment trapping was due to asymmetric tidal mixing, gravitational circulation, tidal rectification, and M2 tidal pumping, while after the DWP, the trapping was primarily due to seaward transport caused by Stokes return flow and fresh water discharge and landward transport due to M2 tidal pumping and asymmetric tidal mixing. During dry seasons, prior to the DWP, trapping of sediment at the bottom relied on landward transports due to Stokes transport, M4 tidal pumping, asymmetric tidal mixing, and gravitational circulation, while after the DWP the sediment trapping was caused by M2 tidal pumping, Stokes transport, asymmetric tidal mixing, tidal rectification, and gravitational circulation.

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.

Influence of the back-barrier basin length on the geometry of ebb-tidal deltas

The characteristics of ebb-tidal deltas are determined by the local hydrodynamics. The latter depend, among others, on the geometry of the adjacent back-barrier basin. Therefore, interventions in the back-barrier basin can affect the geometry of ebb-tidal deltas. In this study, the effect of the length of the back-barrier basin on the sand volume and spatial symmetry of ebb-tidal deltas is quantified with the use of a numerical model. It is found that the length of the back-barrier basin affects the tidal prism, the amplitude and phase of the primary tide and its overtides, and the residual currents that, together, determine the sand volume of the ebb-tidal delta. In particular, it is found that no unique relationship exists between tidal prism and sand volume of an ebb-tidal delta. The spatial symmetry of ebb-tidal deltas is also found to be affected by the length of the back-barrier basin. This is because the basin length determines the phase difference between alongshore and cross-shore tidal currents. The numerical model results give a possible explanation for the changes that are observed in the geometry of the ebb-tidal deltas that are located seaward of the Texel Inlet and Vlie Inlet after the closure of the Zuiderzee.

Effects of bottom slope, flocculation and hindered settling on the coupled dynamics of currents and suspended sediment in highly turbid estuaries, a simple model

This study aims at gaining basic understanding about two specific phenomena that are observed in the highly turbid estuaries tidal Ouse, Yangtze and Ems, i.e. (1) the accumulation of suspended matter in the deeper parts of the estuaries and (2) the relatively high values of turbidity near the surface in the area of the turbidity maximum. A semi-analytical model is analysed to verify the hypothesis that these phenomena result from bottom slope-induced turbidity currents and from hindered settling, respectively. The model governs the dynamics of residual flow, driven by fresh water discharge, salinity gradients and turbidity gradients. It further uses the condition of morphodynamic equilibrium (no divergence of net sediment transport) to compute the residual sediment concentration. New aspects are that depth variations on flow and mixing processes, as well as flocculation and hindered settling of sediment, are explicitly accounted for. Tides act as a source of mixing and erosion of sediment only, thus processes like tidal pumping are not considered. Model results show that the estuarine turbidity maximum (ETM) shifts in the down-slope direction, compared to the case of a constant depth. Slope-induced turbidity currents, which are directed down-slope near the bottom and up-slope near the surface, are responsible for this shift, thereby confirming the first part of the hypothesis above. The down-slope shift of the ETM is reduced by currents resulting from gradients in depth-dependent mixing, which counteract turbidity currents, but which are always weaker. Including flocculation and hindered settling yields increased surface sediment concentrations in the area of the turbidity maximum, compared to the situation of a constant settling velocity, thereby supporting the second part of the hypothesis. Sensitivity experiments reveal that the conclusions are not sensitive to the values of the model parameters.

Long bed waves in tidal seas: an idealized model

An idealized model is proposed to explain the appearance of the long bed waves that have been recently observed in shallow tidal seas. The model assumes that these bedforms grow due to tide-topography interaction. The water motion is described by means of the depth-averaged shallow water equations and the bottom evolution is governed by conservation of sediment mass. The sediment transport formulation includes a critical bottom stress below which no sediment moves. Also, anisotropic sediment transport, due to local bottom slopes in the longitudinal and transverse directions, is taken into account. A linear stability analysis of the flat bottom configuration reveals that different bottom patterns can emerge. In accordance with previous analyses, for strong tidal currents, the fastest growing modes are sand banks. However, if the tidal currents are elliptical and the maximum bottom stress is just above its threshold value for the initiation of sediment motion, the model shows the presence of further growing modes which resemble the long bed waves observed in the field

Dynamic links between shape of the eddy viscosity profile and the vertical structure of tidal current amplitude in bays and estuaries

Several field studies in bays and estuaries have revealed pronounced subsurface maxima in the vertical profiles of the current amplitude of the principal tidal harmonic, or of its vertical shear, over the water column. To gain fundamental understanding about these phenomena, a semi-analytical model is designed and analysed, with focus on the sensitivity of the vertical structure of the tidal current amplitude to formulations of the vertical shape of the eddy viscosity. The new analytical solutions for the tidal current amplitude are used to explore their dependence on the degree of surface mixing, the vertical shape of eddy viscosity in the upper part of the water column and the density stratification. Sources of surface mixing are wind and whitecapping. Results show three types of current amplitude profiles of tidal harmonics, characterised by monotonically decreasing shear towards the surface, “surface jumps” (vertical shear of tidal current amplitude has a subsurface maximum) and “subsurface jets” (maximum tidal current amplitude below the surface), respectively. The “surface jumps” and “subsurface jets” both occur for low turbulence near the surface, whilst additionally the surface jumps only occur if the eddy viscosity in the upper part of the water column decreases faster than linearly to the surface. Furthermore, “surface jumps” take place for low density stratification, while and “subsurface jets” occur for high density stratification. The physics causing the presence of surface jumps and subsurface jets is also discussed.

Vertical structure of residual slope circulation driven by JEBAR and tides: an idealised model

The residual circulation over the continental slope, and in particular, its vertical structure, is analysed by means of an idealised hydrodynamic model. The model is based on the depth-dependent shallow-water equations under uniform along-isobath conditions and is forced by a prescribed meridional density gradient and tidal velocities. By means of expansion in the small Rossby number e solutions are analysed for conditions representative for the continental slopes off the Hebrides and in the Bay of Biscay. The steady solution at zeroth order consists of a linear density-driven flow. At order e a tidally rectified flow is found and a stationary flow due to self-interaction of the zeroth-order density-driven flow. At order e 2 the leading-order effect of the interaction between the zeroth-order density-driven flow and the tides is found: the ‘interaction current’. The solutions up to and including order e 2 constitute an along-isobath steady slope current which is comparable to field data. The slope current and the accompanying cross-shelf circulation depend strongly on the shelf and flow characteristics. For the Hebridean case the density forcing predominates, but for the Biscay case the tidal effects are of the same order of magnitude as the density effects. Under those conditions the interaction current is significant which implies that linear superposition of density and tidal effects differs from the nonlinear combination of both. It is also shown that the depth-average of the interaction current differs essentially from the solution obtained from a depth-averaged model. r 2002 Elsevier Science Ltd. All rights reserved.

Quantifying the Effect of Salinity Stratification on Phytoplankton Density Patterns in Estuaries

To quantify the effect of salinity stratification on phytoplankton density (denoted as P) patterns, experiments were conducted with an idealised model that couples physical and biological processes. Results show that the idealised model is capable of capturing the main features of observed P patterns in the Columbia River estuary during the spring season: during weak stratification, P is almost vertically uniform with values decreasing towards the estuary mouth, whereas during strong stratification, high values of P extend further seawards but are confined to the upper layer. Sensitivity studies reveal that the strong vertical gradients of P can only occur if the intensity of turbulence (measured by depth-averaged values of vertical eddy viscosity and eddy diffusivity) is weak. The advection of P by subtidal currents is important in obtaining a smaller along-estuary gradient of P during weak stratification and in obtaining a smaller horizontal gradient and a larger vertical gradient of P during strong stratification. Accounting for stratification controlled vertical distribution of vertical eddy viscosity and eddy diffusivity is necessary for obtaining realistic P patterns if stratification is strong, but not if stratification is weak. A higher osmotic stress, which leads to faster loss of phytoplankton in salt water, results in a larger along-estuary gradient of P if stratification is weak and in a larger vertical gradient of P if stratification is strong.