Simulation of the Lagrangian tide-induced residual velocity in a tide-dominated coastal system: a case study of Jiaozhou Bay, China

The Eulerian residual transport velocity and the first-order Lagrangian residual velocity for weakly nonlinear systems have been used extensively in the past to depict inter-tidal mass transport. However, these could not explain the observed net surface sediment transport pattern in Jiaozhou Bay (JZB), located on the western Yellow Sea. JZB is characterized by strong tidal motion, complex topography and an irregular coastline, which are features of typical nonlinear systems. The Lagrangian residual velocity, which is applicable to general nonlinear systems, was simulated with the water parcel tracking method. The results indicate that the composition of the Lagrangian residual velocity at different tidal phases coincides well with the observed net surface sediment transport pattern. The strong dependence of water flushing time on the initial tidal phase can also be explained by the significant intra-tidal variation of the Lagrangian residual velocity. To investigate the hydrodynamic mechanism governing the nonlinearity of the M ₂ tidal system, a set of nonlinearity indexes were defined and analysed. In the surface layer, horizontal advection is the main contributor to the strong nonlinearity near the bay mouth, while in the bottom layer, the strong nonlinearity near the bay mouth may result from the vertical viscosity and horizontal advection.     

Numerical computation of the tidally induced Lagrangian residual current in a model bay

With a depth-averaged numerical model, the tidally induced Lagrangian residual current in a model bay was studied. To correctly reflect the long-term mass transport, it is appropriate to use the Lagrangian residual velocity (LRV) rather than the Eulerian residual velocity (ERV) or the Eulerian residual transport velocity (ETV) to describe the residual current. The parameter κ, which is defined as the ratio of the typical tidal amplitude at the open boundary to the mean water depth, is considered to be the indicator of the nonlinear effect in the system. It is found that the feasibility of making the mass transport velocity (MTV) approximate the LRV is strongly dependent on κ. The error between the MTV and the LRV tends to increase with a growing κ. An additional error will come from the various initial tidal phases due to the Lagrangian drift velocity (LDV) when κ is no longer small. According to the residual vorticity equation based on the MTV, the Coriolis effect is found to influence the residual vorticity mainly through the curl of the tidal stress. A significant difference in the flow pattern indicates that the LRV is sensitive to the bottom friction in different forms.     

Analytical solution for the tidally induced Lagrangian residual current in a narrow bay

In a weakly nonlinear tidal system, the depth-averaged equations for the first-order Lagrangian residual velocity (LRV) are deduced systematically. For the case of a narrow bay, the equations are solved analytically and the results for a specific bottom profile are discussed in detail. According to the pattern of the first-order LRV, the bay can be divided into three parts, namely an inner part, a transitional zone, and an outer part. For the given depth profile, the streamline of the first-order LRV for a shorter bay is a part of that for a longer bay. The first-order LRV depends on a nondimensional parameter that combines the influences of the bottom friction coefficient, the tidal period and the averaged water depth. The form of the bottom friction also has a significant influence on the first-order LRV. The second-order LRV, i.e., the Lagrangian drift, is analytically solved and shows dependence on the initial tidal phase. The LRV differs from the Eulerian residual transport velocity both quantitatively and qualitatively. It is demonstrated that the residual currents obtained according to other definitions may cause misunderstanding of the mass transport in water exchange applications.     

A numerical study of horizontal dispersion in a macro tidal basin

Tidal circulation in Cobscook Bay, a macro tidal basin, is simulated using the three-dimensional, nonlinear, finite element ocean model, QUODDY_dry. Numerical particles are released from various transects in the bay at different tidal phases and tracked for several tidal cycles. Initially, nearby particles in the main tidal channel experience a great deal of spreading and straining, and after a few tidal cycles, they are separated in different parts of the bay. The fundamental mechanism for particle dispersion is the chaotic advection that arises from long tidal excursions passing through many residual eddies. A loosely correlated, inverse relationship between the two dimensionless parameters, ν (the ratio of the residual current to the tidal current) and λ (the ratio of the tidal excursion to the main topographic scale), can be constructed for large values of ν. Several Lagrangian statistical measures are used to quantify and distinguish dispersion regimes in different parts of Cobscook Bay. It is found that the effective Lagrangian dispersion coefficient can be estimated using the product of the magnitude of residual currents and the tidal excursion.     

Lateral dynamics and associated transport of sediment in the upper reaches of a partially mixed estuary,Chesapeake Bay,USA

Data from time series of transects made over a tidal period across a section of the upper Chesapeake Bay, USA, reveal the influence of lateral dynamics on sediment transport in an area with a deep channel and broad extents of shallower flanks. Contributions to lateral momentum by rotation (Coriolis plus channel curvature), cross channel density gradients and cross channel surface slope were estimated, and the friction and acceleration terms needed to complete the balance were compared to patterns of observed lateral circulation. During ebb, net rotation effects were larger because of river velocity and reinforcement of Coriolis by curvature. During flood, stratification was greater because of landward advection of strong vertical density gradients. Together, the ebb intensified lateral circulation and flood intensified stratification focused sediment and sediment transport along the left side of the estuary (looking seaward). The tendency for greater stratification on flood and net sediment flux toward the left-hand shoal are contrary to more common models which, in the northern hemisphere, predict greater resuspension on flood and move sediment toward the right-hand shoal. These tidal asymmetries interact with the lateral circulation to focus net sediment flux on the left side of the estuary, and to produce net ebb directed sediment transport at the surface of the same order of magnitude as net flood directed sediment transport at the bottom.     

Transverse structure of tidal and residual flow and sediment concentration in estuaries

An analytical and a numerical model are used to understand the response of velocity and sediment distributions over Gaussian-shaped estuarine cross-sections to changes in tidal forcing and water depth. The estuaries considered here are characterized by strong mixing and a relatively weak along-channel density gradient. It is also examined under what conditions the fast, two-dimensional analytical flow model yields results that agree with those obtained with the more complex three-dimensional numerical model. The analytical model reproduces and explains the main velocity and sediment characteristics in large parts of the parameter space considered (average tidal velocity amplitude, 0.1–1 m s^− 1 and maximum water depth, 10–60 m). Its skills are lower for along-channel residual flows if nonlinearities are moderate to high (strong tides in deep estuaries) and for transverse flows and residual sediment concentrations if the Ekman number is small (weak tides in deep estuaries). An important new aspect of the analytical model is the incorporation of tidal variations in the across-channel density gradient, causing a double circulation pattern in the transverse flow during slack tides. The gradient also leads to a new tidally rectified residual flow component via net advection of along-channel tidal momentum by the density-induced transverse tidal flow. The component features landward currents in the channel and seaward currents over the slopes and is particularly effective in deeper water. It acts jointly with components induced by horizontal density differences, Coriolis-induced tidal rectification and Stokes discharge, resulting in different along-channel residual flow regimes. The residual across-channel density gradient is crucial for the residual transverse circulation and for the residual sediment concentration. The clockwise density-induced circulation traps sediment in the fresher water over the left slope (looking up-estuary in the northern hemisphere). Model results are largely consistent with available field data of well-mixed estuaries.     

Tidally-induced sediment transport patterns in the upper Bay of Fundy: A numerical study

The Minas Basin, the eastern end of the Bay of Fundy, is well known for its high tide ranges and strong tidal currents, which can be exploited to extract electricity power. The properties of the tidally-induced sediment transport in the Minas Basin, where significant changes in tidal processes may occur due to a recently proposed tidal power project, have been studied with a three-dimensional hydrodynamic model, an empirical bed load sediment transport model and surface sediment concentrations derived from the remotely-sensed images. The hydrodynamic model was evaluated against independent observational data, which include tidal elevation, tidal current (in the full water column and bottom layer), residual current profile and tidal asymmetry indicators. The evaluation shows that the model is in good agreement with the observations.The sediment transport includes two components, bed load and suspended particulate load. The bed load is calculated using the modelled bottom shear stress and the observed grain size data. The estimated features of bed load transport roughly agree with the observed patterns of the erosion and deposition in the Minas Basin and Cobequid Bay. The transport of the suspended load is estimated using the modelled velocity fields and the surface sediment concentration derived from remote-sensing images. The comparisons between the modelled results and the limited observations illustrate that the observed directions of suspended sediment transport are basically reproduced by the model. The modelled net suspended sediment input into the Minas Basin through Minas Passage is 2.4×10⁶ m³ yr^?1, which is comparable to the observed value of 1.6×10⁶ m³ yr^?1.The variations of the bed load and the suspended load in space and time are also presented. The total net transport, defined as the mean value of the sum of bed and suspended load transports during the tidal cycle, shows strong spatial variability. The magnitude of the transport flux ranges from 0.1 to 0.2 kg m^?1 s^?1 in Minas Channel and Minas Passage, 0.1 kg m^?1 s^?1 in Cobequid Bay, to 0.01 kg m^?1 s^?1 in the central Minas Basin and Southern Bight. In Minas Channel, the sediment transport follows the structure of the tidal residual circulation, which features a large anticlockwise gyre. The sediment in Minas Passage moves eastward and deposits into the central Minas Basin. However, the sediment from the eastern part of the Basin moves westward and deposits in the central Minas Basin as well. In the Cobequid Bay, sediment moves eastward and deposits in the upper bay.     

On the exact shape of the horizontal profile of a topographically rectified tidal flow

Abstract

Starting from the nonlinear shallow water equations of a homogeneous rotating fluid we derive the equation describing the evolution of vorticity by a fluctuating bottom topography of small amplitude, using a multiple scale expansion in a small parameter, which is the topographic length scale relative to the tidal wave length. The exact response functions of residual vorticity for a sinusoidal bottom topography are compared with those obtained by a primitive perturbation series and by harmonic truncation, showing the former to be invalid for small topographic length scales and the latter to be only a fair approximation for vorticity produced by planetary vortex stretching. In deriving the exact shape of the horizontal residual velocity profile at a step-like break in the bottom topography, it is shown that the Lagrangian profile only exists in a strip having the width of the amplitude of the tidal excursion at both sides of the break, and that it vanishes outside that interval. Moreover, in the limit of small amplitude topography at least, it vanishes altogether for the generation mechanism by means of planetary vortex stretching. The Eulerian profile is shown to extend over twice the interval of the Lagrangian profile both for production by vortex stretching and by differential bottom friction. These finite intervals over which the residual velocity profiles exist for a step-like topography are not reproduced by harmonic truncation of the basic equation. This method gives exponentially decaying profiles, indicating spurious horizontal diffusion of vorticity. In terms of orders of magnitude, the method of harmonic truncation is reliable for residual velocity produced by vortex stretching but it overestimates the residual velocity produced by differential bottom friction by a factor 2.     

The influence of neap–spring tidal variation and wave energy on sediment flux in salt marsh tidal creeks

Sediment flux in marsh tidal creeks is commonly used to gauge sediment supply to marshes. We conducted a field investigation of temporal variability in sediment flux in tidal creeks in the accreting tidal marsh at China Camp State Park adjacent to northern San Francisco Bay. Suspended‐sediment concentration (SSC), velocity and depth were measured near the mouths of two tidal creeks during three 6‐ to 10‐week deployments: two in winter and one in summer. Currents, wave properties and SSC were measured in the adjacent shallows. All deployments spanned the largest spring tides of the season. Results show that tidally averaged suspended‐sediment flux (SSF) in the tidal creeks varied from slightly landward to strongly bayward with increasing tidal energy. SSF was negative (bayward) for tidal cycles with maximum water surface elevation above the marsh plain. Export during the largest spring tides dominated the cumulative SSF for each deployment. During ebb tides following the highest tides, velocities exceeded 1 m s^?1 in the narrow tidal creeks, resulting in negative tidally averaged water flux, and mobilizing sediment from the creek banks or bed. Storm surge also produced negative SSF. Tidally averaged SSF was positive in wavy conditions with moderate tides. Spring tide sediment export at the creek mouth was about twice that at a station 130 m further up the tidal creek. The negative tidally averaged water flux near the creek mouth during spring tides indicates that in the lower marsh some of the water flooding directly across the bay–marsh interface drains through the tidal creeks, and suggests that this interface may be a pathway for sediment supply to the lower marsh as well. Copyright © 2018 John Wiley & Sons, Ltd.     

Suspended sediment transport along an idealised tidal embayment: settling lag, residual transport and the interpretation of tidal signals

We present semi-analytical solutions for suspended sediment concentration (SSC) and residual sediment transport in a simple mathematical model of a short tidal embayment. These solutions allow us to investigate in some detail the characteristic tidal and semi-tidal variation of SSC and the processes leading to residual sediment transport, including settling and scour lags, the roles of ‘local’ and ‘advective’ contributions, and the presence of internally or externally generated overtides. By interpreting the transport mechanisms in terms of the classic conceptual models of settling lag we clarify how these models may be expressed in mathematical terms. Our results suggest that settling lag is usually a more important process than scour lag, and that a local model which neglects advection may predict the direction of net sediment transport incorrectly. Finally, we discuss our results in the context of other transport processes and morphodynamic feedback.     

Numerical modeling of tidal currents, sediment transport and morphological evolution in Hangzhou Bay, China

A 2D depth-averaged numerical model is set up to simulate the macro-scale hydrodynamic characteristics, sediment transport patterns and morphological evolution in Hangzhou Bay, a large macro-tidal estuary on the eastern coast of China. By incorporating the shallow water equations, the suspended sediment transport equation and the mass-balance equation for sediment; short-term hydrodynamics, sediment transport and long-term morphological evolution for Hangzhou Bay are simulated and the underlying physical mechanisms are analyzed. The model reproduces the spatial distribution patterns of suspended sediment concentration (SSC) in Hangzhou Bay, characterized by three high SSC zones and two low SSC zones. It also correctly simulates the residual flow, the residual sediment transport and the sediment accumulation patterns in Hangzhou Bay. The model results are in agreement with previous studies based on field measurements. The residual flow and the residual sediment transport are landwards directed in the northern part of the bay and seawards directed in the southern part. Sediment accumulation takes place in most areas of the bay. Harmonic analysis revealed that the tide is flood-dominant in the northern part of the bay and ebb-dominant in the southern part of the bay. The strength of the flood-dominance increases landwards along the northern Hangzhou Bay. In turn sediment transport in Hangzhou Bay is controlled by this tidal asymmetry pattern. In addition, the direction of tidal propagation in the East China Sea, the presence of the archipelago in the southeast and the funnel-shaped geometry of the bay, play important roles for the patterns of sediment transport and sediment accumulation respectively.     

Baroclinic dynamics of wind-driven circulation in a stratified bay: A numerical study using models of varying complexity

The baroclinic response of a stratified coastal embayment (Lunenburg Bay of Nova Scotia) to the observed wind forcing is examined using two numerical models. A linear baroclinic model based on the normal mode approach shows skill at reproducing the observed isotherm movements and sub-surface currents during a time of strong stratification in the bay. The linear model also shows that the isotherm movement in Lunenburg Bay is influenced by the wind forcing and propagation of baroclinic Kelvin waves from neighbouring Mahone Bay. The effects of nonlinearity and topography are investigated using a three-dimensional nonlinear coastal circulation model. The nonlinear model results demonstrate that the nonlinear advection terms generate a gyre circulation at the entrance of Lunenburg Bay, and the slope bottom topography at the mouth of the bay strengthens the sub-surface time-mean inflow on the southern side of the bay. A comparison of model-calculated currents in different numerical experiments clearly shows that baroclinicity plays a dominant role in the dynamics of wind-driven circulation in Lunenburg Bay.     

Laboratory experiment on the 3D tide-induced Lagrangian residual current using the PIV technique

The 3D structure of the tide-induced Lagrangian residual current was studied using the particle image velocimetry (PIV) technique in a long shallow narrow tank in the laboratory. At the mouth of the tank, a wave generator was used to make periodic wave which represents the tide movement, and at the head of the tank, a laterally sloping topography with the length of one fifth of the water tank was installed, above which the tide-induced Lagrangian residual current was studied. Under the weakly nonlinear condition in the present experiment setup, the results show that the Lagrangian residual velocity (LRV) field has a three-layer structure. The residual current flows inwards (towards the head) in the bottom layer and flows outwards in the middle layer, while in the surface layer, it flows inwards along the shallow side of the sloping topography and outwards along the deep side. The depth-averaged and breadth-averaged LRV are also analyzed based on the 3D LRV observations. Our results are in good agreement with the previous experiment studies, the analytical solutions with similar conditions and the observational results in real bays. Moreover, the volume flux comparison between the Lagrangian and Eulerian residual currents shows that the Eulerian residual velocity violates the mass conservation law while the LRV truly represents the inter-tidal water transport. This work enriches the laboratory studies of the LRV and offers valuable references for the LRV studies in real bays.     

3D analytical solution to the tidally induced Lagrangian residual current equations in a narrow bay

The 3D first-order Lagrangian residual velocity (LRV) equation is established, and its analytical solution is obtained in a narrow bay. The results show clearly the 3D structure of the first-order LRV. When the exponential bottom profile is assumed, the upper half layer of the water flows in through the deep channel from the open boundary directly to the head of the bay. Then the water will return to the area surrounding the lower half of the inflow area. The downwelling area is located mainly at the deep channel, while the upwelling area occupies both sides of the bay. The inter-tidal water transport, obtained by integrating the 3D first-order LRV through the water column, has a pattern similar to the previous study in which the 2D depth-averaged Lagrangian residual current equations were solved. The inter-tidal water transport is used to analyze the water exchange, and it is found that the water exchange at different cross sections increases smoothly with the distance between the cross sections and the head of the bay until about one wavelength. It is also found that the pattern of the breadth-averaged Lagrangian residual current varies with the length of the bay if a non-flat bottom profile is used. The depth-integrated LRV and the breadth-averaged LRV are mainly determined by the different terms of the tidal body force, with the former determined by the bottom friction related term and the latter by the eddy viscosity related term. When the bay is longer than one wavelength, different results in the outer bay can be observed.     

Tidal inlet velocity asymmetry in diurnal regimes

Tidal velocity asymmetry at inlets influences sediment transport pathways and the morphological evolution of estuaries/lagoons connected to these inlets. Generation of overtides is generally seen as the main cause of tidal velocity asymmetry. Whilst majority of studies examining tidal velocity asymmetry have concentrated on inlets located in semi-diurnal tidal regimes, here, attention is focused on the processes responsible for causing tidal velocity asymmetry at inlets located in diurnal tidal regimes. Using field data collected from three West Australian inlets, it is shown that tidal velocity asymmetry in this type of system is caused by the oceanic tidal conditions. It is also shown that in these systems, the occurrence of flood/ebb dominance can be determined using oceanic tidal elevations, which are more readily available than inlet current data. In contrast to semi-diurnal systems the flood/ebb dominance in diurnal systems varies throughout the year depending on the phase angle relationship between the significant oceanic tidal constituents. The net sediment transport in to/out of these systems, which determines the morphological evolution of the systems, is shown to be governed more by the degree of tidal velocity asymmetry rather than the number of occurrences or duration of flood/ebb-dominant periods.     

Development of a Lagrangian sediment model to reproduce the bathymetric evolution of the Mersey Estuary

The development and application of a Lagrangian particle-tracking model to simulate sediment transport in the Mersey Estuary (UK) is described. Each of the particles (up to a million in total) is advected horizontally by the 3-D tidal currents. Related vertical movements are: (1) downwards by settlement at a prescribed velocity w _s and (2) both upwards and downwards by a distance related to the vertical eddy diffusivity. In a novel departure from traditional practice, where initial distributions of surficial sediments are specified, all particles are introduced at the seaward boundary of the model. Provenance studies indicate surficial sediments are overwhelmingly of marine origin. For the predominant fine sediments, ‘cyclical convergence’ in suspended sediment concentrations is approximated after about two spring-neap tidal cycles. Comparisons are shown between the suspended sediment concentrations and net deposition rates computed by this model against observed values and earlier computations utilising both 1-D and 3-D Eulerian models. While all of these results are in broad agreement, the flexibility of the Lagrangian approach for simulating flocculation, consolidation and mixed sediments illustrates its future potential.     

Sediments and water fluxes in a muddy coastline: interplay between waves and tidal channel hydrodynamics

Tidal channels are ubiquitous in muddy coastlines and play a critical role in the redistribution of sediments, thus dictating the general evolution of intertidal landforms. In muddy coastlines, the morphology of tidal channels and adjacent marshes strongly depends on the supply of fine sediments from the shelf and on the resuspension of sediments by wind waves. To investigate the processes that regulate sediment fluxes in muddy coastlines, we measured tidal velocity and sediment concentration in Little Constance Bayou, a tidal channel in the Rockefeller State Wildlife Refuge, Louisiana, USA. The tidal measurements were integrated with measurements of wave activity in the bay at the mouth of the channel, thus allowing the quantification of feedbacks between waves and sediment fluxes. Results indicate that the sediment concentration in the channel is directly related to the wave height in the adjacent bay during flood and high slack water, whereas the concentration during ebb depends on local channel velocity. Moreover, the sediment flux during ebb is of the same order of magnitude as the sediment flux during the previous flood, indicating that only a small fraction of transported sediments are stored in the marsh during a tidal cycle. Finally, very low tides, characterized by high ebb velocities, export large volumes of sediment to the ocean. Copyright © 2010 John Wiley & Sons, Ltd.     

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 M ₂ 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 M ₂ 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 M ₂ 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, M ₄ tidal pumping, asymmetric tidal mixing, and gravitational circulation, while after the DWP the sediment trapping was caused by M ₂ tidal pumping, Stokes transport, asymmetric tidal mixing, tidal rectification, and gravitational circulation.     

Diurnal sea breeze effects on inner-shelf cross-shore exchange

Cross-shore exchange by strong (cross-shore wind stress, τ_sx>0.05 Pa) diurnal (7–25 h) sea breeze events are investigated using two years of continuous wind, wave, and ocean velocity profiles in 13 m water depth on the inner-shelf in Marina, Monterey bay, California. The diurnal surface wind stress, waves, and currents have spectral peaks at 1, 2, and 3 cpd and the diurnal variability represents about 50% of the total variability. During sea breeze relaxation (−0.05<τ_sx<0.05 Pa), a background wave-driven inner-shelf Eulerian undertow profile exists, which is equal and opposite to the Lagrangian Stokes drift profile, resulting in a net zero Lagrangian transport at depth. In the presence of a sea breeze (τ_sx>0.05 Pa), a uniform offshore profile develops that is different from the background undertow profile allowing cross-shore Lagrangian transport to develop, while including Lagrangian Stokes drift. The diurnal cross-shore current response is similar to subtidal (>25 h) cross-shore current response, as found by Fewings et al. (2008). The seasonality of waves and winds modify the diurnal sea breeze impact. It is suggested that material is not transported cross-shore except during sea breeze events owing to near zero transport during relaxation periods. During sea breeze events, cross-shore exchange of material appears to occur onshore near the surface and offshore near the sea bed. Since sea breeze events last for a few hours, the long-term cross-shore transport is incremental each day.     

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.