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.     

Longitudinal variation in lateral trapping of fine sediment in tidal estuaries: observations and a 3D exploratory model

This study investigates the longitudinal variation of lateral entrapment of suspended sediment, as is observed in some tidal estuaries. In particular, field data from the Yangtze Estuary are analysed, which reveal that in one cross-section, two maxima of suspended sediment concentration (SSC) occur close to the south and north sides, while in a cross-section 2 km down-estuary, only one SSC maximum on the south side is present. This pattern is found during both spring tide and neap tide, which are characterised by different intensities of turbulence. To understand longitudinal variation in lateral trapping of sediment, results of a new three-dimensional exploratory model are analysed. The hydrodynamic part contains residual flow due to fresh water input, density gradients and Coriolis force and due to channel curvature-induced leakage. Moreover, the model includes a spatially varying eddy viscosity that accounts for variation of intensity of turbulence over the spring-neap cycle. By imposing morphodynamic equilibrium, the two-dimensional distribution of sediment in the domain is obtained analytically by a novel procedure. Results reveal that the occurrence of the SSC maxima near the south side of both cross-sections is due to sediment entrapment by lateral density gradients, while the second SSC maximum near the north side of the first cross-section is by sediment transport due to curvature-induced leakage. Coriolis deflection of longitudinal flow also contributes the trapping of sediment near the north side. This mechanism is important in the upper estuary, where the flow due to lateral density gradients is weak.     

On the stability relationships between tidal asymmetry and morphologies of tidal basins and estuaries

Simple stability relationships are practically useful to provide a rapid assessment of coastal and estuarine landforms in response to human interventions and long‐term climate change. In this contribution, we review a variety of simple stability relationships which are based on the analysis of tidal asymmetry (TA). Most of the existing TA‐based stability relationships are derived using the one‐dimensional tidal flow equations assuming a certain regular shape of the tidal channel cross‐sections. To facilitate analytical solutions, specific assumptions inevitably need to be made, for example by linearizing the friction term and dropping some negligible terms in the tidal flow equations. We find that three major types of TA‐based stability relationships have been proposed between three non‐dimensional channel geometric ratios (represented by the ratio of channel widths, ratio of wet surface areas and ratio of storage volumes) and the tide‐related parameter a/h (i.e. the ratio between tidal amplitude and mean water depth). Based on established geometric relations, we use these non‐dimensional ratios to restate the existing relationships so that they are directly comparable. Available datasets are further extended to examine the utility of these TA‐based relationships. Although a certain agreement is shown for these relationships, we also observe a large scatter of data points which are collected in different types of landscape, hydrodynamic and sedimentological settings over the world. We discuss in detail the potential reasons for this large scatter and subsequently elaborate on the limited applicability of the various TA‐based stability relationships for practical use. We highlight the need to delve further into what constitutes equilibrium and what is needed to develop more robust measures to determine the morphological state of these systems. Copyright © 2018 John Wiley & Sons, Ltd.     

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.     

The influence of changes in tidal asymmetry on residual sediment transport in the Western Scheldt

This study fits into a wider research program from RWS RIKZ concerning the exchange of sediment between the coast and the tidal basins, Western Scheldt and Wadden Sea, which are the largest basins along the Dutch Coast, over different time-scales. For both basins, questions about the evolution of the import/export at the mouth recently arose. In case of the Western Scheldt, which is the subject of this study, mainly the uncertainty about the future developments after the change from import to export at the mouth was noticed in the 1990s, which necessitated a more detailed study of this area.     

Morphological controls in sandy estuaries: the influence of tidal flats and bathymetry on sediment transport

The morphodynamics of shallow, vertically well-mixed estuaries, characterised by tidal flats and deeper channels, have been investigated. This paper examines what contributes to flood/ebb-dominant sediment transport in localised regions through a 2D model study (using the TELEMAC modelling system). The Dyfi Estuary in Wales, UK has been used as a case study and, together with idealised estuary shapes, shows that shallow water depths lead to flood dominance in the inner estuary whilst tidal flats and deep channels cause ebb dominance in the outer estuary. For medium sands and with an artificially ‘flattened’ bathymetry (i.e. no tidal flats), the net sediment transport switches from ebb-dominant to flood-dominant where the parameter a/h (local tidal amplitude ÷ local tidally averaged water depth) exceeds 1.2. Sea level rise will reduce this critical value of a/h and also reduce the ebb-directed sediment transport significantly, leading to a flood-dominated estuarine system. A similar pattern, albeit with greater transport, was simulated with tidal flats included and also with a reduced grain size. This suggests that analogous classifications for flood/ebb asymmetry of the tide in estuaries as a whole may not represent the local sediment transport in sufficient detail. Through the Dyfi simulations, the above criterion involving a/h is shown to be complicated further by augmented flow past a spit at the estuary mouth which gives rise to a self-maintaining scour hole. Simulations of one year of bed evolution in an idealised flat-bottomed estuary, including tidal flow past a spit, recreate the flood/ebb dominance on either side of the spit and the formation of a scour hole in between. The erosion rate at the centre of the hole is reduced as the hole deepens, suggesting the establishment of a self-maintaining equilibrium state.     

The effect of geometry and tidal forcing on hydrodynamics and net sediment transport in semi-enclosed tidal basins

A new depth-averaged exploratory model has been developed to investigate the hydrodynamics and the tidally averaged sediment transport in a semi-enclosed tidal basin. This model comprises the two-dimensional (2DH) dynamics in a tidal basin that consists of a channel of arbitrary length, flanked by tidal flats, in which the water motion is being driven by an asymmetric tidal forcing at the seaward side. The equations are discretized in space by means of the finite element method and solved in the frequency domain. In this study, the lateral variations of the tidal asymmetry and the tidally averaged sediment transport are analyzed, as well as their sensitivity to changes in basin geometry and external overtides. The Coriolis force is taken into account. It is found that the length of the tidal basin and, to a lesser extent, the tidal flat area and the convergence length determine the behaviour of the tidally averaged velocity and the overtides and consequently control the strength and the direction of the tidally averaged sediment transport. Furthermore, the externally prescribed overtides can have a major influence on tidal asymmetry in the basin, depending on their amplitude and phase. Finally, for sufficiently wide tidal basins, the Coriolis force generates significant lateral dynamics.     

The effect of asymmetric dune roughness on tidal asymmetry in the Weser estuary

The bed of estuaries is often characterized by ripples and dunes of varying size. Whereas smaller bedforms adapt their morphological shape to the oscillating tidal currents, large compound dunes (here: asymmetric tidal dunes) remain stable for periods longer than a tidal cycle. Bedforms constitute a form roughness, that is, hydraulic flow resistance, which has a large-scale effect on tidal asymmetry and, hence, on hydrodynamics, sediment transport, and morphodynamics of estuaries and coastal seas. Flow separation behind the dune crest and recirculation on the steep downstream side result in turbulence and energy loss. Since the energy dissipation can be related to the dune lee slope angle, asymmetric dune shapes induce variable flow resistance during ebb and flood phases. Here, a noncalibrated numerical model has been applied to analyze the large-scale effect of symmetric and asymmetric dune shapes on estuarine tidal asymmetry evaluated by residual bed load sediment transport at the Weser estuary, Germany. Scenario simulations were performed with parameterized bed roughness of symmetric and asymmetric dune shapes and without dune roughness. The spatiotemporal interaction of distinct dune shapes with the main drivers of estuarine sediment and morphodynamics, that is, river discharge and tidal energy, is shown to be complex but substantial. The contrasting effects of flood- and ebb-oriented asymmetric dunes on residual bed load transport rates and directions are estimated to be of a similar importance as the controls of seasonal changes of discharge on these net sediment fluxes at the Lower Weser estuary. This corroborates the need to consider dune-induced directional bed roughness in numerical models of estuarine and tidal environments.     

The influence of river discharge on tidal damping in alluvial estuaries

The tidal range, the difference between high water level and low water level, along an alluvial estuary can be described by Savenije's analytical equation [Journal of Hydrology 243 (2001) 205-215] analytical equation. This equation was derived from the complete St Venant equations in a Lagrangian reference frame. In the derivation of that equation the effect of river discharge was disregarded. Measurements in the Schelde Estuary show that this assumption is only valid in the lower part of the estuary, but that in the upper part the river discharge has an influence on tidal damping. In the downstream part of the estuary, where the cross-sectional area is large compared to the cross-sectional area of the river, it is correct to disregard the river discharge. However, in the upstream part of the estuary, where the cross-sectional area approaches that of the river, the fresh water discharge gains importance over the tidal flow and affects the tidal range. In this paper, the derivation of the analytical equation is expanded to include the effect of the river discharge. It is demonstrated that the river discharge can have a considerable influence on tidal damping in the upper reach of the estuary. The river discharge affects tidal damping primarily through friction. A critical point along the estuary is the point where there is a single slack, upstream of which the fresh water velocity is larger than the tidal velocity. The location of this point varies with the river discharge. From that point onwards the effect of river discharge on damping is dominant. It is the point where the estuary becomes primarily of riverine character.     

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.     

The hyperturbid state of the water column in estuaries and rivers: the importance of hindered settling

Over the last few decades, some estuaries have undergone a transition to a hyperturbid state, characterised by suspended sediment concentrations of several grammes per litre averaged over the water column. To improve our understanding of this transition and of naturally hyperturbid estuaries, we systematically identify the processes allowing for high suspended sediment concentrations using a water column (1DV) model. Under a range of realistic forcing conditions, the state of the water column can be characterised by one of two equilibrium states. The first is an erosion-limited state, in which there still is sediment available for erosion at the bed. We find that this state only occurs with relatively low concentrations. The second is a supply-limited state, in which all erodable sediment is in suspension. The concentration in this state depends entirely on the amount of sediment in the system and can potentially be very high. We identify the conditions under which the state of the water column can jump from a low to a high concentration and identify hysteresis in the transition between the two states. The mechanism responsible for this hysteresis is hindered settling. It thus follows that hyperturbidity is only possible in a supply-limited state. From this observation we derive a necessary condition for an estuarine system to make the transition from low turbidity to hyperturbidity in a 1DV context. This is an important step towards understanding why some estuaries are hyperturbid and assessing the risk that particular estuaries may become hyperturbid in the future.     

Analytical and numerical analysis of tides and salinities in estuaries; part I: tidal wave propagation in convergent estuaries

Analytical solutions of the momentum and energy equations for tidal flow are studied. Analytical solutions are well known for prismatic channels but are less well known for converging channels. As most estuaries have a planform with converging channels, the attention in this paper is fully focused on converging tidal channels. It will be shown that the tidal range along converging channels can be described by relatively simple expressions solving the energy and momentum equations (new approaches). The semi-analytical solution of the energy equation includes quadratic (nonlinear) bottom friction. The analytical solution of the continuity and momentum equations is only possible for linearized bottom friction. The linearized analytical solution is presented for sinusoidal tidal waves with and without reflection in strongly convergent (funnel type) channels. Using these approaches, simple and powerful tools (spreadsheet models) for tidal analysis of amplified and damped tidal wave propagation in converging estuaries have been developed. The analytical solutions are compared with the results of numerical solutions and with measured data of the Western Scheldt Estuary in the Netherlands, the Hooghly Estuary in India and the Delaware Estuary in the USA. The analytical solutions show surprisingly good agreement with measured tidal ranges in these large-scale tidal systems. Convergence is found to be dominant in long and deep-converging channels resulting in an amplified tidal range, whereas bottom friction is generally dominant in shallow converging channels resulting in a damped tidal range. Reflection in closed-end channels is important in the most landward 1/3 length of the total channel length. In strongly convergent channels with a single forward propagating tidal wave, there is a phase lead of the horizontal and vertical tide close to 90^o, mimicking a standing wave system (apparent standing wave).     

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.     

The effect of wettability on capillary trapping in carbonates

We use an organic acid (cyclohexanepentanoic acid) to alter the wettability of three carbonates: Estaillades, Ketton and Portland limestones, and observe the relationship between the initial oil saturation and the residual saturation. We take cores containing oil and a specified initial water saturation and waterflood until 10 pore volumes have been injected. We record the remaining oil saturation as a function of the amount of water injected. In the water-wet case, with no wettability alteration, we observe, as expected, a monotonic increase in the remaining oil saturation with initial saturation. However, when the wettability is altered, we observe an increase, then a decrease, and finally an increase in the trapping curve for Estaillades limestone with a small, but continued, decrease in the remaining saturation as more water is injected. This behavior is indicative of mixed-wet or intermediate-wet conditions, as there is no spontaneous imbibition of oil and water. In contrast, Ketton did not show indications of a significant wettability alteration with a similar observed trapping profile to that observed in the water-wet case. Portland limestone also showed a monotonic increasing trend in remaining saturation with initial saturation but with a higher recovery, and less trapping, than the water-wet case. Again, this is intermediate-wet behavior with no spontaneous imbibition of either oil or water, and slow production of oil after water breakthrough. Finally, we repeat the same experiments but instead we age the three carbonates with a high asphaltenic content and high viscosity crude oil at 70 °C mimicking reservoir conditions. The results show a monotonic increase in residual saturation as a function of initial saturation but with higher recovery than the water-wet cases for Estaillades and Portland, with again no indication of wettability alteration for Ketton. We discuss the results in terms of pore-scale recovery process and contact angle hysteresis. In these experiments, water-saturated micro-porosity appears to protect the solid surfaces from a strong wettability alteration, particularly in Ketton.     

Modelling sediment trapping in vegetative filter strips on steep slopes

The slope effects on sediment trapping process in vegetative filter strips (VFS) are usually neglected in current modelling practices for VFS operation, which hamper the VFS design and performance evaluation, especially on steep slopes. To fill the knowledge gap, 12 laboratory experiments of sediment trapping in VFS were conducted with three different inflow discharge (80, 100, and 120 ml s⁻¹) and four slope angles (5,10, 15, and 20°). The experimental results show that, on steep slopes (10, 15, and 20°), a part of trapped sediment particles in VFS can be eroded again and then dragged to the downstream as bed load, whilst they do not move on gentle slope (5°). To describe the complex processes, a simple and effective modelling framework was developed for sloped VFS by coupling the slope infiltration, runoff, and modified sediment transport model. The model was tested against the experimental results and good agreements between the modelled and observed results were found in both runoff and sediment transport processes for all cases. On steep slopes, the sediment trapping performance of VFS decreases significantly because the erosion of deposited sediment particles can account for more than 60% of the sediment load in the outflow. The slope effect on sediment trapping efficiency of VFS varies greatly with soil, VFS, and slope properties. The model was compared with previous sediment transport equation and found that both methods can satisfactorily predict the sediment trapping of VFS on gentle slopes, but previous sediment transport equation is likely to overestimate the sediment trapping efficiency in VFS on steep slopes. This model is expected to provide a more realistic and accurate method for predicting runoff and sediment reduction in VFS on sloping surfaces.     

Seasonal,tidal, and geomorphic controls on sediment export to Amazon River tidal floodplains

Mainstem–floodplain material exchange in the tidal freshwater reach of major rivers may lead to significant sequestration of riverine sediment, but this zone remains understudied compared to adjacent fluvial and marine environments. This knowledge gap prompts investigation of floodplain-incising tidal channels found along the banks of tidal rivers and their role in facilitating water and suspended-sediment fluxes between mainstem and floodplain. To evaluate this role, and how it evolves along the tidal river and with time, we measured water level, flow velocity, temperature, and suspended-sediment concentration (SSC) in four tidal channels along the tidal Amazon River, Brazil. Eleven deployments were made during low, rising, high, and falling seasonal Amazon discharge. Generally, channels export high-SSC water from the mainstem to the tidal floodplain on flood tides and transfer low-SSC water back to the mainstem on ebbs. Along the length of the tidal river, the interaction between tidal and seasonal water-level variations and channel–floodplain morphology is a primary control on tidal-channel sediment dynamics. Close to the river mouth, where tides are large, this interaction produces transient flow features and current-induced sediment resuspension, but the importance of these processes decreases with distance upstream. Although the magnitude of the exchange of water and sediment between mainstem and floodplain via tidal channels is a small percentage of the total mainstem discharge in this large tidal-river system, tidal channels are important conduits for material flux between these two environments. This flux is critical to resisting floodplain submergence during times of rising sea level. © 2019 John Wiley & Sons, Ltd.