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An estuarine turbidity maximum (ETM) results from various subtidal sediment transport mechanisms related to, e.g., river, tides, and density gradients, which have been extensively analysed in single-channel estuaries. However, ETMs have also been found in estuaries composed of multiple interconnected tidal channels, where the water and suspended fine sediments are exchanged at the junctions with possible occurrence of sediment overspill. The overall aim of this study is to understand the processes that determine the ETM dynamics in such channel networks. Specifically, focusing on the ETMs formation due to sediment transport by river flow and density-driven flow, the dependence of ETM locations in an idealised three-channel network on fluvial sediment input and the local deepening and narrowing of a seaward channel is investigated. It is found that the ETM dynamics in channels of a network is coupled, and hence, changes in one channel affect the ETM pattern in all channels. Sensitivity results show that, keeping river discharge fixed, a larger fluvial sediment input leads to the upstream shift of ETMs and an increase in the overall sediment concentration. Both deepening or narrowing of a seaward channel may influence the ETMs in the entire network. Furthermore, the effect of either deepening or narrowing of a seaward channel on the ETM locations in the network depends on the system geometry and the dominant hydrodynamic conditions. Therefore, the response of the ETM location to local geometric changes is explained by analysing the dominant sediment transport mechanisms. In addition to the convergence of sediment transport mechanisms in single-estuarine channels, ETM dynamics in networks is found to be strongly affected by net exchange of sediment between the branches of a network. We find that considering the sensitivity of net sediment transport to geometric changes is needed to understand the changing ETM dynamics observed in a real estuarine network.

Freshwater pulses (during which river discharge is much higher than average) occur in many estuaries and strongly impact estuarine functioning. To gain insight into the estuarine salinity response to freshwater pulses, an idealized model is presented. With respect to earlier models on the spatiotemporal behavior of salinity in estuaries, it includes additional processes that provide a more detailed vertical structure of salinity. Simulation of an observed salinity response to a freshwater pulse in the Guadalquivir Estuary (Spain) shows that this is important to adequately simulate the salinity structure. The model is used to determine the dependency of the estuarine salinity response to freshwater pulses for different background discharge, tides, and different intensities and durations of the pulses. Results indicate that the change in salt intrusion length due to a freshwater pulse is proportional to the ratio between peak and background river discharge and depends linearly on the duration of the pulse if there is no equilibration during the pulse. The adjustment time, which is the time it takes for the estuary to reach equilibrium after an increase in river discharge, scales with the ratio of the change in salt intrusion length and the peak river discharge. The recovery time, that is, the time it takes for the estuary to reach equilibrium after a decrease in river discharge, does not depend on the amount of decrease in salt intrusion length caused by the pulse. The strength of the tides is of minor importance to the salt dynamics during and after the pulse.

Net water transport (NWT) in estuaries is important for, for example, salt intrusion and sediment dynamics. While NWT is only determined by river runoff in single channels, in estuarine networks, it results from a complex interplay between tides and residual flows. This study aims to disentangle the various contributions of these physical drivers to NWT in estuarine networks and investigate the sensitivities of NWT to variable forcing conditions, interventions, and sea level rise (SLR). To this end, a processes-based perturbative network model is developed, which accounts for the vertical flow structure to resolve density-driven flow driven by a vertically uniform along-channel salinity gradient. Other identified drivers are river discharge and three tidal rectification processes: Stokes transport and its return flow, momentum advection, and velocity-depth asymmetry. The model is applied to the Yangtze Estuary. NWT due to tidal rectifications and density-driven flow can be comparable to river discharge. Specifically in the North Branch, the direction of NWT may differ from the direction of river discharge. Varying river discharge mainly affects NWT as tide-river interaction is weak and density-driven flow is shown to be insensitive to salt intrusion. Conversely, variations in tidal amplitude strongly affect NWT related to tidal rectification and density-driven flow. The deepening (narrowing) of one channel (Deep Waterway Project), affected the NWT mostly through the density-driven flow (advection). Furthermore, NWT distribution in the Yangtze is insensitive to SLR up to 2 m because the effects of SLR on transport due to different drivers compensate each other.

Tidal sand waves are rhythmic bedforms found on sandy continental shelves that pose a threat to offshore activities. While emphasis is placed on studying their natural morphodynamic evolution, little is known about if and how fast sand waves recover after dredging. This work presents an analysis of multibeam echosounder data collected at three former sand extraction sites on the Belgian continental shelf. At one of the sites, sand waves seemed to reappear approximately 5 years after dredging had stopped, which did not happen at the other two sites during the measurement period (5 and 9 years). The lack of recovery in those sites is likely the result of larger depths and smaller local sediment availability compared with the site where recovery occurred. Furthermore, these data reveal that in the latter site sand wave recovery was established mainly through local sediment redistribution. • Tidal sand waves are isolated from bathymetric data of the Belgian continental shelf. • At only one of the three sites, sand waves seemed to regenerate after dredging. • Possible explanations are differences in water depth and local sediment availability. • The regenerating tidal sand waves do so as a result of local redistribution of sand.

The Guadalquivir estuary is a high-nutrient load environment, yet it has a reduced primary production because the high suspended sediment concentration (SSC) causes light attenuation. High-resolution observations revealed relationships between the SSC and Chlorophyll-a (Chla) concentration from seasonal to intratidal time scales. Local maxima of time-averaged Chla levels occurred at locations with relatively low SSC. In the upper (lower) part of the estuary, larger Chla concentrations were observed during the wet (dry) season. In contrast to longer time scales, SSC and Chla exhibited in-phase oscillations during the spring-neap cycle. Both SSC and Chla were found to peak at maximum ebb and flood. There was no positive correlation at certain apogean neap tides, and instead, Chla exhibited daily variations. An idealized model was developed, which mimicked and helped to explain SSC-Chla relationships at different time scales. The model accounts for the vertical advection of Chla and SSC, tidal resuspension, radiation-mediated growth, and effects of the change in stratification stemming from tides and SSC. The specific growth rate of the Chla biomass is inhibited due to high SSC throughout the year. The in-phase relationship at spring-neap and tidal scales seems to be due to resuspension of algal microorganisms attached to sediments. Daily variability of Chla during apogean neap tides emerges because tidal shear stress is low and the strong decline in the suspended particulate matter reduces the light attenuation. The light-mediated growth of part of the biomass, still remaining in the upper layers of the water column, is then driven by the day-night cycle.

The role of the Coriolis effect in the initial formation of bottom patterns in a tidal channel is studied by means of a linear stability analysis. The key finding is that the mechanism generating oblique tidal sand ridges on the continental shelf is also present in confined tidal channels. As a result, the Coriolis effect causes the fastest growing pattern to be a combination of tidal bars and oblique tidal sand ridges. Similar as on the continental shelf, the Coriolis-induced torques cause anticyclonic residual circulations around the ridges, which lead to the accumulation of sand above the ridges. Furthermore, an asymptotic analysis indicates that the maximum growth rate of the bottom perturbation is slightly increased by the Coriolis effect, while its preferred wavelength is hardly influenced.

Tidal sand ridges are large-scale bedforms with horizontal dimensions of several kilometers and heights in the order of tens of meters, which occur on outer shelves of coastal seas. In order to study the long-term evolution of these ridges, an idealized nonlinear numerical model was developed. With this tool, the sensitivity of the characteristics of these finite-height ridges, in particular, their shape and growth time, to 1D/2D configuration (topography varies in one/two horizontal dimensions), tidal ellipticity and critical bed shear stress for sand erosion was investigated. In the case of a 1D configuration, the root mean square height hrms of the bedforms first grows exponentially and hereafter saturates. In the end, ridges in static equilibrium are obtained, i.e., hrms remains constant. In contrast, when the configuration is 2D, ridges are found with spatially meandering crests that oscillate in time. Initially the bedforms are composed of a finite number of bottom modes. The meanders occur if bottom modes with crests normal to those of the initially preferred bedform exist, and their topographic wavenumbers are in the order of that of the preferred bedform or smaller. In addition, the vertical distance between the crest and trough levels should be larger than around 80% of the maximum water depth. Generally, the global growth time, i.e., the time at which hrms stops increasing after the exponential growth stage of the bedforms, is slightly larger for a 2D than for a 1D configuration. The ridge shapes are sensitive to the tidal ellipticity, while they are hardly sensitive to the critical bed shear stress. The global growth time varies non-monotonically with the tidal ellipticity, and it increases if the critical bed shear stress is included. Comparison between the model results and field observations suggests that the model is able to simulate the gross characteristics of the Dutch Banks and the Flemish Banks in the southern North Sea and that these ridges may still be growing.

To gain insight into mechanisms underlying phytoplankton bloom dynamics in turbid, well-mixed estuaries, experiments were conducted with an exploratory model that couples physical and biological processes. The motivation for choosing exploratory models is that they allow investigation of individual processes in isolation, therefore yielding fundamental insight into the mechanisms of the system. The Ems estuary (between the Netherlands and Germany) was selected as the prototype estuary, in which a zone of high turbidity is observed in the middle and upper reach. Results show that the model is capable of capturing the main features of the observed phytoplankton population density (P) patterns, that is, in the lower reach a spring bloom occurs, followed by a secondary bloom in autumn. Results of sensitivity studies reveal that the along-estuary distribution of suspended particulate matter (SPM) is a determining factor for the along-estuary location of blooms and it largely affects the intensity of blooms. The along-estuary advection of nutrients by the subtidal current is important for obtaining blooms with high intensities. In this model, the seasonally varying water temperature has a larger impact on the timing of spring blooms than the seasonally varying incident light intensity. The occurrence of an autumn bloom is due to the fact that during the summer season, the net specific growth rate of phytoplankton decreases. The latter is likely to result from an optimum water temperature (smaller than the maximum water temperature) for phytoplankton growth. Nevertheless, the occurrence and characteristics of autumn blooms are also influenced by seasonal variations in other aspects, for instance, loss of phytoplankton due to grazing.

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.

Tidal sand ridges are large-scale bedforms that occur in the offshore area of shelf seas. They evolve on a time scale of centuries due to tide-topography interactions while being further shaped by wind waves. During their evolution, ridges are also affected by changes in sea level, strength and direction of the tidal current. According to their present-day behavior, ridges are classified as ‘active’ (sand transport everywhere), ‘quasi-active’ (sand transport only on parts of the ridges) and ‘inactive’ (no sand transport anywhere). Using a nonlinear morphodynamic model, the present study extends earlier work by investigating the effect of sea level rise and changes in the amplitude and principal direction of the tidal current on the growth time and height of active tidal sand ridges. Besides, the role of sea level rise and tidal current variation in the presence of quasi-active/inactive ridges is explored. Two specific settings are considered, which are characteristic for the Dutch Banks in the North Sea and for sand ridges in the Celtic Sea. The time range considered here is less than 20,000 years, roughly the period from the Last Glacial Maximum to the present. Generally active tidal sand ridges occur if the tidal current amplitude is larger than 0.5 m/s. For these ridges, with increasing rates of sea level rise, their growth time becomes longer, and the root mean square height keeps on increasing. A smaller initial tidal current amplitude gives rise to a larger growth time, while changes in the principal current direction have a minor effect on the characteristics of the ridges. On the considered time scale, assuming a constant wave climate, quasi-active tidal sand ridges occur mainly as a result of a decreasing tidal current amplitude such that the effective velocity (in the sense of stirring sand) becomes smaller than the critical velocity for sand erosion. The ridges further become inactive on a time scale that depends inversely on the rate of sea level rise. Modeled ridges are compared with observed ridges. Similarities are found and quantitative differences are explained.

Tidal sand ridges and long bed waves are large-scale bedforms that are observed on continental shelves. They differ in their wavelength and in their orientation with respect to the principal direction of tidal currents. Previous studies indicate that tidal sand ridges appear in areas where tidal currents are above 0.5 m s −1 , while long bed waves occur in regions where the maximum tidal current velocity is slightly above the critical velocity for sand erosion and the current is elliptical. An idealized nonlinear numerical model was developed to improve the understanding of the initial formation of these bedforms. The model governs the feedbacks between tidally forced depth-averaged currents and the sandy bed on the outer shelf. The effects of different formulations of bed shear stress and sand transport, tidal ellipticity and different tidal constituents on the characteristics of these bedforms (growth rate, wavelength, orientation of the preferred bedforms) during their initial formation were examined systematically. The results show that the formulations for bed shear stress and slope-induced sand transport are not critical for the initial formation of these bedforms. For tidal sand ridges, under rectilinear tidal currents, increasing the critical bed shear stress for sand erosion decreases the growth rate and the wavelength of the preferred bedforms significantly, while the orientation angle slightly decreases. The dependence of the growth rate, wavelength and the orientation of the preferred bedforms on the tidal ellipticity is non-monotonic. A decrease in tidal frequency results in preferred bedforms with larger wavelength and smaller orientation angle, while their growth rate hardly changes. In the case of joint diurnal and semidiurnal tides, or spring-neap tides, the characteristics of the bedforms are determined by the dominant tidal constituent. For long bed waves, the number of anticyclonically/cyclonically oriented bedforms with respect to the principal current direction increases as the ellipticity of the cyclonic/anticyclonic tidal currents increases. Besides, under anticyclonic tidal currents, the growth rate of cyclonically oriented long bed waves increases as the tidal ellipticity increases. The model was also used to provide a possible explanation for the fact that the Dutch Banks have a larger wavelength than that of the Flemish Banks in the North Sea.

The effect of the joint action of M2 and M4 tidal flow, residual flow and spatial settling lag on the lateral entrapment of sediment is examined in tidally dominated estuaries with an idealized model that assumes along-estuary uniform conditions. Approximate solutions are obtained for arbitrary cross-channel bed profiles by scaling and perturbation analysis. The hydrodynamics include externally driven M2 tidal flow, externally and internally driven M4 tidal flow and residual flow driven by horizontal density gradient, river discharge and nonlinear advection. The sediment concentration includes a mean component, an M2 component driven by bed erosion and an M2 component driven by both bed erosion and inertial terms. Sediment availability is calculated by imposing a morphodynamic equilibrium condition. The model is applied to a transect in the James River estuary where data of flow and suspended sediment concentration are available. Two types of sediment are separately considered, viz., fine silt and coarse silt. Residual advective transport of sediment by the lateral flow induces trapping of sediment over the left shoal (looking landward). Model results also show that the incorporation of M4 tidal flow and spatial settling lag leads to a second sediment trapping region over the right shoal. Model results are qualitatively in good agreement with the observations.

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.

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.

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.

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.