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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.

Double sandbar systems often characterize the surf zone of wave-dominated beaches and display a variety of poorly explained spatial configurations. Here, we explore the morphodynamic stability of double-barred beaches using a model based on linear stability analysis. Surf zone hydrodynamics are described by coupling depth and wave-averaged conservation of mass and momentum with the wave energy and phase equations, including roller dynamics. A simplified sediment transport formulation relates flow to seabed changes. Under normal wave incidence, an alongshore uniform coast with a cross-shore profile characterized by the presence of two sandbars can be unstable, thereby resulting in the development of crescentic and/or rip channel patterns. Our study demonstrates that sandbar coupling can be either in phase (highs and lows of both sandbars are at the same alongshore position) or out of phase (highs and lows of one sandbar correspond to lows and highs of the other sandbar). In line with observations, results of simulations show a large variability in the possible emerging bottom patterns. Our analysis indicates that modes of which the amplitude of the inner sandbar perturbation is larger than that of the outer sandbar are dominant for large height–depth differences between the two sandbar crests and small offshore wave heights. Patterns related to the outer sandbar dominate for small values of the difference in sandbar depth. For intermediate differences between the two sandbar depths, patterns on both longshore bars appear to be fully coupled (similar growth rates and strongly correlated pattern shapes). For relatively large waves and large depth over the outer sandbar, patterns can also develop close to the shoreline and/or inner surf zone together with patterns in the inner or outer sandbar.

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.

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 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.

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.