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We investigate the influence of wind waves and wind-driven flow on sand wave dynamics using a two-model approach. Using a linear stability analysis, we find that waves decrease sand wave growth and wind causes sand wave migration. Combining linear stability analysis with a typical North Sea wave and wind climate explains variability in sand wave migration rates. Using a nonlinear sand wave model we show that waves reduce sand wave height and wind causes sand wave asymmetry as well as migration.

The nonlinear nature of bottom friction in shallow flow complicates its analysis, particularly in idealised models. For tidal flows, Lorentz’ linearisation has been widely applied, using an energy criterion to specify the friction coefficient. Here we propose an extension of this approach to storm surges, leading to a friction coefficient that may gradually vary over a storm event. The derivation is provided along with first results for a single channel.

Barrier coasts display a chain of islands, separated by tidal inlets that connect a back-barrier basin to a sea or ocean. Observations show that barrier island length generally decreases for increasing tidal range and increasing basin area. However, this has neither been reproduced in model studies nor explained from the underlying physics. This is the aim of our study. Here we simulate barrier coast dynamics by combining a widely used empirical relationship for inlet dynamics with a process-based model of the tidal hydrodynamics. Our model results show stable inlet systems with more than one inlet open that support the observed qualitative relationships and fit in existing barrier coast classifications. To explain this, we identify a competition between a destabilizing mechanism (bottom friction in inlets, tending to reduce the number of open inlets) and a stabilizing one (spatially varying pressure gradients over the inlets, tending to keep the inlets open).

The cross-sectional stability of double inlet systems is investigated using an exploratory model that combines Escoffier’s stability concept for the evolution of the inlet’s cross-sectional area with a two-dimensional, depth-averaged (2DH) hydrodynamic model for tidal flow. The model geometry consists of four rectangular compartments, each with a uniform depth, associated with the ocean, tidal inlets and basin. The water motion, forced by an incoming Kelvin wave at the ocean’s open boundary and satisfying the linear shallow water equations on the f -plane with linearised bottom friction, is in each compartment written as a superposition of eigenmodes, i.e. Kelvin and Poincaré waves. A collocation method is employed to satisfy boundary and matching conditions. The analysis of resulting equilibrium configurations is done using flow diagrams. Model results show that internally generated spatial variations in the water motion are essential for the existence of stable equilibria with two inlets open. In the hydrodynamic model used in the paper, both radiation damping into the ocean and basin depth effects result in these necessary spatial variations. Coriolis effects trigger an asymmetry in the stable equilibrium cross-sectional areas of the inlets. Furthermore, square basin geometries generally correspond to significantly larger equilibrium values of the inlet cross-sections. These model outcomes result from a competition between a destabilising (caused by inlet bottom friction) and a stabilising mechanism (caused by spatially varying local pressure gradients over the inlets).

This study investigates the influence of basin geometry on the cross-sectional stability of double inlet systems. The inlet is in equilibrium when the amplitude of the inlet velocities equals the equilibrium velocity (~1 m s-1). This equilibrium is stable when after a perturbation the cross-sections of both inlets return to their original equilibrium value. The necessary amplitudes of the inlet velocities are obtained using an idealized 2DH hydrodynamic that calculates tidal elevation and flow in a geometry consisting of several adjacent rectangular compartments. Model results suggest that regardless of the inclusion or exclusion of bottom friction in the basin, stable equilibrium states exist. Qualitatively, the influence of basin geometry does not change the presence of stable equilibrium. Quantitatively, however, taking a basin surface area of 1200 km2, equilibrium values can differ up to a factor 2 depending on the geometry of the basin.

[1] Tidal sandbanks are large-scale bed features present in many shallow shelf seas. Here we investigate the effect of nonuniform sediment on their dynamics, with a particular aim to explain observed surficial grain size variations over tidal sandbanks from a process-based modeling perspective. To this end, we use a linear stability analysis that describes the positive feedback mechanism between hydrodynamics, sediment, and the seabed responsible for sandbank formation on a horizontal shelf. In this model the sediment transport and bed evolution modules are extended by introducing an active layer and a bimodal sediment mixture. We include a dynamic hiding/exposure description of sediment transport, enhancing the transport of coarse grains and inhibiting the transport of finer grains. The model results show that for symmetrical tidal conditions, coarse grains tend to accumulate at the bank crests. Moreover, the growth rates of the perturbations increase compared to the case of uniform sediment, while the preferred wavelength and bank orientation remain unchanged. For asymmetrical tidal conditions we find a spatial phase shift between topography and the mean grain size fraction, indicating an accumulation of coarse grains on the lee side of the bank. The model results qualitatively agree with observations from banks on the Belgian continental shelf.

To improve our understanding of tidal sandbank dynamics, we have developed a nonlinear morphodynamic model. A crucial property of the model is that it fully resolves the dynamics on the fast (tidal) timescale, allowing for asymmetric tidal flow with an M0, M2, and M4 component. This approach, extending earlier research on the formation of tidal sandbanks, leads to equilibrium profiles. Their heights (60-90% of the water depth) and shapes are controlled by the mode of sediment transport and the hydrodynamic conditions. Bed load transport under symmetrical tidal conditions leads to high spiky banks. Several mechanisms tend to lower and smooth these profiles, such as the relaxation of suspended sediment, wind wave stirring, and tidal asymmetry. This last causes the profiles to be asymmetric, as well. The morphodynamic equilibrium expresses a tidally averaged balance between a destabilizing flux due to fluid drag and the downslope transport induced by both tidal flow and wind wave stirring. The modeled profiles are in fair agreement with observations from the North Sea.