H.M. Schuttelaars

Multiple morphodynamic equilibria in tidal embayments

The possible morphodynamic equilibria of tidal embayments are investigated within the framework of a one-dimensional model The equilibria are defined by a steady profile of the erodible bottom. The extension with respect to earlier studies is that the embayments have arbitrary lengths L with respect to the tidal wavelength. This implies a much richer dynamics due to the possibility of tidal resonance and new sediment transport contributions that are caused by internally generated overtides and residual currents. If the system is only forced by an externally prescribed M2 tide at the seaward boundary, a unique morphodynamic equilibrium is obtained for all embayment lengths smaller than the frictional length scale of the tide. Bottom friction causes tidal resonance to occur for a shorter length than a quarter of the frictionless tidal wavelength. This shift is smaller than would occur in the case of a fixed bed profile since the equilibrium condition induces larger water depths. If an externally prescribed overtide is added to the forcing, more than one type of morphodynamic equilibria can be found. For L values smaller than the M4 resonance length scale the bottom profiles are strongly concave, with locally large water depths, and the water motion resembles a standing tidal wave. For longer embayments another type of equilibria, characterized by a weakly concave bottom profile and a traveling tidal wave, appears. For sufficiently strong amplitudes of the externally prescribed M4 tide, multiple morphodynamic equilibria are found. The maximum L, beyond which morphodynamic equilibria cease to exist, decreases with increasing influence of external overtide and bottom friction. These model results show an overall good agreement with field observations.

Initial formation of channels and shoals in a short tidal embayment

It is demonstrated, by using a simple model, that bedforms in a short tidal embayment can develop due to a positive feedback between tidal currents, sediment transport and bedforms. The water motion is modelled by the depth integrated shallow water equations. The system is forced by a prescribed free-surface elevation at the entrance of the embayment. For the sediment dynamics a diffusively dominated suspended load transport model is considered. Tidal averaging is used to obtain the bottom profiles at the long morphological time scale. The stability of a constantly sloping equilibrium bottom profile is studied for various combinations of the model parameters. It turns out that without a mechanism that generates vorticity this equilibrium profile is stable. In that case small-scale perturbations can at most become marginally stable if no bedload term in the bottom evolution equation is incorporated. If vorticity is generated, in our model by bottom friction torques, the basic state is unstable. The spatial patterns of the unstable modes and their growth rates depend, among other things, on the strength of the bottom friction, the width of the embayment and the grain size: if the sediment under consideration consists of large particles, the equilibrium will be more stable than when smaller particles are considered. Without a diffusive term in the bed evolution equation, small-scale perturbations become unstable. To avoid this physically unrealistic behaviour bedload terms are included in the sediment transport. Furthermore, it is shown that using an asymptotic expansion for the concentration as given in earlier literature is only valid for small or moderate mode numbers and the technique is extended to large mode numbers. A physical interpretation of the results is also given.

THE EFFECT OF GEOMETRY AND BOTTOM FRICTION ON LOCAL BED FORMS IN A TIDAL EMBAYMENT

Using a 2DH idealized local morphodynamic model for a tidal channel, it is demonstrated that estuarine bars with typical length scales on the order of the tidal excursion length can develop as the result of a positive feedback between water motion, sediment transport and the sandy bottom. The water motion is modelled by the depth-averaged shallow water equations and driven by an externally prescribed M2 tide. Sediment is mainly transported as suspended load due to advective processes. Convergences and divergences of the tidally averaged sediment fluxes result in the evolution of the bed. It is shown that the combined effect of bottom friction and advective processes can trigger instabilities that lead to the formation of bottom patterns. Bed slope effects are required in order to prevent infinite braiding of these features. With bed slope effects, bars with longitudinal length scales of the order of the tidal excursion length are most likely to become unstable. This result is found to be independent of the ratio of the width to the tidal excursion length as well as the adopted formulation of the bed shear stress. In the case that the width is much smaller than the tidal excursion length and non-linear bottom friction is used, there is good qualitative agreement with results from 3D models reported in literature which were applied to the same parameter regime. Qualitatively, the results are recovered when bottom friction is linearized. Quantitatively, only small modifications occur: the critical friction parameter is decreased and the longitudinal length scale of the most unstable bed form increases. r 2002 Elsevier Science Ltd. All rights reserved.

Modeling the equilibrium of tide-dominated ebb-tidal deltas

[1]xa0This study focuses on identifying physical mechanisms that lead to symmetric, tide-dominated ebb-tidal deltas. An idealized morphodynamic model is developed and analyzed to demonstrate that these deltas can be modeled as morphodynamic equilibria (no evolving bathymetry). It is assumed that the large-scale alongshore tidal currents are small compared to the cross-shore tidal currents, that waves have shore-normal incidence, that the tidal velocity profile over the inlet is symmetric with respect to the midaxis, and that the Coriolis force can be ignored. The modeled tidal hydrodynamics are characterized by an ebb jet during the ebb phase of the tide and a radial inflow pattern during flood. Two residual eddies are formed. The mechanism behind these current patterns is explained with vorticity concepts. The modeled bottom patterns are similar to those of observed symmetric tide-dominated ebb-tidal deltas. In the center of the tidal inlet an ebb-dominated channel is observed that branches further offshore into two flood-dominated channels. At the end of the ebb-dominated channel a shoal is present. Varying the tidal prism, the width of the tidal inlet, the wave height, and the bed slope coefficient in the sediment transport formulation within the range of observed values leaves these patterns qualitatively unchanged. However, the exact extent and shape of the modeled deltas are affected by these parameters. Compared to observations, the modeled ebb-tidal delta is smaller and the ebb-dominated channel is shorter. The observed exponent in the power law relation between sand volume of the delta and the tidal prism is recovered and explained with the model.

Tidal and morphologic properties of embayments: Effect of sediment deposition processes and length variation

Abstract An idealised morphodynamic model is analysed to study the properties of both the vertical and horizontal tide in a rectangular embayment with an erodible bottom. Forcing is due to a prescribed tidal constituent at the entrance. The model is based on the shallow water equations, sediment is transported as suspended load and the divergence of the tidally averaged sediment flux determines the bottom evolution. It is further assumed that the embayment is in morphodynamic equilibrium, i.e., the bottom profile is steady. The main results are that the tidal and morphologic properties strongly depend on the sediment deposition process and on the embayment length. A depth-dependent deposition term causes bed profiles to become convex. With increasing embayment lengths the profiles become concave and tidal resonance is found at a length which is slightly smaller than a quarter of the frictionless tidal wave-length. This shift is less than in case of a fixed bed because water depths increase with increasing embayment lengths. The morphodynamic equilibria do not exist for lengths larger than the frictional length scale of the tide.