Abstract
The existence of cross-sectionally averaged morphodynamic equilibria of tidal inlets is investigated, using a cross-sectionally averaged model, and their sensitivity to variations of geometry, deposition parameter, frictional effects and advective sediment transport is analysed. Different geometries, from exponentially converging to exponentially diverging, are considered for inlets with lengths typical for the Dutch Wadden Sea. Standard continuation techniques are employed to numerically obtain morphodynamic equilibrium solutions, i.e. solutions for which the tidally averaged bed level does not change anymore. It is known that when the water motion at the entrance of the inlet is only forced by a M2 tidal constituent assuming the water level to be spatially uniform and only diffusive sediment transport is considered, the morphodynamic bed equilibrium has a constantly sloping profile for a rectangular inlet. We find that the bed profile in equilibrium becomes convex (concave) when we change the frictionless embayment geometry to a diverging (converging) geometry. Upon letting the deposition parameter depend on the depth, a more convex bed profile for all geometries considered is found. Including frictional effects in the momentum equation has a minor effect when only diffusion is considered, but the bed profile changes significantly when advection is included. When the tidal forcing of the sea surface elevation depends on a M4 tidal constituent as well, the morphodynamic equilibrium bed varies from very deep to shallow, depending on the relative phase. For a diverging inlet geometry, there are combinations of the relative phase and tidal basin length for which we show the existence of multiple equilibria. This implies that for these geometries, the cross-sectionally averaged bed profile in morphodynamic equilibrium can change significantly when the relative phase or the embayment length is changed. The magnitude of the perturbation necessary to actually evolve towards the other equilibrium and the time scale associated with this change can not be inferred from the analysis presented in this paper.
Highlights
IntroductionAlready quite some research has been conducted on this topic
A barrier coast consists of several barrier islands with a tidal inlet between these islands connecting one or more backThis article is part of the Topical Collection on the 18th conference on Physics of Estuaries and Coastal Seas (PECS), Scheveningen, Netherlands, 9-14 October 2016Responsible Editor: Mick van der WegenAlready quite some research has been conducted on this topic
Even though we observe that the maximum length of the embayment is highly influenced by parameters, we find that the morphodynamic bed equilibria and the balance of their corresponding sediment transport are quite similar when considering the same relative phase
Summary
Already quite some research has been conducted on this topic Both the water motion and the morphodynamic evolution in shallow tidal inlet systems have been studied extensively. The linear dynamics of the tidal motion was first studied by Green (1837) It was shown in Parker (1991) and Zimmerman (1981) that nonlinear interactions result in the generation of overtides and residual currents. The influence of sediment supply on morphodynamic bed equilibria was studied by Van der Wegen et al (2017), Maan et al (2015) and Robert et al (2000), the influence of frictional effects by Lanzoni and Seminara (1998, 2002), and Schuttelaars and de Swart (2000), the influence of including mud in the sediment transport by Van Ledden et al (2004) and the influence of geometry by Lanzoni and Seminara (1998, 2002) and Van Leeuwen et al (2000)
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