Existence and Stability of Morphodynamic Equilibria in Double Inlet Systems

Abstract

<p>Tidal inlet systems, ubiquitous along sandy coasts, are very valuable areas in terms of ecology<br>(breeding and feeding areas), economy (gas–mining and dredging) and recreation, and important<br>for coastal safety. To properly manage these systems, good insight into their morphodynamic<br>behaviour is essential.<br>In this presentation, we focus on morphodynamic equilibria of so-called double inlet systems,<br>i.e., systems in which the tidal basin is connected to the open sea by two tidal inlets. In our model,<br>the water motion is described by the cross-sectionally averaged shallow water equations, and forced<br>by prescribed tidal elevations at both seaward sides. The sediment transport is modeled by an<br>advection–diffusion equation with source and sink terms, while the bed evolution is governed by the<br>convergences and divergences of sediment transports. The sediment transport consists of various<br>contributions, a diffusive contribution, a transport term related to the variations in topography<br>and an advective contribution (ter Brake and Schuttelaars, 2010).<br>To directly identify morphodynamic equilibria, we employ continuation methods and bifurcation<br>techniques. By systematically varing the amplitude φ<sub>M2</sub> at one of the inlets, while keeping all other<br>parameters fixed, a region in the φ<sub>M2</sub> parameter space is found where the bed level reaches the<br>water surface, resulting in two single inlet systems. Outside this region, morphodynamic equilibria<br>exist. These equilibria are characterized by their minimum water depth and location. There are<br>branches of stable equilibria, while there are also branches of unstable equilibria, coinciding with<br>the stable equilibria at so-called limit points. Varying both the amplitude and phase of the M2 tide<br>at one of the inlets while keeping the other parameters fixed, results in limit points in A<sub>M2</sub> − φ<sub>M2</sub><br>space that form an ellipse.<br>In our presentation, we will systematically discuss the number and stability of morphodynamic<br>equilibria and compare our results to observations in the Marsdiep-Vlie system, a double inlet<br>system in the Nothern Dutch Wadden Sea.<br>References<br>ter Brake, M. C. and Schuttelaars, H. M. (2010). Modeling equilibrium bed profiles of short tidal embayment. on<br>the effect of the vertical distribution of suspended sediment and the influence of the boundary conditions. Ocean<br>Dynamics, 60:183–204.</p>