Existence and Stability of Morphodynamic Equilibria in Double Inlet Systems

Tidal inlet systems, ubiquitous along sandy coasts, are very valuable areas in terms of ecology
(breeding and feeding areas), economy (gas–mining and dredging) and recreation, and important
for coastal safety. To properly manage these systems, good insight into their morphodynamic
behaviour is essential.
In this presentation, we focus on morphodynamic equilibria of so-called double inlet systems,
i.e., systems in which the tidal basin is connected to the open sea by two tidal inlets. In our model,
the water motion is described by the cross-sectionally averaged shallow water equations, and forced
by prescribed tidal elevations at both seaward sides. The sediment transport is modeled by an
advection–diffusion equation with source and sink terms, while the bed evolution is governed by the
convergences and divergences of sediment transports. The sediment transport consists of various
contributions, a diffusive contribution, a transport term related to the variations in topography
and an advective contribution (ter Brake and Schuttelaars, 2010).
To directly identify morphodynamic equilibria, we employ continuation methods and bifurcation
techniques. By systematically varing the amplitude φ_M2 at one of the inlets, while keeping all other
parameters fixed, a region in the φ_M2 parameter space is found where the bed level reaches the
water surface, resulting in two single inlet systems. Outside this region, morphodynamic equilibria
exist. These equilibria are characterized by their minimum water depth and location. There are
branches of stable equilibria, while there are also branches of unstable equilibria, coinciding with
the stable equilibria at so-called limit points. Varying both the amplitude and phase of the M2 tide
at one of the inlets while keeping the other parameters fixed, results in limit points in A_M2 − φ_M2
space that form an ellipse.
In our presentation, we will systematically discuss the number and stability of morphodynamic
equilibria and compare our results to observations in the Marsdiep-Vlie system, a double inlet
system in the Nothern Dutch Wadden Sea.
References
ter Brake, M. C. and Schuttelaars, H. M. (2010). Modeling equilibrium bed profiles of short tidal embayment. on
the effect of the vertical distribution of suspended sediment and the influence of the boundary conditions. Ocean
Dynamics, 60:183–204.