Initial formation of channel–shoal patterns in double–inlet systems

Channel–shoal patterns are often observed in the back–barrier basins of inlet systems and are important from both an economical and ecological point of view. Focussing on double–inlet systems, the initial formation of these patterns is investigated using an idealized model. The model is governed by the depth–averaged shallow water equations, a depth–integrated concentration equation and a tidally–averaged bottom evolution equation. Focussing on rectangular basins and neglecting the effects of earth rotation, it is found that laterally uniform morphodynamic equilibria can become linearly unstable, resulting in initial patterns that resemble channels and shoals. When the water motion is only forced by an M₂ tidal constituent, the existence of (laterally uniform) morphodynamic equilibria for which both inlets are connected strongly depends on the relative phase and amplitudes of the tidal forcing. If such equilibria exist, they can be either stable against small perturbations or linearly unstable. If these equilibria are linearly unstable, two instability mechanisms can be identified, the first related to the convergences and divergences of diffusive transports, the second mechanism related to a combination of advective and diffusive transports. In the former case, all eigenvalues are real and the bedforms grow exponentially in time. In the latter case, the eigenvalues are complex, resulting in bedforms that both migrate and grow in time. In case external overtides and a time–independent discharge are included, no diffusive instabilities are found anymore for the parameters considered in this paper. This implies that all instabilities are migrating in time. In all cases considered, the bed perturbations have only an appreciable amplitude at locations where the underlying laterally uniform equilibrium has a local minimum in water depth. This is consistent with observations from numerical models and laboratory experiments.