Non-linear modelling of shoreface-connected sand ridges

A nonlinear morphodynamic model, consisting of the 2DH shallow water equations, a local sediment transport parametrization and a bottom evolution equation, is used to investigate the long-term behaviour of finite-amplitude shoreface-connected sand ridges. These bedforms are trapped on the inner shelf, have alongshore spacings of 5-8 km and the crests form an oblique angle with the coast. The model allows for a basic state which describes a steady alongshore uniform flow over the inner shelf. The instability of this flow with respect to bottom perturbations, as triggered by the transverse shelf slope, causes the formation of ridges of which the initial behaviour is described by linearized equations.

The nonlinear behaviour is computed by expanding the flow and bottom in eiegenfunctions of the linear problem and appears to be controled by the bedslope coefficient gamma in the sediment transport. For large gamma only one mode initially has a positive growth rate and solutions tend to finite-amplitude ridges, with an amplitude proportional to (gamma(-1) - gamma(c)(-1))(1/2). For smaller gamma more modes initially grow and the dynamics is no longer dominated by the linearly most preferred mode. As a result multiple attractors are found and even aperiodic behaviour is observed. Typical amplitudes and corresponding bottom and how patterns correspond quite well with observations.