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. The long-term evolution of shoreface-connected sand ridges is investigated with a nonlinear spectral model which governs the dynamics of waves, currents, sediment transport and the bed level on the inner shelf. Wave variables are calculated with a shoaling-refraction model instead of using a parameterisation. The spectral model describes the time evolution of amplitudes of known eigenmodes of the linearised system. Bottom pattern formation occurs if the transverse bottom slope of the inner shelf, β, exceeds a critical value βc. For fixed model parameters the sensitivity of the properties of modelled sand ridges to changes in the number (N−1) of resolved subharmonics (of the initially fastest growing mode) is investigated. For any N the model shows the growth and subsequent saturation of the height of the sand ridges. The saturation time scale is several thousands of years, which suggests that observed sand ridges have not reached their saturated stage yet. The migration speed of the ridges and the average longshore spacing between successive crests in the saturated state differ from those in the initial state. Analysis of the potential energy balance of the ridges reveals that bed slope-induced sediment transport is crucial for the saturation process. In the transient stage the shoreface-connected ridges occur in patches. The overall characteristics of the bedforms (saturation time, final maximum height, average longshore spacing, migration speed) hardly vary with N. However, individual time series of modal amplitudes and bottom patterns strongly depend on N, thereby implying that the detailed evolution of sand ridges can only be predicted over a limited time interval. Additional experiments show that the critical bed slope βc increases with larger offshore angles of wave incidence, larger offshore wave heights and longer wave periods, and that the corresponding maximum height of the ridges decreases whilst the saturation time increases.

Patch behaviour and predictability properties of modelled finite-amplitude sand ridges on the inner shelf