Formation of rhythmic sorted bed forms: an idealised model

An idealised model is presented to study the formation of sorted bed forms generated by a wind-driven along-shore current. The study employs a linear stability analysis to describe the time development of perturbations of both bottom composition and bed elevation, superimposed on a flat bed composed of a sediment mixture homogeneously distributed in space. The model considers both bed and suspended loads and takes into account the averaged influence of waves on the flow field and the transport of sediment. The results show that the positive coupling between waves, along-shore current and the erodible heterogeneous bed leads to the amplification of two modes, which exhibit distinct characteristics. A first mode is found to be dominant when moderate hydrodynamic conditions are considered and is primarily amplified by the convergence of sediment transport induced by the changes in the bed elevation. This mode has wavelengths of the order of hundred metres and has coarse (fine) sediments in its troughs (crests). By increasing the height of the waves and/or the strength of the steady current, the second mode can become dominant. This mode is characterised by shorter wavelengths and results from the interaction between the convergence of sediment transport related to changes in the bottom composition and that induced by perturbations of the bed elevation. These bed features can have an up-current or a down-current shift between the centre of the coarse-grained bands and the trough of the bottom wave. Typical growth times of the amplified features are of the order of hundreds of days and the migration rates, in the direction of the along-shore current, range between 0.1 and 10 m per day. A qualitative comparison of the model results with field observations indicates that the generation of two distinct modes provides a possible explanation for the broad range of characteristics of the natural bed features.