a1 Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90095-1567, USA
a2 Department of Mathematics and Department of Physics, University of Arizona, Tucson, AZ 85721, USA
Up-current-rotated, shoreface-connected ridges are found in various coastal areas around the world. An often-quoted conjecture is that these ridges form during storm conditions through free instabilities in the erodible bed. Under these conditions both waves and currents are expected to play a significant role in the hydrodynamics. Although some existing models have included the effects of waves parametrically in their bottom friction terms and sediment equations, the dynamical effects of wave–current interaction have not been explored. In this paper we begin to rectify this by considering the effects of wave–current interaction on the bed-form instabilities of a simple model. This raises the possibility of unsteady alongshore flows and questions about the roles of wave parameters and boundary conditions, which we address here. We show that the flow is stable under the wave forcing; however the waves do affect the bed-form instability. The main dynamical effect of the waves is in altering the shapes of the unstable modes. Under various conditions, however, waves may enhance or suppress the instability or introduce new unstable modes. They also affect the celerity of the ridges. In addition, we investigate the mechanisms whereby the waves affect the instability. We also show a potential problem with the parameterization in terms of wave orbital velocity.
(Received January 18 2005)
(Revised December 05 2006)
p1 Present address: NIWA, PO Box 8602 Christchurch, New Zealand.