Long waves over a bi-viscous seabed: transverse patterns

The coupled interaction of long standing hydrodynamic waves with a deformable non-Newtonian seabed is examined using a two-layer model for which the upper layer fluid is inviscid and the lower layer is bi-viscous. The two-dimensional response of the system to forcing by a predominantly longitudinal (cross-shore) standing wave perturbed by a small transverse (along-shore) component is determined. With a constant yield stress in the bi-viscous lower layer, there is little amplification of these transverse perturbations and the model response typically remains quasione-dimensional. However, for a bi-viscous layer with a pressure-dependent yield stress (which represents the effect that the seabed deforms less readily under compression and hence renders the rheology history dependent), the initially small transverse motions are amplified in some parameter regimes and two-dimensional, permanent bedforms are formed in the lower layer. This simple dynamical model is, therefore, able to explain the formation of permanent bedforms with significant crossand along-shore features by predominantly crossshore standing wave forcing.