Pattern formation on the interface of a two-layer fluid: bi-viscous lower layer

A theoretical model of the interaction of standing waves with a deformable sea-bed is derived in the long-wave limit. The coupled response of this two-layer model for which the upper-layer fluid is inviscid and the lower layer bi-viscous is determined for periodic forcing by an external sw-face pressure. It is shown that for permanent features to form in the lower layer, the nonlinear transfer of energy from the directly forced wave to even spatial harmonics of the forcing must occur. Nonlinearity due to a history-dependent bi-viscous rheology is shown to result in the formation of permanent, half-wavelength bedforms with crests located under the antinodes of the overlying wave motion. (C) 2001 Elsevier Science B.V. All rights reserved.