Damping of surface waves by a floating viscoplastic plate

Abstract

A theoretical model is presented to explore how surface waves in an inviscid fluid layer are damped by the bending stresses induced in a overlying floating film of yield-stress fluid. The model applies in the long-wavelength limit, combining the shallow-water equations for the inviscid fluid with a theory for the bending of a thin viscoplastic plate described by the Herschel-Bulkley constitutive law. An exploration of the energetics captured by the model suggests that waves decay to rest in finite time, a result that is confirmed using a combination of approximate, numerical and asymptotic solutions to the model equations. In the limit that the plate behaves like a perfectly plastic material, the sloshing motions take the form of triangular waves with bending restricted to narrow viscoplastic hinges.