Wave-induced Roll Motion beneath an Ice Cover

Abstract

A pair of gravity waves propagating at oblique angles along the sea-ice interface in a viscous, rotating ocean is studied theoretically. The motion is described by a Lagrangian formulation. Two theoretical models of the ice cover are considered. Consequences on wave attenuation from these descriptions of the ice are discussed, and the results are compared with field data from the Bering Sea. By use of a series expansion in wave steepness, the nonlinear wave-induced motion is calculated. The mean motion is computed analytically in the case of a nonrotating ocean and numerically in the more general case of a rotating ocean. The induced current is shown to have an exceptional feature; its existence depends on the presence of friction, whereas its magnitude in all directions is independent of the value of the viscosity coefficient. In particular, the computed vertical current is found to be an order of magnitude larger than that obtained for a free surface. Finally, we discuss the importance of wave-induced currents on the vertical transport of nutrients near the ice edge.