Application of a Robin boundary condition to surface waves

Abstract

Surface effects on deep-water gravity waves are investigated theoretically by the application of a Robin boundary condition with a complex Robin parameter, R=Rr+iRi. The Robin condition combines the shear stress and the horizontal velocity at the ocean surface. We show that this condition describes wave damping related to surface phenomena like elastic films or thin viscous fluid layers. It may also model wave generation by oscillating surface stresses depending on the signs and magnitudes of Rr and Ri.