Mean drift velocity in the Stokes interfacial edge wave

Abstract

[1] The Stokes interfacial edge wave in a viscous rotating two-layer system is studied theoretically. The mean wave-induced Lagrangian drift velocity is obtained from the vertically integrated Eulerian equations of momentum and mass, correct to second order in wave steepness. The analysis is valid for shallow-water waves in the case when the upper layer is much thicker than the lower layer. In the lower layer the effect of viscosity is confined to a frictional boundary layer at the bottom. The waves are trapped by the bottom slope and can propagate in either direction along the bottom contours (in the y direction). Assuming that the waves attenuate in space as they propagate, this yields a Stokes drift velocity and a mean energy density E that decay exponentially in y. In this problem −∂E/∂y is the relevant radiation stress forcing in the wave propagation direction. It is explained why this differs from the radiation-stress forcing of −∂E/∂y for plane waves in an unbounded nonrotating shallow ocean. The bottom stress acting on the mean Eulerian wave-induced flow is modeled by a turbulent friction coefficient. The results show that the maximum mean Eulerian drift current is considerably larger than the maximum Stokes drift velocity. Since the Eulerian current becomes negative at larger seaward distances, the total mean Lagrangian drift current is confined to a rather narrow wedge in the lower layer.