Vertical Transport of Momentum by Internal Waves in a Shear Current

Abstract

Free internal waves are considered in the Boussinesq approximation with account for the rotation of the Earth and a plane–parallel current normal to the direction of wave propagation. A boundary-value problem for the amplitude of vertical velocity is solved analytically for homogeneous stratification at a constant velocity shear; the dispersion relation is found. Vertical wave fluxes of momentum and two components of the Stokes drift velocity are determined. The Stokes drift velocity transversal to the direction of wave propagation is nonzero in the presence of a shear current. Similar calculations are performed also for a two-layer model. The vertical wave flux of momentum can exceed the corresponding turbulent flux.