Mean flows induced by internal gravity wave packets propagating in a shear flow

Abstract

An inviscid, incompressible, stably stratified fluid occupies a horizontal channel, along which an internal gravity wave packet is propagating in the presence of a basic shear flow. By using a generalized Lagrangian mean formulation, the equation for wave action conservation is derived to describe the manner in which the basic flow affects the waves. Equations describing the second-order (in amplitude) wave-induced Lagrangian mean flows are obtained. Two kinds of applications are discussed: (i) steady mean flows, due to waves encountering an inhomogeneity in their environment, such as a varying channel depth; (ii) mean flows induced by modulations in the wave amplitude.