Vertical Mass Transport by Weakly Nonlinear Inertia-Gravity Internal Waves

Abstract

In the Boussinesq approximation, free inertia-gravity internal waves are considered in a two-dimensional vertically non-uniform flow. In the linear approximation was find vertical distribution of the amplitude of the vertical velocity and the dispersion relation. The boundary-value problem for internal waves has complex coefficients when the flow velocity component, transverse to the wave propagation direction depends on the vertical coordinate. Therefore, the eigenfunction and frequency of the wave are complex (it is shown that there is a weak damping of the wave). Vertical wave mass fluxes are nonzero. The vertical component of the Stokes drift velocity also differs from zero and contributes to the wave transport. A non-oscillating on a time scale of the wave correction to the average density, which is interpreted as an irreversible vertical fine structure generated by a wave, is determined on the second order of amplitude.