Title:
Long Waves and Flows Induced by Non-Breaking Internal Waves

Abstract:

Theory and simulations of horizontally periodic, vertically localized internal wavepackets have shown that they induce a flow as a direct consequence of the divergence of the momentum flux, being largest where the wavepacket amplitude is largest.  This induced flow is uniform in the horizontal but (unlike the flow resulting from breaking waves) it evolves in time, translating vertically at the group velocity of the waves.  If the waves are of moderately large amplitude, the divergent-flux induced flow can Doppler-shift the waves leading to modulational stability or instability, depending upon the wave frequency.  In particular, hydrostatic anelastic wavepackets can overturn tens of kilometers higher in the atmosphere than predicted by linear theory as a consequence of weakly nonlinear interactions of the waves with the mean flow they induce.  For wavepackets that are localized both horizontally and vertically, the divergent-flux induced flow is itself divergent.  This results in the generation of long internal waves with structure qualitatively similar to the bow-wake behind a ship.  The weakly nonlinear interactions between the wavepacket and the induced long waves likewise result in the modulationally stable or unstable evolution of the wavepacket.  Weakly nonlinear effects in non-uniformly stratified fluid and in shear also result in dynamics that are qualitatively different from the predictions of linear theory.