**
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.