  The atmosphere is a nonlinear stratified fluid in which internal gravity
waves are present. These waves interact with the flow, resulting in wave
turbulence that displays important differences with the turbulence observed in
isotropic and homogeneous flows. We study numerically the role of these waves
and their interaction with the large scale flow, consisting of vertically
sheared horizontal winds. We calculate their space and time resolved energy
spectrum (a four-dimensional spectrum), and show that most of the energy is
concentrated along a dispersion relation that is Doppler shifted by the
horizontal winds. We also observe that when uniform winds are let to develop in
each horizontal layer of the flow, waves whose phase velocity is equal to the
horizontal wind speed have negligible energy. This indicates a nonlocal
transfer of their energy to the mean flow. Both phenomena, the Doppler shift
and the absorption of waves traveling with the wind speed, are not accounted
for in current theories of stratified wave turbulence.
