The Stability of Inertio-Gravity Waves

 Previous linear stability analyses of inertia-gravity waves approximated the velocity field as steady plane-parallel horizontal flow with different approximations of the spatial structure. We employ a Floquet method that accounts for the wave spatial periodicity, tilt and time dependence, and use a physically relevant ratio of Coriolis to buoyancy frequency of the middle atmosphere. Our results for constant large amplitude waves shows the general trend of how the fastest growing instability changes with frequency.

 Such a scan of stability properties passes through (and below) the vertical overturning threshold as frequency approaches f. We find a dynamic oblique mode that dominates in sub-overturning wave amplitude at frequencies around f/0.7 to f/0.8. This result may help to interpret an instability found in non-linear simulations seen by Lelong and Dunkerton (1997), which does not correspond to any modes found in earlier linear stability studies of inertio-gravity waves. We also find wave-scale dynamic modes, which become nearly isotropic in wavevector orientation as the frequency approaches f. These modes dominate for both sub-overturning and overturning amplitudes at very low frequencies, e.g. when frequency is below f/0.95.