Stable and unstable near-resonant states in multilevel, severely truncated, quasi-geostrophic models
Multilevel, severely truncated, quasi-geostrophic models with damping that extend from the surface to 100 km, are used to study the stationary-wave response to orography and the concomitant feedbacks on the zonal flow. For a typical winter zonal-wind profile, it is shown that large amplitude or resonant planetary waves of intermediate zonal wavenumbers of about 4 or 5 occur with an equivalent barotropic structure. It is also shown that wave-zonal flow interaction with a mountain torque and temperature transport is stable to small perturbations on the low side of resonance and unstable on the high side of resonance. Resonant zonal wavenumbers of lower wave wavenumber also occur for the same zonal profile and have a node in the vertical with a small amplitude maximum near the surface and a larger amplitude maximum in the stratosphere. Instability depends on the presence of the orography and the basic asymmetric state as Newtonian damping and surface friction are sufficient to damp the baroclinic instability associated with a linear inviscid model.