Baroclinic, Alfvén and Rossby waves in geostrophic flow

We find a necessary condition for instability that proves the existence of a short wave cutoff of unstable baroclinic waves for finite magnetic field. We also place bounds on the phase velocities of neutral waves in the system.

For zero basic baroclinic and a uniform magnetic field, the neutral oscillations are zonally propagating geostrophic Alfvén waves. The lowest mode is purely horizontal and travels at the ordinary Alfvén speed, but all higher modes, which contain vertical as well as horizontal motion, move more slowly. With β ≠0, we get, in general, combined Alfvén-Rossby waves, which, in the limit of large rotation, yield a class of waves very similar to those found by Hide.