On the unstable mode merging of gravity-inertial waves with Rossby waves

We recapitulate the results of the combined theory of gravity-inertial-Rossby waves in a rotating, stratified atmosphere. The system is shown to exhibit a "local" (JWKB) instability whenever the phase speed of the low-frequency-long wavelength westward propagating Rossby wave exceeds the phase speed ("Kelvin" speed) of the high frequency-short wavelength gravity-inertial wave. This condition ensures that mode merging, leading to instability, takes place in some intermediate band of frequencies and wave numbers. The contention that such an instability is "spurious" is not convincing. The energy source of the instability resides in the background enthalpy which can be released by the action of the gravitational buoyancy force, through the combined wave modes.