The effect of rotation is particularly interesting. In mid-latitudes, the diurnal frequency sigma is less than the Coriolis parameter (f), so gravity wave propagation is prevented. A mean wind Doppler shifts the frequency in principle, but in practice, little gravity wave energy is found either upwind or downwind of the source.
A more profound impact of rotation is that it allows convective heating to generate Potential Vorticity (PV). Daily pulses of PV will drift downwind of the source region, but can they generate vertical motion to trigger convection? Here the wind shear plays a critical role. According to the principle of Galilean Invariance, a PV pulse drifting in a constant wind, just like a stationary one, will produce no vertical motion. In contrast, in a sheared mean wind, the vertical motions will accompany the PV pulse.
While the combined role of PV and background shear are already well known in the Q-G limit (e.g. the omega-equation and Q-vectors) we take a linearized gravity wave approach. Within a linear framework, we examine the gravity waves generated by the drifting PV pulse, and their possible role in triggering convection.