Gravity Waves Produced by Potential Vorticity Anomalies

The gravity waves (GWs) produced by potential vorticity (PV) anomalies in a vertical wind shear are evaluated for an unbounded rotating stratified flow. In this set-up, the disturbances have two inertial layers, one on each side of the PV anomaly that produces them. Between these layers the disturbance is well predicted by the quasi-geostrophic theory, beyond these layers it corresponds to propagating GWs.

This GW signal is predicted analytically using a Green's function method. The Green's functions used belong to the continuum of solutions of the non-geostrophic Eady problem of baroclinic instability. We find that the non-dimensional EP-flux of the GWs in the far field is approximately exp(-pi N/Uz)/8, where N is the Brunt-Vaisala frequency and Uz the wind shear. Between the two inertial layers the EP-flux is twice that outside of them,which means that substantial wave-flow interactions occur in the inertial layers. This formula is found to be useful for a large range of PV distribution, is easy to translate in dimensional form and from the large scale flow characteristics.

The case of a PV disturbance with amplitude 1PVU and depth 1km is then analysed. When this disturbance enters in the troposphere, the EP-fluxes are between 0.1mPa and 100mPa when the Richardson number J=N/Uz is between 1 and 10. These values compare with those observed in the low stratosphere, which suggests that we have identified a substantial GW source, and that this source can be parameterized in GCMs.