Gravity Waves Generated by Sheared Potential Vorticity Anomalies
Journal of the Atmospheric Sciences
The gravity waves generated by potential-vorticity anomalies in a rotating stratified shear flow are examined under the assumptions of constant vertical shear, twodimensionality and unbounded domain. Near a potential-vorticity anomaly, the associated perturbation is well modelled by quasi-geostrophic theory. This is not the case at large vertical distances, however, and in particular beyond the two inertial layers that appear above and below the anomaly; there, the perturbation is made of
... on is made of vertically propagating gravity waves. This structure is described analytically, using an expansion in the continuous spectrum of the singular modes that results from the presence of critical levels. Several explicit results are obtained. These include the form of the Eliassen-Palm flux as a function of the Richardson number N 2 /Λ 2 , where N is the Brunt-Väisälä frequency and Λ the vertical shear. Its non-dimensional value is shown to be approximately exp(−πN/Λ)/8 in the far-field, gravity-wave region, and approximately twice that between the two inertial layers. These results, which imply substantial wave-flow interactions in the inertial layers, are valid for Richardson numbers larger than 1, and for a large range of potential-vorticity distributions; In dimensional form they provide simple relationships between the Eliassen-Palm fluxes and the large-scale flow characteristics. As an illustration, we consider a potential-vorticity disturbance with an amplitude of 1 PVU and a depth of 1 km, and estimate that the associated Eliassen-Palm flux ranges between 0.1 mPa and 100 mPa for a Richardson number between 1 and 10. These values of the flux compare with those observed in the lower stratosphere, which suggests that the mechanism identified in this paper provides a substantial gravity-wave source, one that could be parameterized in GCMs.