J. G. Esler (gavin@math.ucl.ac.uk) Department of Mathematics, University College London. L. M. Polvani Department of Applied Physics and Applied Mathematics, Columbia University.
Layers of anomalous potential vorticity (PV), are known to arise as a consequence of irreversible Rossby wave breaking, for instance near the tropopause or at the edge of the stratospheric polar vortex. Dynamical instabilities of these PV layers may be important both in setting mixing timescales for the layers themselves and, potentially, as a mechanism for generating unbalanced motions from initially balanced flow. To address this problem, we study the dynamics of layers of constant Ertel's PV in a nonhydrostatic, Boussinesq model both analytically and numerically. Considering an infinite layer, with anomalous PV dQ and oriented arbitrarily in space, the problem is simplified to two dimensions by defining rotated coordinates Z perpendicular to the layer and X and Y along the layer, parallel to and perpendicular to the slope respectively. The evolution in Y and Z alone is then considered. We find that for dQ > 8, in nondimensional units, the balanced state associated with the layer becomes Kelvin- Helmholtz unstable for certain angles of orientation. Furthermore, we show that a weak shear flow can act to tilt a PV layer from a stable to an unstable configuration. In this flow, geostrophic and hydrostatic balance are maintained up to the time of onset of the instability. This may provide a mechanism for the spontaneous emission of gravity waves from a (slightly perturbed) initially balanced state, as well as for the rapid mixing of the layer and its chemical contents. Unlike the barotropic-baroclinic instability that is also exhibited by these layers, the Kelvin-Helmholtz instability takes place on too rapid a timescale to be easily suppressed by external strain imposed on the layer.