Stratospheric vacillations in a minimal contour dynamics model

Abstract

AbstractA low-dimensional dynamical system that describes dynamical variability of the stratospheric polar vortex is presented. The derivation is based on a linearized, contour-dynamics representation of quasigeostrophic shallow water flow on a polar f-plane. The model consists of a single linear wave mode propagating on a near-circular patch of constant potential vorticity (PV). The PV jump at the vortex edge serves as an additional degree of freedom. The wave is forced by surface topography, and interacts with the vortex through a simplified parameterization of diabatic wave/mean flow interaction. The approach can be generalized to other geometries.The resulting three-component system depends on four non-dimensional parameters, and the structure of the steady state solutions can be determined analytically in some detail. Despite its extreme simplification, the model exhibits variability that is closely analogous to the Holton-Mass model, a well-known and more complex dynamical model of stratospheric variability. The present model exhibits two stable steady solutions, one consisting of a strong vortex with a small amplitude wave and the second consisting of a weak vortex with a large amplitude wave. Periodic and aperiodic limit cycles are also identified, analogous to similar solutions in the Holton-Mass model. Model trajectories also exhibit a number of behaviors that have been identified in observations. A key insight is that the time-mean state of the vortex is predominantly controlled by the properties of the linear mode, while the strength of the topographic forcing plays a far weaker role away from bifurcations.