Linear and Nonlinear Vortex Motion in an Asymmetric Balance Shallow Water Model

Abstract

Abstract This work extends asymmetric balance (AB) theory to the beta plane (β-AB). The physical problem examined is the motion of a coherent vortex on a beta plane in a finite depth fluid in the absence of an environmental steering flow. A useful attribute of the β-AB formulation is that it allows one to separate the linear and nonlinear balance contributions to the vortex motion when the standard Rossby number is not small compared to unity. It is therefore well suited for testing the hurricane-motion paradigm proposed by Willoughby for equivalent barotropic dynamics. The β-AB model is formulated first for linear shallow water dynamics on a circular vortex forced by the meridional gradient of planetary vorticity (the beta effect) in an earth-based coordinate system. The linear dynamics precludes wave–wave and wave–mean flow interactions. From incipient vortices to hurricanes, the β-AB model correctly develops the wavenumber-one asymmetries (the “beta” gyres) necessary for vortex self-advection. Cyclonic...