An analytical theory of distributed axisymmetric barotropic vortices on the β-plane

Abstract

An analytical theory of barotropic β-plane vortices is presented in the form of an asymptotic series based on the inverse of vortex nonlinearity. In particular, a solution of the initial value problem is given, in which the vortex is idealized as a radially symmetric function of arbitrary structure. Motion of the vortex is initiated by its interaction with the so-called ‘β-gyres’ which, in turn, are generated by the vortex circulation. Comparisons of analytical and numerical predictions for vortex motion are presented and demonstrate the utility of the present theory for times comparable to the ‘wave’ timescale. The latter exceeds the temporal limit derived from formal considerations. The properties of the far-field planetary wave radiation are also computed.This theory differs from previous calculations by considering more general initial vortex profiles and by obtaining a more complete solution for the perturbation fields. Vortex trajectory predictions accrue error systematically by integrating vortex propagation rates which are too strong. This appears to be connected to higher-order planetary wave radiation effects.