AN ANALYTICAL THEORY OF DISTRIBUTED AXISYMMETRICAL BAROTROPIC VORTICES ON THE BETA-PLANE

An analytical theory of barotropic beta-plane vortices is presented in the form of an asymptotic series based on the inverse of vortex nonli nearity. In particular, a solution of the initial value problem is giv en, in which the vortex is idealized as a radially symmetric function of arbitrary structure. Motion of the vortex is initiated by its inter action with the so-called 'beta-gyres' which, in turn, are generated b y the vortex circulation. Comparisons of analytical and numerical pred ictions 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 comp uted. This theory differs from previous calculations by considering mo re general initial vortex profiles and by obtaining a more complete so lution for the perturbation fields. Vortex trajectory predictions accr ue error systematically by integrating vortex propagation rates which are too strong. This appears to be connected to higher-order planetary wave radiation effects.