Gm. Reznik et Wk. Dewar, AN ANALYTICAL THEORY OF DISTRIBUTED AXISYMMETRICAL BAROTROPIC VORTICES ON THE BETA-PLANE, Journal of Fluid Mechanics, 269, 1994, pp. 301-321
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.