An extended analytic theory of tropical‐cyclone motion in a barotropic shear flow

An earlier analytic theory for the motion of a barotoropic vortex in a zonally varying basic shear flow on a beta‐plane is consolidated and extended. It is shown that the theory can be derived from a power‐series expansion of variables representing the vortex asymmetry in terms of a single nondimensional parameter ϵ = BL 2 / U , where B is the Meridional gradient of basis state absolute vorticity and L and U are the lenght and velocity scales, respectively, for the outer part of the vortex. The derivation requires inter alia that ϵ ≪ 1 and that the magnitude of the basis flow scales with ϵ. Insight is provided into the dynamics of vortex motion when the latter condition is not fulfilled, as in cases of moderate and large shear. For vortices that decay appreciably more rapidly with radius than those studies in the earlier work it is necessary to include additional terms when calculating the asymmetric vorticity to obtain an accurate prediction of the vortex track. Analytic expressions have been obtained for these terms that lead to a theory that is valid for a broad range of vortex profiles. Comparisons are made between the present theory and two recent analyses for the case of zero basis flow, contrasting the important differences in approach. The present theory gives results that are very close to one of these, a semi‐spectral numerical Method. The paper concludes with a brief discussion of aspects of vortex stability.