Barotropic vortex adjustment to asymmetric forcing with application to tropical cyclone motion

Abstract

A nondivergent. barotropic analytical model to predict steady tropical cyclone (TC) propagation relative to the large-scale environment is developed in terms of a "selfadvection" process in which the TC is advected by an azimuthal wavenumber one gyre flow that results from TC-environment interaction. The model is comprehensive in that it includes the first-order effects of all of the dynamical influences that are presently understood to be important to barotropic propagation: gradients of planetary and environmental vorticity, changes in TC wind structure, and environmental windshear. An unforced version of the model is used to show that angular windshear in the symmetric TC circulation acts to damp perturbations from axisymmetry by tilting the perturbations downshear. The resultant transfer of kinetic energy from perturbation to symmetric circulation thus tends to restore axisymmetry. Thus, steady propagation of TC-like barotropic vortices is a manifestation of a stable response to asymmetric forcing. To predict both the asymmetric gyre flow and the propagation it induces, the forced Barotropic Self-Advection Model (BSAM) is closed by seeking a particular pattern in the vorticity tendencies of the TC-cnvironmental interaction flow. For realistic combinations of environmental vorticity gradients and linear windshear, the BSAM predicts propagation speeds and directions that are consistent with TC propagation characteristics obsened in composite data. The capability of the BSAM to account for variable TC structure is used to show that errors in determining TC outer wind strength of ±1 m s can result in an 85 km forecast error at 48 h. Finally, and most importantly, the capability of the BSAM to initialize a barotropic numerical model so that quasi-steady TC propagation occurs almost immediately is demonstrated for several simple dynamical situations.