Frictionally Controlled, Thermally Driven Circulations in a Circular Vortex with Application to Tropical Cyclones

Abstract

Based upon an argument by Charney and Eliassen, a tropical cyclone is envisaged as a combined system of a quasi-gradient circular vortex and a slow meridional circulation. The driving mechanism of this circulation is the release of latent heat, which is in turn controlled by the mass convergence in the surface boundary layer. A consistent set of dynamic equations is derived from scale and energy considerations, followed by the presentation of a two-level approximation in which potential temperature is specified only at the mid-tropospheric level. A perturbation analysis based on the linearized system shows that the exponential growth rates are of the correct order of magnitude. A numerical integration of this set of equations is performed, starting from hypothetical initial distributions of tangential velocities. Unlike the too rapid and too intense development of meridional circulations observed in the numerical integrations of some previous hurricane models, the result obtained here shows a slowly developing circulation; the maximum tangential velocity is increased from 5 m sec⁻¹ (initial value) to 40 m sec⁻¹ in 60 hours and this velocity is twice as large as the maximum inflow. However, the circulation does not seem to approach a steady state. Other shortcomings of the model as revealed by the numerical integration are discussed.