Potential Vorticity Inversion for Tropical Cyclones Using the Asymmetric Balance Theory

Abstract

Abstract A three-dimensional model is developed, based upon the recently derived asymmetric balance (AB) formulation of Shapiro and Montgomery, to study the evolution of rapidly rotating vortices, including hurricanes. A particular advantage of the AB theory, unlike other balanced models, is its ability to incorporate divergence of the same order as the vorticity. The main assumption of the AB theory is that the squared local Rossby number ≪1, where the squared local Rossby number is defined by the ratio of the orbital frequency squared to the inertial stability. The AB theory leads to a set of prognostic equations that are manipulated so that the first- and second-order local time tendencies can be evaluated diagnostically at a given time. Using the diagnostic version of the AB equations the potential vorticity (PV) distribution from a primitive equation (PE) model is inverted to obtain the corresponding balanced height and wind fields. As far as the authors are aware, this is the first time that the AB ...