Nonhydrostatic, Three-Dimensional Perturbations to Balanced, Hurricane-Like Vortices. Part II: Symmetric Response and Nonlinear Simulations

Abstract

This paper is the second part of a study on the dynamics of nonhydrostatic perturbations to dry, balanced, atmospheric vortices modeled after tropical cyclones. In , the stability and evolution of asymmetric perturbations were presented. This part is devoted to the stability and evolution of symmetric perturbations—particularly those that are induced by the wave–mean flow interactions of asymmetric perturbations with the symmetric basic-state vortex. The linear model shows that the vortices considered in are stable to symmetric perturbations. Furthermore, the model can be used to derive the steady, symmetric response to stationary symmetric forcing, similar to the results from quasi-balanced dynamics as originally presented by Eliassen. The secondary circulations that develop act to oppose the effects of the forcing, but also to warm the core and intensify the vortex. The model is also used to simulate the response to impulsive symmetric forcings, that is, symmetric perturbations. Much like the asymmetries considered in , symmetric perturbations go through two kinds of adjustment: a fast adjustment that generates gravity waves, and then a slow adjustment leading to a final state that represents a net change in both the wind and mass fields of the symmetric vortex. The nonhydrostatic, unsteady, symmetric response of the tropical-storm-like vortex to the evolving asymmetries from is presented. In contrast with results from previous studies with initially two-dimensional or balanced asymmetric vorticity perturbations, asymmetric temperature perturbations are found to have a negative effect on overall intensity. These changes are about two orders of magnitude smaller than those caused by symmetric perturbations of equal amplitude. The asymmetric/symmetric adjustment process for purely asymmetric temperature perturbations are also simulated with a fully nonlinear, compressible model. Excellent agreement is found between the linear, nonhydrostatic and the nonlinear, compressible models. The vortex intensification caused by a localized, impulsive thermal perturbation can be accurately estimated from the projection of this perturbation onto the purely symmetric motions.