Nonhydrostatic, Three-Dimensional Perturbations to Balanced, Hurricane-like Vortices. Part I: Linearized Formulation, Stability, and Evolution

Abstract

Abstract In this paper, the first of two parts, the dynamics of linearized perturbations to hurricane-like vortices are studied. Unlike previous studies, which are essentially two-dimensional or assume that the perturbations are quasi-balanced, the perturbations are fully three-dimensional and nonhydrostatic. The vortices used as basic states are also three-dimensional (though axisymmetric), with wind fields modeled closely after observations of hurricanes and tropical storms, and are initially in hydrostatic and gradient wind balance. The equations of motion, computational methods for solving them, and methods for generating the basic-state hurricane-like vortices are presented. In particular, three basic states are studied: a vortex modeled after an intense (category 3) hurricane, a moderate (category 1) hurricane, and a weak tropical storm. The stability of each vortex is considered. The category 3 vortex is found to be rather unstable, with its fastest growing mode occurring for azimuthal wavenumber t...