Understanding Instabilities of Tropical Cyclones and Their Evolution with a Moist Convective Rotating Shallow-Water Model

Instabilities of hurricane-like vortices are studied with the help of a rotating shallow-water model, including the effects of moist convection. Linear stability analysis demonstrates that dominant unstable modes are mixed Rossby–inertia–gravity waves. It is shown that, depending on fine details of the vorticity profile, a wavenumber selection of the instability may operate or not, leading in some cases to an unstable mode with a distinctively maximal growth rate and in other cases to an ensemble of unstable modes with close growth rates. Numerical simulations are performed in order to investigate nonlinear saturation of the instability and to understand the dynamical role of moisture. In agreement with previous studies, the authors confirm axisymmetrization of vorticity in the course of the development of the instability, which induces changes of intensity of the hurricane. In “dry” simulations, winds are intensified only inside the radius of maximum wind, while the maximum value of the wind decreases. “Moist precipitating” simulations (with and without evaporation) exhibit a net increase of winds, also at the radius of maximum wind, as compared to the dry simulations. Dynamical effects of moisture on the reorganization of the vortex and on the efficiency of inertia–gravity wave emission are quantified and shown to be considerable. Periodic bursts in the emission of waves related to the development of the unstable modes inside the vortex are evidenced, as well as the appearance of convectively coupled waves in the moist precipitating simulations with evaporation.