On the instabilities of tropical cyclones generated by cloud resolving models

An approximate method is developed for finding and analysing the main instability modes of a tropical cyclone whose basic state is obtained from a cloud resolving numerical simulation. The method is based on a linearised model of the perturbation dynamics that distinctly incorporates the overturning secondary circulation of the vortex, spatially inhomogeneous eddy diffusivities, and diabatic forcing associated with disturbances of moist convection. Although a general formula is provided for the latter, only parameterisations of diabatic forcing proportional to the local vertical velocity perturbation and modulated by local cloudiness of the basic state are implemented herein. The instability analysis is primarily illustrated for a mature tropical cyclone representative of a category 4 hurricane. For eddy diffusivities consistent with the fairly conventional configuration of the simulation that generates the basic state, perturbation growth is dominated by a low azimuthal wavenumber instability having greatest asymmetric kinetic energy density in the lower tropospheric region of the inner core of the vortex. The characteristics of the instability mode are inadequately explained by nondivergent 2D dynamics. Moreover, the growth rate and modal structure are sensitive to reasonable variations of the diabatic forcing. A second instability analysis is conducted for a mature tropical cyclone generated under conditions of much weaker horizontal diffusion. In this case, the linear model predicts a relatively fast high-wavenumber instability that is insensitive to the parameterisation of diabatic forcing. The prediction is in very good quantitative agreement with a previously published analysis of how the instability develops in a cloud resolving model on the way to creating mesovortices slightly inward of the central part of the eyewall.