Impact of vortex structure on tropical cyclone response to diabatic heating

The purpose of this project is to see what conclusions can be drawn about the relationships between the vortex structure, the diabatic heating, and the temperature and azimuthal wind tendencies in idealized tropical cyclones. The theoretical argument is based on the balanced vortex model, in particular on the associated geopotential tendency equation. This is a second-order partial differential equation containing the diabatic forcing and three spatially varying coefficients: the static stability, the baroclinicity, and the inertial stability. Under the simplifying assumptions that baroclinic effects can be neglected and that diabatic heating and the associated response is confined to the first internal mode, the geopotential tendency equation reduces to a radial structure equation. This is a second-order ordinary differential equation that can be solved numerically for various vortex profiles. These solutions illustrate how the vortex response to diabatic heating depends on whether this heating lies in the low inertial stability region outside the radius of maximum wind or in the high inertial stability region inside the radius of maximum wind, and how that response is modified by vorticity skirts and vortex hollowness.