Time evolution of the intensity and size of tropical cyclones

The purpose of this paper is to analyze the life cycle of tropical cyclones in terms of a K-Vmax diagram. Such a diagram summarizes the time evolution of the integrated kinetic energy K and the maximum tangential wind Vmax, which respectively measure vortex size and intensity. A typical life cycle consists of an incipient stage in which K and Vmax slowly increase until Vmax≈25 m s⁻¹, a deepening stage in which K and Vmax increase more rapidly until Vmax≈60 m s⁻¹, and finally a mature stage in which K continues to grow at approximately the same rate while Vmax remains fixed or even decreases. This typical life cycle can be diagnostically analyzed using a theoretical argument that is based on the balanced vortex model and, in particular, on the associated geopotential tendency equation. This is a second order partial differential equation containing the diabatic forcing and, under idealized conditions, two spatially varying coefficients: the static stability and the inertial stability, whose ratio determines the local Rossby length ℓ. Thus, the balanced azimuthal wind and temperature tendencies in a tropical vortex depend not only on the diabatic forcing, but also on the spatial distribution of ℓ. Under the simplifying assumption that the diabatic heating and the associated response are confined to the first internal vertical mode, the geopotential tendency equation reduces to a radial structure equation, which can be solved numerically. These solutions illustrate how the vortex response to diabatic heating depends on whether this heating lies in the large Rossby length region outside the radius of maximum wind or in the small Rossby length region inside the radius of maximum wind. Tangential wind tendencies are found to be hypersensitive to the location of the diabatic heating relative to the small Rossby length region in the vortex core.