Time evolution of the intensity and size of tropical cyclones

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.