Dynamical system analysis of a low-order tropical cyclone model

Tropical cyclone dynamics is investigated by means of a conceptual box model. The tropical cyclone (TC) is divided into three regions, the eye, eyewall and ambient region. The model forms a low-order dynamical system of three ordinary differential equations. These are based on entropy budget equations comprising processes of surface enthalpy transfer, entropy advection, convection and radiative cooling. For tropical ocean parameter settings, the system possesses four non-trivial steady state solutions when the sea surface temperature (SST) is above a critical value. Two steady states are unstable while the two remaining states are stable. Bifurcation diagrams provide an explanation why only finite-amplitude perturbations above a critical SST can transform into TCs. Besides SST, relative humidity of the ambient region forms an important model parameter. The surfaces that describe equilibria as a function of SST and relative humidity reveal a cusp-catastrophe where the two non-trivial equilibria split into four. Within the model regime of four equilibria, cyclogenesis becomes very unlikely due to the repelling and attracting effects of the two additional equilibria. The results are in qualitative agreement with observations and evince the relevance of the simple model approach to the dynamics of TC formation and its maximum potential intensity.