A Simple Derivation of Tropical Cyclone Ventilation Theory and Its Application to Capped Surface Entropy Fluxes

In a recent study, a theory was presented for the dependence of tropical cyclone intensity on the ventilation of dry air by environmental vertical wind shear. This theory was found to successfully capture the statistics of intensity dynamics in the historical record. This theory is rederived here from a simple three-term power budget and extended to analytical solutions for the complete phase space, including the change in storm intensity itself. The derivation is then generalized to the case of a capped surface entropy flux wind speed, including analytical solutions defined relative to both the traditional potential intensity and the capped-flux potential intensity. The results demonstrate that a cap on the surface entropy flux wind speed reduces the potential intensity of the system and effectively amplifies the detrimental effect of ventilation on the tropical cyclone heat engine. However, such a cap does not alter the qualitative structure of the phase-space solution for intensity change phrased relative to the capped-flux potential intensity. Thus, the wind speed dependence of surface entropy fluxes is important for intensity change in real-world storms, though it is not a necessary condition for intensification in general. Indeed, a residual power surplus may remain available to intensify a storm even in the presence of a cap, though intensification may be fully suppressed for sufficiently strong ventilation. This work complements a recent numerical simulation study and provides further evidence that there is no disconnect between extant tropical cyclone theory and the finding in numerical simulations that a storm may intensify in the presence of capped surface entropy fluxes.