A critical analysis of the assumptions underlying the formulation of maximum potential intensity for tropical cyclones

TL;DR

This paper critically examines the assumptions behind Emanuel's maximum potential intensity theory for tropical cyclones, revealing inconsistencies in the thermal wind balance and entropy gradients at the storm's maximum wind point.

Contribution

The study revisits the derivation of E-PI, showing that key assumptions about entropy and angular momentum gradients at maximum wind are incompatible with the equations of motion.

Findings

E-PI's key equation requires temperature increase towards storm center at maximum wind

Thermal wind equation indicates temperature should decrease towards the storm center

Flow at maximum wind altitude must be supergradient, affecting entropy-angular momentum relationship

Abstract

Emanuel's concept of maximum potential intensity (E-PI) estimates the maximum velocity of tropical cyclones from environmental parameters assuming thermal wind (gradient-wind and hydrostatic balances) and slantwise neutrality in the free troposphere. E-PI's key equation relates proportionally the radial gradients of saturated moist entropy and angular momentum. Here the E-PI derivation is reconsidered to show that the thermal wind and slantwise neutrality imply zero radial gradients of saturation entropy and angular momentum at an altitude where, for a given radius, the tangential wind has a maximum. It is further shown that, while E-PI's key equation requires that, at the point of maximum tangential wind, the air temperature must increase towards the storm center, the thermal wind equation dictates the opposite. From the analysis of the equations of motion at the altitude of maximum tangential wind in the free troposphere, it is concluded that here the air flow must be supergradient. This implies that the supergradiency factor (a measure of the gradient-wind imbalance) must change in the free troposphere as the air flow tends to restore the balance. It is shown that such a change modifies the derivative of saturation entropy over angular momentum, which cannot therefore remain constant in the free troposphere as E-PI requires. The implications of these findings for the internal coherence of E-PI, including its boundary layer closure, are discussed.