  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.
