Can one reconcile the classical theories and the WISHE theories of tropical cyclone intensification?

An effort is made to reconcile the classical balance theories of tropical cyclone intensification by Shapiro and Willoughby and Schubert and Hack and the various prognostic (or WISHE-) theories of Emanuel. As a start, it proves insightful to extend the classical theories to account for explicit latent heat release in slantwise ascending air. While such an effort uncovers enroute a range of old modelling issues concerning the representation of deep convection in a balance framework, the analysis provides a new perspective on these issues. The bottom line is that the two theories cannot be reconciled. The behaviour of the classical model with explicit latent heat release included is illustrated by a particular calculation starting with an axisymmetric vortex in a conditionally-unstable atmosphere. As soon as condensation occurs aloft, the moist Eliassen equation for the overturning circulation becomes hyperbolic in the convectively-unstable region and the model cannot be advanced forwards beyond this time unless the Eliassen equation is suitably regularized to remove these hyperbolic regions. However, regularization suppresses deep moist convection, leaving no mechanism to reverse the frictionally-induced outflow in the lower troposphere required to concentrate absolute angular momentum there. For this reason, the initial vortex spins down, even following the formation of elevated cloud with the accompanying latent heat release. The fact that the flow configuration in the explicit moist version of the classical theories is similar to that in the WISHE theories raises several fundamental questions concerning the physics of vortex spin up in the WISHE theories, calling into question the utility of these theories for understanding tropical cyclone intensification in nature.