The heating induced low-level secondary circulation below the heating maximum has a local component of flow both inwards and upwards across the absolute angular momentum (M-) surfaces towards low values of M. Except in the frictional boundary layer, where M is not materially conserved, the advection of M towards low values of M is accompanied by a local spin up of the tangential wind speed. The intensification rate of the vortex is essentially constant up to the time when regions of instability ensue. This result is in contrast to the previous
suggestions that the rate should increase as the vortex intensifies because the heating becomes progressively more “efficient” when the local inertial stability increases.
The solutions provide a context for re-examining the axisymmetric balance formulation for tropical cyclone intensification in the light of the classical paradigm articulated by Ooyama as well as another widely-invoked intensification paradigm.