Axisymmetric Balance Dynamics of Tropical Cyclone Intensification and Its Breakdown Revisited

Abstract

This paper revisits the evolution of an idealized tropical cyclone–like vortex forced by a prescribed distribution of diabatic heating in the context of both inviscid and frictional axisymmetric balance dynamics. Prognostic solutions are presented for a range of heating distributions, which, in most cases, are allowed to contract as the vortex contracts and intensifies. Interest is focused on the kinematic structure and evolution of the secondary circulation in physical space and on the development of regions of sym- metric and static instability. The solutions are prolonged beyond the onset of unstable regions by regularizing the Sawyer–Eliassen equation in these regions, but for reasons discussed, the model ultimately breaks down. The intensification rate of the vortex is essentially constant up to the time when regions of instability ensue. This result is in contrast to 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 reexamining the classical axisymmetric paradigm for tropical cyclone intensification in the light of another widely invoked intensification paradigm by Emanuel, which postulates that the air in the eyewall flows upward and outward along sloping absolute angular momentum (M) surfaces after it exits the frictional boundary layer. The conundrum is that the classical mechanism for spinup requires the air above the boundary layer to move inward while materially conserving M. Insight provided by the balance solutions helps to refine ideas for resolving this conundrum.