The generalised buoyancy/inertial forces and available energy of axisymmetric compressible stratified vortex motions

Abstract

Adiabatic and inviscid axisymmetric perturbations to a stable reference vortex in gradient wind balance are known to experience two kinds of restoring forces: one that is proportional to both the perturbation density and the reference pressure gradient, and one that is purely radial and proportional to the squared angular momentum perturbation. We show that the work required to move a fluid parcel against such forces from its equilibrium to actual position is path-independent and formally equivalent to the available energy accounting for momentum constraints previously constructed by Andrews (2006) and Codoban and Shepherd (2006). Physically, this work represents the energy of the unbalanced part of the vortex and hence a form of eddy energy. It can be partitioned into available acoustic energy, slantwise available potential energy and centrifugal potential energy. We show that the conditions required for these energies to be positive definite correspond to the classical conditions for symmetric stability, valid for both small and finite-amplitude perturbations. The new available energy framework possesses various advantageous features over previous approaches that shed new light on how the thermodynamic and mechanical sinks/sources of energy control the intensification of the balanced and unbalanced parts of a warm core cyclonic vortex. These features should prove useful in the future to re-examine and clarify the links between the different existing paradigms of tropical cyclone (TC) intensification within a single unifying theoretical framework.