Available Potential Energy Density Budget for an Axisymmetric Tropical Cyclone

An understanding of the evolution of available potential energy (APE) in a tropical cyclone (TC) offers the possibility of a greater physical insight into the contribution of irreversible processes to TC intensification. In particular, an APE viewpoint is more flexible than theories that consider the entropy budget of a TC or treat it as a heat engine; irreversible processes such as diffusion or phase changes of water are sources of entropy by definition, but they may function either as sources or sinks of APE. However, there are conceptual difficulties with the construction of APE in a moist atmosphere, as it relies on the specification of a reference state, which is not uniquely defined.

In this study we investigate the APE density in a TC simulated by the axisymmetric model of Rotunno and Emanuel [1987]. The APE density is defined for each parcel as the work released when an air parcel moves from its initial position to its level of neutral buoyancy in a reference state. We derive the form of the APE density from the model equations, and use a simple time-evolving reference state of mean horizontal density to show that the majority of APE density in the modelled TC is at the sea surface and in the eyewall region, as expected. We test other proposed formulations of APE density to examine how the definition of the reference state affects the apparent distribution of APE.

Using a Boussinesq approximation, we can identify APE generation and dissipation terms arising due to the diffusion of heat and water vapour to establish the relative importance of these processes. We question whether the choice of reference state can affect whether a given process appears to be a source or sink of APE.