Diabatic and frictional controls of an axisymmetric vortex using available potential energy theory with a non-resting state

The concept of thermodynamic efficiency is central to the theoretical understanding of tropical cyclone intensity and intensification, but the issue has remained controversial owing to the existence of distinct and incompatible definitions. Physically, thermodynamic efficiency relates to the fraction of the surface enthalpy fluxes and diabatic processes that contributes to the generation of the potential energy available (APE) for conversions into kinetic energy, so that the main difficulty is how best to define APE. In this study, we revisit the available energetics of axisymmetric vortex motions by redefining APE relative to a non-resting reference state in gradient wind balance instead of a resting state. Our approach, which accounts for both diabatic and frictional effects, reveals that the choice of reference state significantly impacts the prediction of APE generation and its conversion to kinetic energy. By using idealised numerical experiments of axisymmetric tropical cyclone intensification, we demonstrate that the APE production estimated from a non-resting reference state is a much more accurate predictor of APE to KE conversion than those based on other choices of reference states such as initial, mean, and sorted profiles. These findings suggest that incorporating the balanced dynamical structure of tropical cyclones into APE-based theories could lead to improved potential intensity models, with implications for forecasting and understanding cyclone behaviour.