Dynamic Energy Efficiency of Heat and of Momentum in Balanced Vortex

The tropical cyclone dynamics can be understood in the framework of balanced vortex driven by the heat and momentum source/sink. In this study, we derive the formula for the dynamic energy efficiency of heat and of momentum in balanced vortex. The derivation is an extension of the dynamic efficiency of heat (Hack and Schubert 1986). We first derive the available potential energy (APE) and kinetic energy (KE) equations of the gradient wind balanced system. The energy conversion term between the APE and KE then is written as the product of the heat and momentum source/sink and the dynamic energy efficiency factors of heat and momentum. The dynamic energy efficiency of heat and of momentum is determined by solving the Eliassen transverse circulation equation with the right hand side of the equation the radial temperature gradient. With the known vortex structure of inertial stability, static stability, and baroclinicity, and also the region of convective heating, the system dynamic energy factors of heat and of momentum can be computed. We will demonstrate the usefulness of the formula with observations from the TCS08 aircraft observations as well as numerical model simulations.