Energy Production, Frictional Dissipation, and Maximum Intensity of a Numerically Simulated Tropical Cyclone

Abstract

A tropical cyclone (TC) viewed as a heat engine converts heat energy extracted from the ocean into the kinetic energy of the TC, which is eventually dissipated due to surface friction. Since the energy production rate is a linear function while the frictional dissipation rate is a cubic power of surface wind speed, the dissipation rate is generally smaller than the production rate initially but increases faster than the production rate as the storm intensifies. When the dissipation rate eventually reaches the production rate, the TC has no excess energy to intensify. Emanuel hypothesized that a TC achieves its maximum potential intensity (E-MPI) when the surface frictional dissipation rate balances the energy production rate near the radius of maximum wind (RMW). Although the E-MPI agrees well with the maximum intensity of numerically simulated TCs in earlier axisymmetric models, the balance hypothesis near the RMW has not been evaluated. This study shows that the frictional dissipation rate in a numerically simulated mature TC is about 25% larger than the energy production rate near the RMW, while the dissipation rate is lower than the energy production rate outside the eyewall. This finding implies that the excess frictional dissipation under the eyewall should be partially balanced by the energy production outside the eyewall and thus the local balance hypothesis underestimates the TC maximum intensity. Both Lagrangian and control volume equivalent potential temperature (?e) budget analyses demonstrate that the energy gained by boundary layer inflow air due to surface entropy fluxes outside of and prior to interaction with the eyewall contributes significantly to the energy balance in the eyewall through the lateral inward energy flux. This contribution is further verified using a sensitivity experiment in which the surface entropy fluxes are eliminated outside a radius of 30?45 km, which leads to a 13.5% reduction in the maximum sustained near-surface wind speed and a largely reduced size of the model TC.