Energy Production, Frictional Dissipation, and Maximum Intensity of Tropical Cyclones

A tropical cyclone (TC) viewed as a heat engine converts heat energy extracted from the ocean to kinetic energy of the TC, which eventually dissipates due to surface friction. Since the energy production rate is a linear function while the frictional dissipation rate is the cubic power of surface wind speed, the latter is generally smaller than the former initially but increases faster than the former as the storm intensifies. When the latter eventually reaches the former, the TC has no excessive 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. It is showed here that the frictional dissipation rate in a numerically simulated mature TC in this study 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 implies that the excessive frictional dissipation under the eyewall should be partially balanced by the energy production outside the eyewall and thus the local balance hypothesis would thus underestimate the TC maximum intensity. Both a Lagrangian and a control-volume equivalent potential temperature (e) budget analyses demonstrate that the energy gained due to surface entropy fluxes outside the eyewall for the air before arriving at the eyewall in the boundary layer contributes significantly to the energy balance in the eyewall through the lateral inward energy flux. This 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 of the maximum intensity and a largely reduced size of the model TC.