Thermodynamics of a tropical cyclone: generation and dissipation of mechanical energy in a self-driven convection system

The formation process of circulatory motion of a tropical cyclone is investigated from a thermodynamic viewpoint. The generation rate of mechanical energy by a fluid motion under diabatic heating and cooling, and the dissipation rate of this energy due to irreversible processes are formulated from the first and second laws of thermodynamics. This formulation is applied to a tropical cyclone, and the formation process of the circulatory motion is examined from a balance between the generation and dissipation rates of mechanical energy in the fluid system. We find from this formulation and data analysis that the thermodynamic efficiency of tropical cyclones is about 40% lower than the Carnot maximum efficiency because of the presence of thermal dissipation due to irreversible transport of sensible and latent heat in the atmosphere. We show that a tropical cyclone tends to develop within a few days through a feedback supply of mechanical energy when the sea surface temperature is higher than 300 K, and when the horizontal scale of circulation becomes larger than the vertical height of the troposphere. This result is consistent with the critical radius of 50 km and the corresponding central pressure of about 995 hPa found in statistical properties of typhoons observed in the western North Pacific.