On the Dynamics and Energy Transformations in Steady-State Hurricanes

Abstract

A dynamic model of the inflow layer in a steady mature hurricane is evolved, relating wind speed, pressure gradient, surface shearing stress, mass flow, and convergence. The low-level air trajectories are assumed to be logarithmic spirals. With this hypothesis, properties such as maximum wind and central pressure are determined through choice of a parameter depending on the inflow angle: a moderate hurricane arises with inflow angles of about 20°, while 25° gives an intense or extreme storm. Most of this study treats the moderate storm. In order to maintain its core pressure gradients, an oceanic source of sensible and latent heat is required. As a result, latent heat release in the inner hurricane area occurs at higher heat content (warmer moist adiabats) than mean tropical subcloud air. The heat transfer from the ocean and the release of latent heat in the core determine the pressure gradient along the trajectory, and this prescribes the particular trajectory selected by the air among an infinite number available from the logarithmic spiral family. This selection principle is evolved using recent work on “relative stability” of finite amplitude thermal circulations. Of an infinite number of dynamically possible spirals, the one is realized which maximizes the rate of kinetic energy production under the thermodynamic constraints, here formulated in terms of the relation between heat release and pressure gradient. Finally, rainfall, efficiency of work done by the storm, and kinetic energy budgets are examined in an attempt to understand the difference between the hurricane—a rare phenomenon—and the common sub-hurricane tropical storm. DOI: 10.1111/j.2153-3490.1960.tb01279.x