The Mean State of Axisymmetric Hurricanes in Statistical Equilibrium

Abstract

Abstract Numerical experiments are performed to determine the mean state of an axisymmetric hurricane in statistical equilibrium. Most earlier studies used a damping scheme on the temperature field as a parameterization of radiative cooling, which the authors demonstrate yields storms that have little convection outside the eyewall and do not achieve statistical equilibrium. Here the effects of infrared radiation are explicitly simulated, which permits the storm to achieve radiative–convective equilibrium. Beginning from a state of rest, a storm spontaneously develops with maximum surface wind speeds in excess of 100 m s−1 by day 10. This transient “superintense” storm weakens and is replaced by an equilibrium storm that lasts over 400 days with a time-mean maximum wind speed that compares closely with a diagnostic estimate of potential intensity (PI). The main assumptions of PI theory are found to be consistent with the properties of the equilibrium storm, but the thermodynamic cycle does not resemble a Carnot cycle, with an implied efficiency of about half that of the Carnot limit. Maximum radiative cooling is found in the midtroposphere outside the storm, where convective clouds detrain into the dry layer of storm-outflow subsidence, producing a large vertical gradient in water vapor and cloud water. Sensitivity experiments reveal that the results are robust to changes in the prestorm thermodynamic sounding, ambient rotation, horizontal turbulent mixing, and details in the radiative heating field. Subject to the assumptions in this study, it can be concluded that 1) the undisturbed tropical atmosphere is unstable to axisymmetric hurricanes, 2) PI theory accurately bounds time-mean storm intensity (but not transient fluctuations), and 3) equilibrium storm intensity is insensitive to turbulent mixing in the radial direction.