Self-stratification of tropical cyclone outflow. Part I: Implications for storm structure

Extant theoretical work on the steady state structure and intensity of idealized axisymmetric tropical cyclones relies on the assumption that isentropic surfaces in the storm outflow match those of the unperturbed environment at large distances from the storm's core. These isentropic surfaces generally lie just above the tropopause, where the vertical temperature structure is approximately isothermal, so it has been assumed that the absolute temperature of the outflow is nearly constant. Here we show that this assumption is not justified, at least when applied to storms simulated by a convection-resolving axisymmetric numerical model, in which much of the outflow occurs below the ambient tropopause and develops its own stratification, unrelated to that of the unperturbed environment. We here propose that this stratification is set in the storm's core by the requirement that the Richardson Number remain near its critical value for the onset of small-scale turbulence. We test this ansatz by calculating the Richardson Number in numerically simulated storms, and then show that the assumption of constant Richardson Number determines the variation of the outflow temperature with angular momentum or entropy and thereby sets the low-level radial structure of the storm outside its radius of maximum surface winds. In Part II we will show that allowing the outflow temperature to vary also allows one to discard an empirical factor that was introduced in previous work on the intensification of tropical cyclones.