Examination of the output of detailed numerical simulations of tropical cyclones reveals that this does not happen because the strong vertical shears that develop in the outflow lead to the production of small-scale turbulence whose effect, broadly, is to keep the outflow Richardson Number at or above some critical value. We show that this leads to a decided temperature gradient in the outflow which, through the thermal wind equation, strongly affects the radial structure and intensity of the entire storm. We further show that variable outflow temperature allows surface enthalpy fluxes to be positively correlated with boundary layer entropy, permitting the storm to intensify even in the absence of entrainment of dry air into the boundary layer outside the eyewall. This leads to a simple analytic expression for storm intensification that does not require the presence of an ad hoc entrainment parameter that was introduced in previous work.