A critique of Emanuel's hurricane model and potential intensity theory

We present a critique of Emanuel's steady state hurricane model, which is a precursor to his theory for hurricane potential intensity. We show that a major deficiency of the theory is the tacit assumption of gradient wind balance in the boundary layer, a layer that owes its existence to gradient wind imbalance in the radial momentum equation. If, as in Emanuel's model, gradient wind balance is assumed in the inner region where the flow exits the boundary layer, solutions of the full boundary layer equations in this region yield unrealistic radial profiles of tangential wind speed, vertical velocity and surface pressure. Furthermore, these solutions require knowledge of the tangential wind profile above the boundary layer in the outer region where there is subsidence into the layer and they depend on the radial extent of the tangential velocity profile. This effect is not considered in Emanuel's theory. When the gradient wind approximation is not made in the inner region, the solutions are much more realistic vis-á-vis hurricanes, but then the radial pressure gradient above the boundary layer must be prescribed or determined independently of the boundary layer. The deductions made herein highlight a fundamental problem with Emanuel's theory for potential intensity, since that theory makes the same assumptions as in the steady state hurricane model. Our current findings together with recent studies examining intense hurricanes are used to suggest a way forward toward a more consistent theory for hurricane potential intensity.