Comparison of an analytical and a numerical model for hurricane potential intensity

We report on our comparison of an analytic model for hurricane potential intensity (E-PI) with the maximum intensity found in our numerical model simulations. The analytical model for E-PI rests on three primary assumptions: gradient-wind/hydrostatic balance in the free atmosphere, reversible or pseudoadiabatic thermodynamics, and a simple boundary-layer closure. Numerical simulations with relatively small horizontal diffusion produce intensities far in excess of E-PI. However we find that the radial diffusion (not well known from theory or observations) has a strong control on the degree to which simulated intensity exceeds E-PI. In the simulations with relatively low-diffusion, we find the thermodynamical and the boundary-layer components of the E-PI theory to be accurate, but that the gradient-wind-balance assumption is violated. The violation manifests itself as an “overshoot” in the azimuthal wind as a result of the down-the-pressure-gradient flow in the boundary layer where gradient-wind balance is disrupted (a well-known effect in rotating-flow-boundary-layer problems). We will show that, at least in cases with a modest overshoot (stronger horizontal diffusion), the E-PI theory can be considered as the leading-order theory in a small parameter measuring the strength of boundary-layer-friction to that of the free-atmosphere pressure gradient. The overshoot then emerges as a small correction.