Hurricane super-intensity through mixing

This paper discusses how mixing can lead to super-intense hurricanes, i.e. hurricanes whose wind speed exceeds the theoretical prediction of the Emanuel (1986) Maximum Potential Intensity theory (MPI). The MPI framework is based on three key assumptions. First, slantwise convection ensures that both the entropy and angular momentum are constant along the streamlines of the circulation within the free troposphere. Second, the azimuthal wind is in gradient wind balance outside the planetary boundary layer. These two first assumptions make it possible to derive the pressure and wind fields from the distributions of entropy and angular momentum at the top of the boundary layer. The third assumption is that these entropy and angular momentum distributions can be obtained directly from a simple closure on the surface fluxes of entropy and momentum. By combining these three assumptions, Emanuel (1986) predict the maximum wind speed in a hurricane.

Recent studies based on both observations and numerical modeling indicate the possibility of super-intense hurricanes whose wind speed can actually exceed the theoretical MPI prediction. In a joint paper, we analyze such super-intensity obtained in a numerical model and show that it can be attributed in part to dynamical effects associated with the over-shoot of the hurricane inflow and in part to thermodynamics effects. The present paper discusses these thermodynamic effects in greater detail and shows that mixing within the boundary layer can lead to more intense hurricane.

Within the boundary layer, there are strong vertical gradients of both entropy and angular momentum, and entropy and angular momentum surfaces are strongly tilted. This implies that, due to the intense turbulence near the surface, both entropy and momentum are mixed across angular and entropy surfaces. Including such mixing in the closure for the boundary layer entropy and momentum enhances the entropy gradient near the radius of maximum wind. Consequently, because of the assumptions of gradient wind balance and slantwise convection, mixing increases the maximum wind speed. A key prediction here is that mixing does not increase the entropy gradient and wind speed through the entire storm. In fact, mixing weakens the entropy gradient in the inner part of the eye-wall, but enhances them near the outer eye-well where the radius of maximum wind is located under the MPI theory.

In numerical simulations, we evaluate that mixing enhances the entropy gradient at the radius of maximum wind by 10 to 20 percent, which translates in an increase of 5 to 10 percent in maximum wind speed. We also propose scaling arguments relating this thermodynamic super-intensity to the turbulent diffusivity within the planetary boundary layer, and show that our scaling is consistent with numerical simulations. Yhis analysis indicates that, while MPI indeed provides a good approximation for hurricane intensity, its prediction should not be construed as a strict upper bound on wind speed or pressure gradient. This also points out to the fact that the maximum wind speed in a hurricane can be critically sensitive to effects of turbulence within the planetary boundary layer.