The closure to the MPI theory is based on a theory for the boundary layer. The frictional dissipation and energy production in the in-flowing boundary layer air is described in terms of surface fluxes of heat and momentum. Assuming that the entropy and the angular momentum are conserved and well mixed within the turbulent boundary layer, in steady axisymmetric flow, it may be shown that the ratio of the entropy changes along the angular momentum lines is given by the ratio of heat flux and momentum flux at the surface. However, the surface flux closure underestimates the theoretical strength of Emanuel's hurricane. In the companion presentation we propose a correction to Emanuel 86 theory.
In this set of experiments an axisymmetric, nonhydrostatic version of the ZetaC model, with the GFDL radiation package on a 10 degrees domain, has been used. In the moist simulations we use the Lin microphysics. The horizontal resolution of the model is 1 km so convection is fully resolved. Simulations are run for about 25 days, producing a steady state. In the series of experiments performed, surface temperature, tropopause temperature, latitude (Coriolis parameter), resolution, surface heat flux and other parameters are varied.
Our analysis of the numerical simulations suggests that the entropy distribution in the boundary layer cannot be determined solely from the surface fluxes. In particular, turbulent mixing across entropy and angular momentum surfaces is associated with a strengthening of the entropy gradient near the radius of maximum wind. In our simulations, this thermodynamic effect did result in a 5 to 10 percent increase in the maximum wind speed. Numerical simulations show that the maximum tangential winds are stronger than theory predicts, which means that the MPI theory is not really an upper bound for intensity. The superintensity can be explained by the presence of ageostrophic winds within the eyewall inflow region.