Supergradient Winds in Simulated Tropical Cyclones

In a previous paper a formula was derived for the maximum potential intensity of the tangential wind in a tropical cyclone called PI⁺. The formula, PI⁺² = EPI² + αr_mw_mη_m, where EPI is the maximum potential intensity of the gradient wind and αr_mw_mη_m represents the supergradient winds. The latter term is the product of the radius r_m, the vertical velocity w_m, the azimuthal vorticity η_m at the radius and height of the maximum tangential wind (r_m, z_m) and the (nearly constant) α. Examination of a series of simulations of idealized tropical cyclones indicate an increasing contribution from the supergradient-wind term to PI⁺ as the radius of maximum wind increases. In the present paper, the physical content of the supergradient-wind term is developed showing how it is directly related to tropical-cyclone boundary-layer dynamics. It is found that r_mw_mη_m ∝ u²_minz_m(r_m)/l_v(z_m) ∝ r_m where −u_min is the maximum boundary-layer radial inflow velocity and l_v(z) is the vertical mixing length.