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 + alpha r(m)w(m)eta(m), where EPI is the maximum potential intensity of the gradient wind and alpha r(m)w(m)eta(m) represents the supergradient winds. The latter term is the product of the radius r(m), the vertical velocity w(m), the azimuthal vorticity eta(m) at the radius and height of the maximum tangential wind (r(m), z(m)), and the (nearly constant) alpha. 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 rmwm eta m PROP;umin2zm(rm)/l upsilon(zm) PROP;rm, where -u(min) is the maximum boundary layer radial inflow velocity and l(upsilon)(z) is the vertical mixing length.
