A simple model of the hurricane boundary layer

A simple, steady, moist, axisymmetric, constant-depth, slab model for the hurricane boundary layer is investigated. High-resolution solutions of the boundary-layer equations are obtained by integrating inwards from some large radius, at which it is assumed that geostrophic balance and convective-radiative balance exist. In all the solutions obtained, the tangential wind speed in the boundary layer approaches that above the boundary layer in the inner-core region and the maximum wind speed in the boundary layer is comparable with, or even marginally higher than that above. A new feature of one of the solutions described is the existence of spatial oscillations in vertical velocity at the top of the boundary layer, inside the radius of maximum tangential wind speed. These oscillations may be interpreted as frictionally damped inertial waves. They are accompanied by annular regions in which the tangential flow alternates between supergradient and subgradient. The existence of boundary-layer-induced oscillations in vertical velocity in reality would have implications for the organization of convection in the core region of a hurricane. It is shown that an approximation to determine the radial flow in the boundary layer suggested by Willoughby overestimates the vertical motion at the top of the boundary layer by a factor of about two, but the analysis leads us to question the utility of the approximation. We investigate also the thermodynamic structure of the boundary layer and the radial distribution of surface fluxes for vortices with the same maximum tangential wind speed above the boundary layer and the same radius of maximum wind (RMW), but having different widths. It is found that the equivalent potential temperature (theta(e)) in the boundary layer continues to increase with decreasing radius inside the RMW. Moreover, the negative radial gradient of theta(e) in the inner-core region, which is related to that of virtual temperature above the boundary layer in the eyewall region, is relatively insensitive to the vortex width, but the maximum values of theta(e) increase with the width. The strength and radial distribution of the latent-heat flux is insensitive to the vortex width in the inner-core region, but varies markedly with width in the outer part of the vortex. Realistic radial distribution of relative humidity are obtained only when shallow convection is represented in the model. The inclusion of dissipative heating in the thermodynamic equation leads to an increase in theta(e) of the order of 1.5 K in the inner-core region of the vortex and to a reduction in the boundary-layer relative humidity of 5%.