The linear model for the boundary layer of a rapidly-rotating axisymmetric vortex is re-examined in the light of a scale analysis of the full equations of motion. An analytic solution is obtained with the assumptions: (1) that the eddy diffusivity is a constant above the constant-stress surface layer, (2) its value is determined locally by the parameters of the surface layer, including the surface roughness, and (3) the velocity components and stress are continuous at the top of this layer. The accuracy of the linear approximation is estimated by calculating from the solution the relative magnitude of the nonlinear terms that are neglected. We argue that the boundary-layer problem is well-posed only at outer radii where there is subsidence into the layer, while at inner radii where there is ascent, only the radial pressure gradient may be prescribed, and not the wind components. We examine the radius at which the vertical flow changes sign for different tangential wind profiles in the subsidence region. We calculate also the radial variation of eddy diffusivity predicted by the surface layer constraint. To our knowledge a fully consistent formulation for the inner region has yet to be worked out.
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