Limitations of a linear model for the hurricane boundary layer

The linear model for the steady boundary layer of a rapidly rotating axisymmetric vortex is derived from a detailed scale analysis of the full equations of motion. The previously known analytic solution is re-appraised for vortices of hurricane scale and strength. The internal consistency of the linear approximation is investigated for such a vortex by calculating from the solution the magnitude of the nonlinear terms that are neglected in the approximation compared with the terms retained. It is shown that the nonlinear terms are not negligibly small in a large region of the vortex, a feature that is consistent with the scale analysis. We argue that the boundary-layer problem is well-posed only at outer radii where there is subsidence into the layer. At inner radii, where there is ascent, only the radial pressure gradient may be prescribed and not the wind components at the top of the boundary layer, but the linear problem cannot be solved in these circumstances. We examine the radius at which the vertical flow at the top of the boundary layer changes sign for different tangential wind profiles relevant to hurricanes and show that this is several hundred kilometres from the vortex centre. This feature represents a further limitation of the linear model applied to hurricanes. While the present analysis assumes axial symmetry, the same limitations presumably apply to non-axisymmetric extensions to the linear model. Copyright (C) 2009 Royal Meteorological Society