The surface boundary layer of a hurricane. II

Abstract

In an earlier paper, a momentum integral method was developed by one of the authors (Smith, 1968) to investigate the gross features of the surface friction layer of a steady, axisymmetric hurricane, which is specified by its radial pressure variation near the sea surface. Thus, by choosing suitable vertical profiles of inflow and swirling velocity components in the boundary layer, the technique provides estimates for the radial distribution of mean inflow, of boundary layer thickness and of mean upflow through the top of the layer. It therefore gives a measure of the constraint imposed by the inflow layer on the vortex which produces it.

In the present work, the method is used to investigate the effects of turbulent structure on the boundary layer characteristics. The turbulence is represented by an eddy viscosity KM_M, and solutions corresponding to a variety of models for the variation of KM_M, together with an appropriate surface boundary condition, are compared. These models range from an eddy viscosity which is everywhere constant and with the condition of no-slip at the surface, to a KM_M which has both radial and vertical structure and which varies linearly with height in the first few tens of metres above the sea surface. In the latter case, one is able to parameterize the roughness of the sea surface.

The solutions indicate that in actual hurricanes, an increase of KM_M towards the region of maximum winds produces a significant increase in the upflow compared with a similar layer in which KM_M has no radial variation. Moreover, the radial profile of boundary layer thickness differs markedly between the two cases. Solutions for three surface boundary conditions are compared and the volume inflow and upflow rates at a given radius are also found to increase with an increase in the constraint at the sea surface, that is, with an increase in surface stress.

An error in one of the calculations of the first paper is also resolved.