Vortex boundary layer under quadratic surface stress

Abstract

The influences of the quadratic surface stress on the two-dimensional structure of boundary-layer flows in hurricane-like and tornado-like vortices are investigated by solving the nonlinear boundary-layer equations in the vertical direction through power series expansion and expressing the expansion coefficients in terms of parameters of the vortex profile. It is found that the series solutions converge rapidly and the vertical velocity w_bcreated by the boundary-layer flow is upward everywhere for the hurricane type vortex, with the maximum vertical velocity w_bmoccurring inside the radius of maximum tangential wind. This result is of utmost importance for the hurricane development problem on account of the organizing influence of w_bon cumulus convection and latent heat release in the conditionally unstable tropical atmosphere. On the other hand, the vertical velocity created by the boundary layer of the pure potential vortex with zero absolute vorticity is downward.