Shock-Like Structures in the Tropical Cyclone Boundary Layer

This paper presents high horizontal resolution solutions of an axisymmetric, constant depth, slab boundary layer model designed to simulate the radial inflow and Ekman pumping of a tropical cyclone. For intense tropical cyclones the u(du/dr) term in the radial equation of motion quickly produces a shock-like structure in the radial wind, i.e., near the radius of maximum tangential wind the boundary layer radial inflow decreases from approximately 20 m/s to zero over a radial distance of 1 or 2 km. Associated with this large boundary layer convergence is a spike in the radial distribution of Ekman pumping, with updrafts larger than 25 m/s at a height of 500 m. It is argued that observed hurricane updrafts of this magnitude so close to the ocean surface are due to the dry dynamics of the frictional boundary layer rather than moist convective dynamics. The shock-like structure in the boundary layer radial wind also has important consequences for the evolution of the tangential wind and the vertical component of vorticity. On the inner side of the shock the tangential wind tendency is essentially zero, while on the outer side of the shock the tangential wind tendency is large due to the large radial inflow there. The result is the development of a U-shaped tangential wind profile and the development of a thin region of large vorticity. In many respects the model solutions resemble the remarkable structures observed in the boundary layer of Hurricane Hugo (1989).