Tropical cyclone boundary layer shocks and shock-like structures

This talk presents analytical and numerical solutions of an axisymmetric, f-plane, constant depth tropical cyclone slab boundary layer model in order to understand the role of friction in eyewall placement, potential vorticity rings, and concentric eyewall interaction. For intense tropical cyclones, the u(∂u/∂r) term in the radial momentum equation produces a discontinuity, also referred to as a shock. The analytical solutions, which neglect horizontal diffusion, allow true discontinuities to develop in the radial and tangential momentum with associated singularities in boundary layer pumping and vorticity. The analytical solutions show the time and radius of shock formation with and without the inclusion of surface drag for various tropical cyclone categories. In the numerical model, which includes horizontal diffusion, shock-like structures develop due to forcing from the gradient wind above the boundary layer. The numerical results are used to examine shock interactions during concentric eyewall cycles.