Simple nonlinear bounday layer model for tropical cyclones

We present a simple, nonlinear similarity solution for the boundary layer underneath a gradient wind vortex over the ocean. The similarity solution reduces the nonlinear PDEs governing the cyclone boundary layer into a system of ODEs, which allows us to study the individual and combined effects of each of the nonlinear contributions to the dynamics. As an example, the formation and nonlinear enhancement of the super-gradient jet present in the upper region of the PBL is examined. This simple model is a useful tool for understanding the relationships between the surface wind vector field and the surface pressure field, which has applications for analyzing satellite SAR and scattereomter wind fields. Because the similarity model is independent of the choice of turbulence closure, we can examine the effects of several standard choices that are representative of those in common use in numerical models. We show that the surface wind factor, inflow angle, dissipational heating and transport of TKE into the surface layer, where it is available for surface wave and current generation, are all sensitive to the choice of turbulence parameterization above the surface layer. Other applications include geophysical fluid dynamics. Classical theories of vortex stability, which ignore the presence of boundary layers, only require that the angular momentum increase outwards. We demonstrate that incorporating linearized boundary layer dynamics does not appreciably affect the stability of a marginally stable vortex. However, nonlinear boundary layer dynamics can destabilize such a vortex.