A Parametric Wind–Pressure Relationship for Rankine versus Non-Rankine Cyclostrophic Vortices

A parametric tangential wind profile model is presented for depicting representative pressure deficit profiles corresponding to varying tangential wind profiles of a cyclostrophic, axisymmetric vortex. The model employs five key parameters per wind profile: tangential velocity maximum, radius of the maximum, and three shape parameters that control different portions of the profile. The model coupled with the cyclostrophic balance assumption offers a diagnostic tool for estimating and examining a radial profile of pressure deficit deduced from a theoretical superimposing tangential wind profile in the vortex. Analytical results show that the shape parameters for a given tangential wind maximum of a non-Rankine vortex have an important modulating influence on the behavior of realistic tangential wind and corresponding pressure deficit profiles. The first parameter designed for changing the wind profile from sharply to broadly peaked produces the corresponding central pressure fall. An increase in the second (third) parameter yields the pressure rise by lowering the inner (outer) wind profile inside (outside) the radius of the maximum. Compared to the Rankine vortex, the parametrically constructed non-Rankine vortices have a larger central pressure deficit. It is suggested that the parametric model of non-Rankine vortex tangential winds has good potential for diagnosing the pressure features arising in dust devils, waterspouts, tornadoes, tornado cyclones, and mesocyclones. Finally, presented are two examples in which the parametric model is fitted to a tangential velocity profile, one derived from an idealized numerical simulation and the other derived from high-resolution Doppler radar data collected in a real tornado.