A Parametric Wind-Pressure Relationship for Concentric Cyclostrophic Vortices

In situ probes that make near-ground pressure and wind measurements within close range of an intercepted tornado do not recognize whether the measurements may result from the tornado being embedded in a background vortex (such as a tornado cyclone or mesocyclone or the combination of the two). In this study, the Wood-White parametric tangential velocity profile model coupled with the cyclostrophic balance assumption is used to deduce representative pressure deficit profiles from tangential velocity profiles that exhibit single-, dual-, and triple-maximum concentric tangential wind peaks associated with a tornado vortex, tornado cyclone, and a larger-scale background vortex. The model employs five key parameters: tangential velocity maximum, radius of the maximum, and three different shape velocity parameters that control different portions of the profile. The model offers a diagnostic tool for estimating and examining radial profiles of pressure deficit deduced from a theoretical superposition of tangential velocity profiles that may resemble those in real tornadoes, tornado cyclones, and larger-scale background vortices including mesocyclones. The balance was partitioned into separate pressure components that corresponded to multiple-maxima cyclostrophic wind profiles in order to quantitatively evaluate the significant fluctuations in central pressure deficits. The model vortex intensity, in terms of varying growth, size and decay velocity profiles, was analyzed in relation to changing each of five key parameters for a given vortex. Analytical results show that the first parameter designed for changing the tangential velocity profile from sharply to broadly peaked produces the corresponding central pressure fall. An increase in the second (third) parameter yields a central pressure rise (fall) by lowering (rising) the inner (outer) velocity profile inside (outside) the radius of the maximum wind. Finally, we present a few examples, some from VORTEX2, in which the parametric model is fitted to a tangential velocity profile derived from high-resolution Doppler radar data collected in a real tornado vortex embedded in a tornado cyclone.