Why the swirl ratio is a useless parameter

Since the earliest work on understanding tornadic vortices, the "swirl ratio" has been identified as the most important parameter for predicting vortex structure. Broadly speaking, the swirl ratio can be thought of as the ratio of the flow circulation to the flow rate in the low-level inflow region; sometimes it is measured simply as the ratio of the tangential to radial velocities in the inflow.

While there is no doubt that the structure of any particular tornado-like vortex changes as the swirl ratio varies, the utility of the swirl ratio is severely limited by two critical facts: first, that the transitional values of the swirl ratio depend on the Reynolds number; and second, that the swirl ratio is not well-defined for an atmospheric vortex.

This first limitation is supported by numerous laboratory and numerical experiments, and in the laminar approximation it can be shown from dimensional analysis. The second limitation is a consequence of the fact that the swirl ratio is a diagnostic, rather than predictive, parameter. That is to say, the swirl ratio is determined by the flow associated with the tornado itself; one cannot use the swirl ratio to predict the size, shape, or intensity of the vortex until it has already formed.

Ideas for predicting tornado-like vortex structure and intensity from environmental fields, for both laminar and fully turbulent flows, will be discussed.