## Swirl Ratio

The swirl ratio is basically a measure of the tornado-scale helicity.

where v0 is the tangential velocity on the periphery of the circulation at the "corner turn" (between Region II and III in diagram below) and w is the updraft strength at the center of the tornado vortex.

The "swirl" occurs because air attempting to rotate fritcionlessly around a cyclone that has low end mesoscale dimensions is really in cyclostrophic, as opposed to geostrophic, balance. In essence, air attempting to move into a low pressure area is not able to because of strong centrifugal accelerations. Recall that when this occurs, there will be large magnitude vertical vorticity because of the small radius of curvature around the mesoscale low pressure area. This, in turn, will create pressure perturbations at the center of rotation, lowering the pressure there and causing enhanced vertical pressure gradient accelerations beneath that layer and reduced vertical pressure gradient accelerations above that layer. The horizontal pressure gradient accelarations beneath that level will induce the air out of cyclostrophic balance, producing a vortex at the ground (associated with strong radial inflow at ground level with a near right angle turn). This occurs at S=1 or so. This explanation for a tornado is related to the so-called "Dynamic Pipe Effect."

The swirl ratio actually is a ratio of the circulation around the periphery of the vortex to the updraft strength, and, as such, is a measure of the amount of mass rotating around the circulation center at a given level. Large swirl ratios imply increasing amount of mass, and if the veritical velocities are not strong enough to "evacuate" that mass from a given level, then the circulation breaks down into multiple circulation centers.

The swirl ratio itself is also a measure of the intensity of each circulation center. Hence, the larger the swirl ratio, the stronger the circulation center, the stronger the pressure fall at the center. Recall that above the level of strongest circulation, isobars get further apart in the vertical. Thus, the larger the swirl ratio, the greater the degree to which subsidence characterizes the center of the vortex. In the figure at bottom, S=.2 to .4 for (a), S=1 for (b) and then up to 2.5 for (e)-(f).