An Analytical Model of One- and Two-Celled Vortices: Preliminary Testing

Tangential winds in atmospheric vortices (mesocyclones, tornadoes and dust devils) are often approximated by continuous functions that are zero at the vortex center, increase to a maximum at its core radius, and then decrease asymptotically to zero infinitely far from the center. It can be seen from proximity radar observations of tornadoes by mobile, high-resolution Doppler radars that the wind profiles are different from one vortex to another. Some vortices exhibit evidence of a two-cell structure (i.e., sinking motion near the vortex center and rising motion just outside the core radius at which maximum tangential wind occurs); others do not. Additionally, the slopes of the velocity profiles outside the core radii sometimes exhibit different decay rates from one vortex to another.

In an attempt to determine the degrees of varying tangential wind profiles in atmospheric vortices, a new analytical model is presented. The model employs four parameters: maximum tangential wind (Vx), core radius (Rx) at which maximum tangential wind occurs, k which controls the concavity of the tangential velocity profile near the vortex center, and n which controls the decay rate of the profile (i.e., rate at which tangential velocity decays with increasing radial distance, r, outside the core). When k is less than or equal to 0.5, the tangential velocity profile near the vortex center has negative curvature (curve turns to right with increasing r) and a local vertical vorticity is maximum at the center, suggestive of a one-celled vortex. When k > 0.5, the profile has positive curvature (curve turns to left) near the center and an annulus of maximum vorticity is formed while being displaced away from the center toward the strongest gradient of the profile inside the core radius, consistent with a two-celled vortex. When n (which always exceeds k) is small, the tangential velocity profile outside the core radius is nearly flat (i.e., small decay rate). Increasing the n values increases the decay rate.

Least squares fits of four model parameters to Doppler-analyzed and -derived tangential wind profiles provide evaluation of the parameters' distributions and critical examination of the profile's realism. Mobile, high-resolution Doppler radar measurements of the 15 May 1999 Stockton, Kansas and 30 May 1998 Spencer, South Dakota tornadoes are used to test against the fitted parameters of the analytical model.

Comparison of the fitted wind profiles and those analyzed or derived from Doppler radar observations shows good agreements. The results will be presented at the Conference.