A note on the shear-forced dynamics of tornadoes

This note presents an axisymmetric model of a tornado-like vortex with internal vertical wind shear. By employing a prescribed incompressible circulation-strain flow that captures the horizontal variation of the vertical wind, we show that the model admits an exact viscous Feynman-Kac representation for the tornado structure. In the presence of vortex vertical shear, the tilting term induces radial phase mixing that rapidly deforms the vortex structure, thus causing the radius of the maximum azimuthal wind to broaden and shift upward. At the long-time limit, the vortex approaches the Burgers radial scale while both the wind and vorticity decay exponentially. This class of solutions may help explain why tornadoes often weaken rapidly once an internal vertical shear structure emerges after touchdown.