Numerical simulations of an isolated vortices embedded within a vorticity gradient

Tornadoes generally are not isolated singular vortices, but usually are accompanied by satellite voritices of varying spatial scale. While the interaction between these surrounding vortex structures and the parent tornado is a highly complex and nonlinear problem, we employed simplified numerical experiments to examine this two-way interaction in idealized cases. Using a three-dimensional, nonhydrostatic model, we initialized a large cylindrical Rankine vortex with a solid-body core and a linearly diminishing vorticity ‘skirt' surrounding the core. We then inserted a small cylindrical perturbation vortex inside this vorticity gradient. We hypothesized that if the perturbation vortex was of the same sign as the Rankine vortex, the smaller vortex would be drawn in toward (and merged into) the core as it was advected around by the background flow. Conversely, we anticipated that if the vortices were of opposite sign, the perturbation vortex would be ejected away from the core. Additionally, we expected that a stronger perturbation vortex and/or vorticity gradient would accelerate the merger or expulsion effect. Thus, we ran a parametric suite of simulations with varying combinations of values (vorticity sign and magnitude, initial positions, and vorticity gradient strength and radius) for both vortices. In general, our hypotheses were confirmed, but there were some unexpected results as well.

Keywords: tornado, vortex, vortex interaction, vorticity gradient, numerical simulation