Idealized 3-D Numerical Simulations of Tornado-like Multi-vortex Systems: Comparison with Theory

The interaction of satellite vortex structures and their impact on the development and maintenance of tornadoes are examined in an idealized numerical environment. Continuing from prior work (Adams et al., 2012), idealized numerical simulations were performed, initializing one or several perturbation columns of vertical vorticity within the “vorticity skirt” region of a larger Rankine vortex. We then tracked the mean position of the perturbation vortices over time, calculating its radial (inward) velocity and acceleration. Referencing previous work (Schecter and Dubin 2001), theoretical equations for the radial velocity and acceleration of a 2D perturbation point vortex embedded in a vorticity gradient were applied to our parameter space. We then compared these theoretical values to the results of the numerical experiments, as well as our own modified theoretical predictions based on an analogy between fluid mechanics and electromagnetism. Additionally, we also assessed the overall impact of the perturbation vortices on the evolution of the larger vortex. Correlations between the theoretical and numerical results suggest that a more universal representation of the forces governing the evolution of 3D multi-vortex systems can be achieved through the analogy.