3-Dimensional Numerical Simulations of a Vortex Embedded within a Background Vorticity Gradient: Comparison with Theory

Furthering the progress from previous research (Adams et al, 2012, 2013), a more in-depth study of the interaction between a perturbation vortex and a background vorticity field was performed. Using an idealized 3-dimensional non-hydrostatic numerical model, a suite of simulations with varying parameters was run in which a vortex with a finite thickness was embedded within a background vorticity field and was observed as it was advected about the center. The observations were then quantified and compared to behavior outlined by Schecter and Dubin (2001) in a similar study, in which expressions describing the inward radial velocity of the perturbation vortex were derived. These expressions were then adapted to our system and tested with a similar set of varying parameters, however, with a more comprehensive set of parameters than before. Secondarily, Buker et al. (2010) proposed a relationship describing the acceleration of the vortex in a similar situation. These equations were also applied to our model, and a detailed comparison was made between our results, the equations for velocity derived by Schecter and Dubin, and the equations for acceleration derived by Buker et al. Our findings outline correlations between the theoretical work of others and the results produced by the model and implicate a better representation of the forces governing multi-vortex systems, as well as show promise for application outside of these idealized simulations.