A Numerical and Analytical Study of Vortex Rings with Swirl

We study the growth of disturbances to vortex rings with swirl, which are exact solutions of the Euler equations of inviscid ow, using two contrasting methods. The motion of the perturbed vortex rings can be regarded as a prototype for the inviscid dynamics of vortex structures in 3D. Exact rings with swirl are computed as steady, axisymmetric ows using a variational method. Asymptotic analysis in the short wave limit, similar to geometric optics, leads to ordinary diierential equations for perturbations along particle paths. These ODE's can be solved for the rings of interest, yielding predicted maximum growth rates for small disturbances. These rates are compared with the direct simulation of sample disturbances using a 3D vortex method to calculate the evolution according to the Euler equations.