The interaction of perturbed vortex rings and its sound generation

Interactions of two coaxial vortex rings of thin cores with and without azimuthal instability and the far field sound radiated have been studied numerically using the vortex blob method and acoustic analogy. The azimuthal instability waves of wavenumbers 1 ≤ m ≤ 5 are represented by weak axial and radial sinusoidal perturbations. It was found that the behaviour and the far field sound radiated of two perturbed vortices during the three slip throughs of 3 ≤ m ≤ 4 and during the first slip through of 1 ≤ m ≤ 5 are the same as those of unperturbed case m = 0. Because of their mutual induction, an unstable mode of the trailing vortex is found during the third slip through at m = 1 and 5, significantly lower wavenumbers compared with those of a single vortex ring. The far field sound radiated and their directivity, though still quadrupole, are different from those of unperturbed cases, showing the effect of perturbation on the interaction of the two vortices. A criterion for the onset of unstable mode is also established.