Sound radiation from elliptic vortex rings: Evolution and interaction

Sound generation from the evolution and interaction of elliptic vortex rings is calculated numerically. An elliptic vortex ring emits a strong sound signal due to significant distortion and stretching of the vortex filament. At the far field, the acoustic pressure is linearly dependent on the third time derivatives of the vortex positions. Therefore, a numerical scheme of high resolution is employed to describe in detail the elliptic vortex ring motions, which are highly non-linear. Discretized vortex filaments are interpolated by using a parametric blending function to remove a possible numerical instability. The distorted vortex filament, owing to the self-induced velocity and the induced velocity from the other vortex segments, is redistributed at each time step. The accuracy and efficiency of the scheme are validated by comparisons with the analytic solution of circular vortex ring interaction. Acoustic signals from the evolution of a single elliptic vortex ring are obtained with various aspect ratios of the axes. Vortex motions and acoustic signals from two identical elliptic vortex rings, placed initially with selected separation distances, are calculated. Distinct periods are obtained from the evolution of each single elliptic vortex ring and the pairing process of two elliptic vortex rings. The calculated periods in the acoustic signals depend to a significant degree on the initial aspect ratio of the ring and the separation distance.