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 stro ng sound signal due to significant distortion and stretching of the vo rtex filament. At the far field, the acoustic pressure is linearly dep endent on the third time derivatives of the vortex positions. Therefor e, a numerical scheme of high resolution is employed to describe in de tail the elliptic vortex ring motions, which are highly non-linear. Di scretized vortex filaments are interpolated by using a parametric blen ding function to remove a possible numerical instability. The distorte d 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 comp arisons 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 a nd acoustic signals from two identical elliptic vortex rings, placed i nitially 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 calcul ated periods in the acoustic signals depend to a significant degree on the initial aspect ratio of the ring and the separation distance. (C) 1997 Academic Press Limited.