Sound generation by head-on and oblique collisions of two vortex rings

Abstract

Sound generation by head-on and oblique collisions of two vortex rings with equal strength is investigated by a direct numerical simulation. The three-dimensional, unsteady, compressible Navier–Stokes equations are solved by a finite difference method, not only for a near-vortical field but also for a far-acoustic field. The theory of vortex sound is also applied to investigate the detailed relation between the vortex ring motion and the acoustic wave mode. Generation of two sound pressure waves, which are called the first and second pulses, is observed in the numerical results. The theoretical results show that, for the head-on collision, the generations of the first and second pulses are due to the variations of vorticity moment, associated with a decrease in the translational velocity of the vortex ring near the collision plane and its stretching motion, respectively. On the other hand, for the oblique collision, in addition to such generation mechanisms, the reconnection of vortex lines also affects the generation of the second pulse. The reconnection of vortex lines occurs more rapidly for a smaller collision angle, and therefore its contribution to the second pulse becomes large. In fact, in the oblique collision at a right angle, the generation of the second pulse is closely related to the reconnection of vortex lines, which can be seen by analyzing both the near and far fields. Furthermore, for a smaller collision angle, the reconnection of vortex lines leads to more rapid variation of the vorticity, which enhances asymmetric features of the second pulse exhibited by the octupole mode (third-order wave mode).