Direct simulation of acoustic sound generated by two vortex rings

Acoustic sounds generated by oblique collisions of two vortex rings with an equal strength are simulated numerically. By a finite difference method, the three-dimensional, unsteady, compressible Navier-Stokes equations are solved directly. The sixth-order accurate compact Fade scheme is used for spatial derivatives, together with the fourth-order accurate Runge-Kutta scheme for time integration. Four different values of collision angle of the two vortex rings are prescribed and effects of the collision angle on the vortex motion and sound generation are examined. Results show that the quadrupolar component of vortex sound is predominant for the case of head-on collision while for the case of oblique collision the octupolar component is also observed.