SOUND GENERATION IN OBLIQUE COLLISION OF 2 VORTEX RINGS

A theory of vortex sound formulated in the form of multipole expansion s is applied to the oblique collision of two vortex rings at right ang les. Using the theoretical formula for the far-field acoustic pressure excited by a time-dependent localized vorticity distribution, the coe fficients of the multipole modes of the wave pressure are estimated by the numerical data of computer simulation. Time evolution of the vort icity field is obtained by solving a viscous incompressible vorticity equation with a vorticity-potential method developed for a three-dimen sional vorticity field in a bounded domain, Numerical simulations are carried out for two kinds of vortex rings with the same core parameter s but different ring radii, and the details of the vortex motion durin g the oblique collision are studied numerically. Computed main-mode am plitudes of the wave pressure excited by the vortex motion are found t o be consistent with those of the experimentally observed acoustic wav e not only qualitatively but also quantitatively. From comparison of t he quadrupole and octapole modes of the far-field acoustic pressure be tween the computation and the experiment, it is possible to estimate t he slenderness ratio of a core radius to a ring radius of the experime ntal vortex ring. It is remarkable that the present simulation gives d ata identifying the source region for the wave emission. Strong acoust ic source is identified at the location where vorticity field varies v er) rapidly during vortexline reconnection.