OBLIQUE COLLISION OF 2 VORTEX RINGS AND ITS ACOUSTIC-EMISSION

A theory of vortex sound is formulated in the form of multipole expans ions and an explicit formula is presented for the wave pressure excite d by a time-dependent vorticity field localized in space. This is appl ied to the case of the oblique collision of two vortex rings at right angles, in which higher-order terms are important to represent asymmet ric emission. The vortex motion and the generated waves are also studi ed experimentally and numerically. The initial setup of the two vortic es is arranged so that they come into contact by their own motions and perform a reconnection of the vortex lines. The acoustic waves genera ted by the vortex motion have been observed in the far field in the la boratory, and the detected pressure signals are represented as a serie s of several dominant modes of the spherical harmonics. Morphological development of the vortices and trajectories of the vortex cores in th e collision process are observed by optical means. Computer simulation of the vortex motion has been carried out for a viscous incompressibl e fluid at a lower Reynolds number than that of the experiment. The ev olution of the vorticity field thus obtained can be used to predict th e wave profile by using the theoretically derived formula. The corresp onding wave modes, obtained from both Iaboratory experiment and comput er simulation independently, are compared. It is remarkable that two m ain quadrupole modes (two second-order spherical harmonics) are in qua litative agreement between the two cases. Third-order modes are also e stimated, and one mode is responsible for the characteristic emission of asymmetric waves observed in the experiment, which is associated wi th the details of the collision process.