Oblique collision of two vortex rings and its acoustic emission

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Abstract
A theory of vortex sound is formulated in the form of multipole expansions and an explicit formula is presented for the wave pressure excited by a time-dependent vorticity field localized in space. This is applied to the case of the oblique collision of two vortex rings at right angles, in which higher-order terms are important to represent asymmetric emission. The vortex motion and the generated waves are also studied experimentally and numerically. The initial setup of the two vortices is arranged so that they come into contact by their own motions and perform a reconnection of the vortex lines. The acoustic waves generated by the vortex motion have been observed in the far field in the laboratory, and the detected pressure signals are represented as a series of several dominant modes of the spherical harmonics. Morphological development of the vortices and trajectories of the vortex cores in the collision process are observed by optical means. Computer simulation of the vortex motion has been carried out for a viscous incompressible fluid at a lower Reynolds number than that of the experiment. The evolution of the vorticity field thus obtained can be used to predict the wave profile by using the theoretically derived formula. The corresponding wave modes, obtained from both laboratory experiment and computer simulation independently, are compared. It is remarkable that two main quadrupole modes (two second-order spherical harmonics) are in qualitative agreement between the two cases. Third-order modes are also estimated, and one mode is responsible for the characteristic emission of asymmetric waves observed in the experiment, which is associated with the details of the collision process.

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