Vortex sound with special reference to vortex rings: theory, computer simulations, and experiments

This is a review paper on vortex sound with special reference to vortex rings and sound emission detected in experimental tests. Any unsteady vortex motion excites acoustic waves. From the fundamental conservation equations of mass, momentum and energy of fluid flows, one can derive a wave equation of aerodynamic sound. The wave equation of acoustic pressure can be reduced to a compact form, called the equation of vortex sound. This equation predicts sound generation by unsteady vortex motions. On the other hand, based on the matched asymptotic expansion (using the multipole expansions), one can derive a formula of wave pressure excited by time-dependent vorticity field localized in space. The theoretical predictions are compared with experimental observations and direct computer simulations. The systems considered are, head-on collision or oblique collision of two vortex rings, vortex-cylinder interaction, vortex-edge interaction, and others. Scaling laws of the pressure of emitted sound are predicted by the theory and compared with experimental observations. Comparison between theories and observations shows excellence of the theoretical predictions. Direct numerical simulations are reviewed briefly for sound generation by collisions of two vortex rings and that by a cylinder immersed in a uniform stream (aeolian tones). Vortex sound in superfluid is also reviewed about experimental observations and computational studies on the basis of the Gross-Pitaevski equation.