Acoustic emissions by vortex motions

Abstract

Fundamental aspects of the acoustic emission by vortex motions are considered by summarizing our recent work. Three typical cases are presented as illustrative examples: (i) head-on collision of two vortex rings, (ii) a vortex ring moving near a circular cylinder, and (iii) a vortex ring moving near a sharp edge of a semi-infinite plate. The theory of aerodynamic sound for low-Mach-number motion of an inviscid fluid predicts that the amplitude of the acoustic pressure in the far field is proportional to U4, U3 and U2.5 for (i)-(iii) respectively, where U is the translation velocity of a single vortex ring. Therefore the vortex-edge interaction generates the most powerful sound among the three cases at low Mach numbers. Our observations have confirmed these scaling laws. In addition to the scaling properties, we show the wave profiles of the emission as well as the directionality pattern. The head-on collision radiates waves of quadrupole directionality, whereas waves of dipole property are originated by the vortex-cylinder interaction. The third, vortex-edge, interaction generates waves of a cardioid directionality pattern. The wave profiles of all three cases are related to the time derivatives of the volume flux (through the vortex ring) of an imaginary potential flow which is characteristic of each configuration, although the orders of the time derivatives are different for each case. The observed profiles are surprisingly well fitted to the curves predicted by the theory, except the final period of the first case, in which viscosity is assumed to play an important role. The observed wave profiles are shown in a perspective diagram.