Acoustic wave radiated by head-on collision of two vortex rings

Abstract

An attempt has been made to detect the acoustic wave radiated by the collision of two vortex rings and to compare it with predictions made by the theory of aerodynamic sound with and without fluid viscosity. The vortex rings generated in the experiment had translational speed 40 ≾ U ≾ 80 m/s and radius 5 ≾ R ≾ 9 mm, and their motion was studied optically by means of a photo-sensor system. The pressure signals of the emitted wave were measured by a microphone and analysed by digital methods. It has been found that the detected acoustic pressure p obeys the scaling law p ∝ ( ρ 0 / c 2 ) U 4 R / r predicted by the theory ( ρ 0 and c are the density and sound speed respectively in the undisturbed state, r is the distance of the observation point from the collision centre), and p possesses a typical peak value p * ≈ 5 Pa for U = 76 m/s and r/R = 93, and that the total acoustic energy of radiation is about 0.4 ( U/c ) 5 times the initial kinetic energy of the vortex system. Analysis of the observed signals shows that the acoustic pressure is com­posed of quadrupole and monopole radiation. Although the inviscid theory can account for the initial part of the detected signal quantita­tively, it fails to predict the appearance of the monopole, and it is also not possible to give even a qualitative description of the quadrupole in the later stages. A viscous theory is presented to obtain an improved fit to the observed profile. In the latter theory the monopole radiation is related to the viscous decay of total kinetic energy, and the main quadruple is affected by the decay of the vortex strength as a result of pair annihilation under the action of viscosity. Thus resonable agree­ment has been obtained between the detected and predicted waves. This has made it clear that the initial inviscid phase is followed by phases dominated by the action of viscosity.