An Axisymmetric Viscous Vortex Motion and Its Acoustic Emission

Numerical simulation of head-on collision of two vortex rings has been made for various values of a translation Reynolds number from 50 to 500, and the profile of the acoustic wave emitted by the vortex collision is determined by using the computed development of the stream function and vorticity distributions. It is found for the higher Reynolds number range that there is an early stage during which the strength of each vortex is conserved, however, the strength decreases rapidly from an instant when the cores of the two vortices come into contact. The total kinetic energy decreases similarly. The enhancement of the energy dissipation is found to be related to the vortex stretching at the time of collision. The wave pressure is composed of two components, and comparison with experimental data obtained at much higher Reynolds numbers indicates reasonable agreement for the main quadrupole component.