Recombination of two vortex filaments and jet noise

The recombination of two vortex filaments in a viscous incompressible fluid is analysed by the use of the vorticity equation. The analysis is confined to a local flow field, where the recombination process occurs, and is based on several assumptions, such as the conservation of the fluid impulse, spatial symmetry of the flow field etc. The flow field is expanded as polynomials of coordinates, and variations of their coefficients are obtained by the use of the vorticity equation. It is proved that the process is completed within a short time ofO (σ ²/Γ) and the viscous effect is essential;σ and Γ are the size and the circulation of the vortex filaments, respectively. This result is applied to predict the far-field noise of a circular jet by assuming that the main noise source is the recombination process in deformed vortex rings in the jet near field. The predicted noise intensity shows theU dependence and has an additional new factor (d/σ)⁶;U is the jet velocity andd is the average spacing between vortex rings.