Scaling laws in vortex reconnection

This work is motivated by our longstanding claim that reconnection of coherent structures is the dominant mechanism of jet noise generation and plays a key role in both energy cascade and fine-scale mixing in fluid turbulence (Hussain 1983, 1986). To shed further light on the mecha nism involved and quantify its features, reconnection of two anti-parallel vortex tubes is studied by direct numerical simulation of the incompressible Navier-Stokes equations over a wide range (250- 9000) of the vortex Reynolds number. Re (= circula tion/viscosity) at much higher resolutions than have been attempted. Unlike magnetic or superfluid reconnections, viscous reconnection is never complete, leaving behind a part of the initial tubes as aL/thrcad- saL™, which then undergo successive reconnections (our cascade and mixing scenarios) as the newly formed aL/bridgesaL™ recoil from each other by self-advection. We find that the time t_R for orthog onal transfer of circulation scales as t_R Re^-3/4The shortest distance d between the tube centroids scales as d ≈ a(Re(t_o - t))^3/4 before reconnection (collision) and as d ≈ b(Re(t - t_o))² after reconnection (repulsion), where t_o is the instant of smallest separation between vortex centroids. We find that b is a constant, thus suggesting self-similarity, but a is dependent on Re. Bridge repulsion is faster than collision and is more autonomous as local induction predominates, and given the associated acceleration of vorticity, is potentially a source of intense sound generation. At the higher Re's studied, the tails of the colliding threads are compressed into a planar jet w ith multiple vortex pairs. For Re > 6000, there is an avalanche of smaller scales during the reconnection - the rate of small scale generation and the spectral content (in vorticity, transfer function and dissipation spectra) being quite consistent with the structures visualized by the ₂ criterion. The maximum rate of vortex circulation transfer, enstrophy production and dissipation scale asRe ¹ , Re^7/4 , Re ^-1/2 respectively. A more detailed study of subsequent reconnection of threads requires much higher-resolution simulations that are currently not feasible.