Scaling laws in vortex reconnection

Fazle Hussain, Karthik Duraisamy

Research output: Contribution to conferencePaper

Abstract

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 tR for orthog onal transfer of circulation scales as tR Re-3/4The shortest distance d between the tube centroids scales as d ≈ a(Re(to - t))3/4 before reconnection (collision) and as d ≈ b(Re(t - to))2 after reconnection (repulsion), where to 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 , Re7/4 , Re -1/2 respectively. A more detailed study of subsequent reconnection of threads requires much higher-resolution simulations that are currently not feasible.

Original languageEnglish
StatePublished - 2010
Event13th Asian Congress of Fluid Mechanics, ACFM 2010 - Dhaka, Bangladesh
Duration: Dec 17 2010Dec 21 2010

Conference

Conference13th Asian Congress of Fluid Mechanics, ACFM 2010
CountryBangladesh
CityDhaka
Period12/17/1012/21/10

Keywords

  • Coherent structures. turbulent cascade
  • Vortex reconnection

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    Hussain, F., & Duraisamy, K. (2010). Scaling laws in vortex reconnection. Paper presented at 13th Asian Congress of Fluid Mechanics, ACFM 2010, Dhaka, Bangladesh.