Monday 19 Mar 2018: Helicity, enstrophy and circulation scaling for Navier-Stokes reconnection
Prof. Robert Kerr - University of Warwick
Three-dimensional images of evolving numerical trefoil vortex knots are used to study the growth and decay of the enstrophy and helicity. In Kerr (2018a), negative helicity density (h<0) is found to play several roles. During anti-parallel reconnection, sheets of oppositely signed helicity dissipation create negative helicity such that the global helicity H can be preserved through the first reconnection as suggested theoretically (Laing et al 2015 Sci. Rep. 5 9224) and observed experimentally (Scheeler et al 2014a Proc. Natl Acad. Sci. 111 15350–5). This negative helicity is transported to large scales which prevents a bottleneck of small-scale positive helicity forming where the enstrophy grows with ν-independent decreasing 1/√(√νZ(t)) up to the end of the first reconnection. Kerr (2018b) shows that the new enstrophy scaling begins with a finite exchange of circulation and compares with mathematical bounds for enstrophy growth when the domain is too small. Finally, algorithms for calculating the topological twist Tw and centreline helicity Hc of closed vortex trajectories are introduced that extend writhe Wr and self-linking LS algorithms discussed in Kerr (2018a). Being able to determine all of these topological numbers will allow their cross-validation.
Kerr, R.M. 2018a: Trefoil knot timescales for reconnection and helicity. Fluid Dynamics Res. 50, 011422.
Kerr, R.M. 2018b: Enstrophy and circulation scaling for Navier-Stokes reconnection. J. Fluid Mech. 839, R2.