Helicity spectra and topological dynamics of vortex links at high Reynolds numbers

Demosthenes Kivotides, Anthony Leonard

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Abstract

We employ reconnection-capable, vortex filament methods and finite-volume, Navier-Stokes flow solvers to investigate the topological and helicity dynamics of vortex links for medium and high Reynolds numbers. Our vortex-dynamical model is based on discretization of vortex tubes into bundles of numerical analogues of vortex lines. Due to their nearly singular nature, the numerical vortex lines have topological writhe but not twist. By means of our reconnecting vortex tube model, it is shown that the helicity of a vortex link is conserved during the unknotting process. The dynamics of linking and writhe topological measures indicate that most of the initial linking becomes writhe during the post-reconnection evolution. The helicity spectra of the vortex link present alternating-sign helicity fluctuations at all (potential flow) scales up to the vortex core. At pre-reconnection times, these fluctuations are damped by Biot-Savart vortex stretching and helicity becomes single signed. The post-reconnection spectra indicate an inverse helicity cascade corresponding to the creation of a homogenized vortex blob, a process reminiscent of coherent structure formation in turbulence. An accompanying Navier-Stokes calculation of vortex link dynamics at Reynolds numbers confirms the post-reconnection transformation of linking into different topological measures, the pre-reconnection damping of helicity spectra fluctuations and the spectral shift to low wavenumbers at post-reconnection times. Due to viscous dissipation action, however, this shift is accompanied by progressive reduction of helicity peak values.

Original languageEnglish
Article numberA25
Number of pages18
JournalJournal of Fluid Mechanics
Volume911
Early online date28 Jan 2021
DOIs
Publication statusPublished - 25 Mar 2021

Keywords

  • Navier-Stokes
  • Reynolds numbers
  • conservation laws

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