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

Demosthenes Kivotides,Anthony Leonard

doi:10.1017/jfm.2020.1003

Abstract

Highlights

Physics is often formulated in terms of conservation laws which, according to Noether’s theorem, correspond to symmetries of key variables and their dynamical equations under 911 A25-1D
Vortex links are destroyed by reconnections which are facilitated by viscous diffusion that allows vortex lines to slip past each other
Our research suggests that disconnecting the reconnection phenomenon from its underlying physical mechanism (e.g. viscous dissipation in classical fluids, quantum stress action in quantum fluids or scissors and glue in Christmas ribbons (Pfister & Gekelman 1990)) can help understand better the experiments of Scheeler et al (2014)

Summary

Introduction

Physics is often formulated in terms of conservation laws which, according to Noether’s theorem, correspond to symmetries of key variables and their dynamical equations under 911 A25-1D. In the case of inviscid, incompressible fluids, there are additional conservation laws that emanate from the fluid–particle relabelling symmetry (Padhye & Morrison 1996; Kambe 2007; Fukumoto 2008; Araki 2015, 2018; Kedia et al 2018) This symmetry entails that, in the field-theoretic picture, the Eulerian flow velocity u(x, t) remains invariant when, in the corresponding material or Lagrangian picture, the initial-time fluid–particle coordinate parametrization is arbitrarily changed. This leads to the global invariance of the inner product of velocity with frozen in the flow vector fields (Fukumoto 2008), whose initial values could be identified with the above mentioned arbitrary change of fluid–particle labels.

Objectives

Methods

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Conclusion