Intrinsic winding of braided vector fields in tubular subdomains

Prior, Christopher B; Yeates, Anthony R

Abstract

Braided vector fields on spatial subdomains which are homeomorphic to the cylinder play a crucial role in applications such as solar and plasma physics, relativistic astrophysics, fluid and vortex dynamics, elasticity, and bio-elasticity. Often the vector field's topology—the entanglement of its field lines—is non-trivial, and can play a significant role in the vector field's evolution. We present a complete topological characterisation of such vector fields (up to isotopy) using a quantity called field line winding. This measures the entanglement of each field line with all other field lines of the vector field, and may be defined for an arbitrary tubular subdomain by prescribing a minimally distorted coordinate system. We propose how to define such coordinates, and prove that the resulting field line winding distribution uniquely classifies the topology of a braided vector field. The field line winding is similar to the field line helicity considered previously for magnetic (solenoidal) fields, but is a more fundamental measure of the field line topology because it does not conflate linking information with field strength.

Citation

Prior, C. B., & Yeates, A. R. (2021). Intrinsic winding of braided vector fields in tubular subdomains. Journal of Physics A: Mathematical and Theoretical, 54(46), Article 465701. https://doi.org/10.1088/1751-8121/ac2ea3

• Journal Article Type: Article
• Acceptance Date: Oct 11, 2021
• Online Publication Date: Nov 3, 2021
• Publication Date: 2021-11
• Deposit Date: Jan 14, 2022
• Publicly Available Date: Jan 14, 2022
• Journal: Journal of Physics A: Mathematical and Theoretical
• Print ISSN: 1751-8113
• Electronic ISSN: 1751-8121
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 54
• Issue: 46
• Article Number: 465701
• DOI: https://doi.org/10.1088/1751-8121/ac2ea3
• Public URL: https://durham-repository.worktribe.com/output/1219940