Intrinsic winding of braided vector fields in tubular subdomains

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 vortex dynamics, elasticity, bio-elasticity. Often field’s topology—the entanglement of its field lines—is non-trivial, can significant evolution. We present complete topological characterisation (up isotopy) using quantity called line winding. This measures each with all other lines field, may be defined for an arbitrary tubular subdomain by prescribing minimally distorted coordinate system. propose how define coordinates, prove that resulting winding distribution uniquely classifies topology braided field. The is similar helicity considered previously magnetic (solenoidal) fields, but more fundamental measure because it does not conflate linking information strength.