SPIRALITY OF VANISHING HELICITY FLOWS IN SOLID TORI DOMAINS

Abstract

Ideal nature of inviscid flows and persistency of field lines found a nice bridge between their dynamical properties and topological considerations which on the top of them is knottedness. Helicity as the simplest invariance in topological dynamics, lies in the cross road of these disciplines, both conceptually and practically. Spirality is a Lagrangian invariant that targeted in this paper which imparts the behaviors of each field line. In the present article a necessary and separately a sufficient condition are obtained for vanishing the spirality via a certain gauge transformation in a zero helicity flow. Geometrical interpretations of these conditions are presented and the possible relation between the existence of such a gauge and occurring singularities in vortex dynamics are discussed.