Physical interpretation of certain invariants for vortex filament motion under LIA

Abstract

In the context of the localized induction approximation (LIA) for the motion of a thin vortex filament in a perfect fluid, the present work deals with certain conserved quantities that emerge from the Betchov–Da Rios equations. Here, by showing that these invariants belong to a countable family of polynomial invariants for the related nonlinear Schrödinger equation (NLSE), it is demonstrated how to interpret them in terms of kinetic energy, pseudohelicity, and associated Lagrangian. It is also shown that under LIA both linear momentum and angular momentum are conserved quantities and the relation between these quantities and the whole family of polynomial invariants is discussed.