Variational principle in dynamics of a vortex filament

Abstract

A variational principle governing the dynamics of a vortex filament in unbounded incompressible inviscid fluid flow was suggested by Rasetti and Regge [Physica A 80, 217 (1975)]. This variational principle holds in the approximation taking into account the logarithmically large terms, on the order of ln(La) , L and a being the length and the cross-section radius of the filament, respectively. In this approximation, the Hamiltonian is a function of L . Accordingly, the filament length L is constant in the course of motion. In this paper, a variational principle is obtained that takes into account also the terms on the order of unity. A characteristic feature of the more precise theory is the evolution of the filament length. The variational principle of the vortex filament dynamics is derived from the variational principle for the arbitrary vortex motion of an incompressible inviscid fluid found recently.