On the dynamics of vortex filaments and their core structure

Abstract

We give a brief review of the asymptotic theory of slender vortex filaments with emphases on (i) the choices of scalings and small parameters characterizing the physical problem, (ii) the key steps in the formulation of the theory and (iii) the assumptions and/or restrictions on the theory of Callegari and Ting (1978). We present highlights of an extension of the 1978 asymptotic theory:the analyses for core structures with axial variation. Making use of the physical insights gained from the analyses, we present a new derivation of the evolution equations for the core structure. The new one is simpler and straightforward and shows the physics clearly.