A Topological Defect Model Of Superfluid Vortices

. This paper introduces a nonlinear Schrodinger model for superfluid that captures the process of mutual friction between the superfluid and normal fluid components of helium II. Superfluid vortices are identified as topological defects in the solution of this equation. A matched asymptotic analysis of Neu [7] is adapted to derive an asymptotic dynamics for the vortices in the case they are widely separated compared with their core size. This motion agrees with the classical Hall and Vinen motion [5] in which phenomenological drag terms are added, ad hoc, to the motion of vortices in an inviscid fluid. Several simple examples are considered to illustrate the unique character of the motion of superfluid vortices. Finally, the motion of vortices in uniformly rotating helium II is considered, and a continuum approximation to their dynamics is obtained in the case of very many vortices. 1. Introduction When liquid helium is cooled to a temperature close to absolute zero it undergoes a pha..