Relativistic solution of Iordanskii problem in multi-constituent superfluid mechanics

Abstract

Flow past a line vortex in a simple perfect fluid or superfluid gives rise to a transverse Magnus force that is given by the well known Joukowski lift formula. The problem of generalising this to multiconstituent superfluid models has been controversial since it was originally posed by the work of Iordanski in the context of the Landau 2-constituent model for He-4 at finite temperature. The present work deals not just with this particular case but with the generic category of perfect multiconstituent models including the kind proposed for a mixture of He-4 and He-3 by Andreev and Bashkin. It is shown here (using a relativistic approach) that each constituent will provide a contribution proportional to the product of the corresponding momentum circulation integral with the associated asymptotic current density.