Generalization of the Kutta–Joukowski theorem for the hydrodynamic forces acting on a quantized vortex

Abstract

The hydrodynamic forces acting on a quantized vortex in a superfluid have long been a highly controversial issue. A new approach, originally developed in the astrophysical context of compact stars, is presented to determine these forces by considering small perturbations of the asymptotically uniform flows in the region far from the vortex in the framework of Landau–Khalatnikov two-fluid model. Focusing on the irrotational part of the flows in the Helmholtz decomposition, the classical Kutta–Joukowski theorem from ordinary hydrodynamics is thus generalized to superfluid systems. The same method is applied to predict the hydrodynamic forces acting on vortices in cold atomic condensates and superfluid mixtures.