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

TL;DR

This paper generalizes the classical Kutta-Joukowski theorem to superfluid systems, providing a new method to calculate hydrodynamic forces on quantized vortices using a perturbation approach in the Landau-Khalatnikov two-fluid model.

Contribution

It introduces a novel approach, borrowed from astrophysics, to extend the Kutta-Joukowski theorem for superfluid vortices, applicable to cold atomic condensates and superfluid mixtures.

Findings

Generalized Kutta-Joukowski theorem for superfluids.

Predicted hydrodynamic forces on vortices in superfluid systems.

Applicable to cold atomic condensates and superfluid mixtures.

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.