Introduction to Superfluid Vortices and Turbulence

Abstract

My aim in this article is to introduce the basic properties of quantized vortex lines in Helium II and summarize the main experimental observations of superfluid turbulence. Then I shall discuss a selection of the theoretical methods used to study quantized vorticity and turbulence and the results obtained using these methods.

The liquid state of ⁴He exists in two phases: a high temperature phase called Helium I, and a low temperature phase, called Helium II. The two phases are separated by a transition called the lambda transition, which occurs at the critical temperature T = Tλ = 2.172 K at saturated vapour pressure and marks the onset of Bose Einstein condensation (BEC) and quantum order. The phenomenon of BEC is described in the article of Stringari. Helium I is a classical fluid which obeys the ordinary Navier - Stokes equations. Hereafter the focus of attention is only Helium II.

A simple, phenomenological model which explains the motion of Helium II is the two - fluid theory of Tisza and Landau [1]. In this model Helium II is described as the intimate mixture of two fluid components which penetrate each others, the normal fluid and the superfluid. Each fluid component has its own density and velocity fleld, ρn and vn for the normal fluid and ρs and vs for the superfluid. The total density of Helium II is ρ = ρn + ρs. The superfluid component is irrotational, and, since it carries nor entropy nor viscosity, is similar to a classical, inviscid Euler fluid. The normal fluid component is a gas of thermal excitations called phonons and rotons depending on the wavenumber. The normal fluid carries the entire entropy and viscosity of Helium II and is similar to a classical, viscous Navier - Stokes fluid.