Superfluid turbulence

Abstract

At low temperatures (below 5 Kelvin), helium is a liquid with a very low kinematic viscosity. It was proposed that wind tunnels could be built using liquid helium as the test fluid. The primary advantages of such wind tunnels would be a combination of large Reynolds numbers and a relatively small apparatus. It is hoped that this combination will allow the study of high Reynolds number flows in an academic setting. There are two basic types of liquid helium wind tunnels that can be built, corresponding to the two phases of liquid helium. The high temperature phase (between approximately 2 to 5 Kelvin) is called helium 1 and is a Navier-Stokes fluid. There are no unanswered scientific questions about the design or operation of a wind tunnel in the helium 1 phase. The low temperature phase (below approximately 2 Kelvin) of liquid helium is called helium 2. This is a quantum fluid, meaning that there are some properties of helium 2 which are directly due to quantum mechanical effects and which are not observed in Navier-Stokes fluids. The quantum effects that are relevant to this paper are: (1) helium 2 is well described as a superposition of two separate fluids called the superfluid and the normal fluid. The normal-fluid component is a Navier-Stokes fluid and the superfluid is an irrotational Euler fluid; and (2) circulation in the superfluid exists only in quantized vortex filaments. All quantized vortex filaments have identical circulations kappa and core size a. The objective of the research at CTR was to develop an understanding of the microscopic processes responsible for the observed Navier-Stokes behavior of helium 2 flows.