Mechanical momentum transfer in wall-bounded superfluid turbulence

TL;DR

This paper introduces a new effective viscosity, rm(T), in superfluid turbulence that explains the transfer of mechanical momentum to walls via quantum vortex tangles, differing from the traditional energy dissipation mechanism.

Contribution

It identifies and characterizes a novel temperature-dependent effective viscosity rm(T) responsible for momentum transfer in superfluid turbulence, distinct from Vinen's viscosity.

Findings

rm(T) varies markedly with temperature.

Vortex-tension force relates to the gradient of Reynolds stress tensor.

The new viscosity explains momentum flux in superfluid turbulence.

Abstract

In classical turbulence the kinematic viscosity $\nu$ is involved in two phenomena. The first is the energy dissipation and the second is the mechanical momentum flux toward the wall. In superfluid turbulence the mechanism of energy dissipation is different, and it is determined by an effective viscosity which was introduced by Vinen and is denoted as $\nu'$. In this paper we show that in superfluid turbulence the transfer of mechanical momentum to the wall is caused by the presence of a quantum vortex tangle, giving rise to another effective "momentum" viscosity that we will denote as $\nu_\text{m}(T)$. The temperature dependence of the second effective viscosity is markedly different from Vinen's effective viscosity $\nu'(T)$. We show that the notion of vortex-tension force, playing an important role in the theory of quantum turbulence, can be understood as the gradient of the Reynolds stress tensor which is in fact determined by the second newly defined kinematic viscosity $\nu_\text{m}(T)$.