Transition to Superfluid Turbulence

TL;DR

This paper investigates the transition to turbulence in superfluid 3He-B, revealing a temperature-dependent, velocity-independent parameter that governs vortex proliferation and employing a novel vortex injection technique to study this phenomenon.

Contribution

It introduces a new understanding of turbulence transition in superfluids based on a dimensionless parameter 1/q and employs a novel vortex injection method for experimental analysis.

Findings

Transition to turbulence is governed by the parameter 1/q, not the Reynolds number.

Vortex proliferation occurs at high 1/q values, indicating destabilization.

A new measurement technique involving vortex injection was successfully used.

Abstract

Turbulence in superfluids depends crucially on the dissipative damping in vortex motion. This is observed in the B phase of superfluid 3He where the dynamics of quantized vortices changes radically in character as a function of temperature. An abrupt transition to turbulence is the most peculiar consequence. As distinct from viscous hydrodynamics, this transition to turbulence is not governed by the velocity-dependent Reynolds number, but by a velocity-independent dimensionless parameter 1/q which depends only on the temperature-dependent mutual friction -- the dissipation which sets in when vortices move with respect to the normal excitations of the liquid. At large friction and small values of 1/q < 1 the dynamics is vortex number conserving, while at low friction and large 1/q > 1 vortices are easily destabilized and proliferate in number. A new measuring technique was employed to identify this hydrodynamic transition: the injection of a tight bundle of many small vortex loops in applied vortex-free flow at relatively high velocities. These vortices are ejected from a vortex sheet covering the AB interface when a two-phase sample of 3He-A and 3He-B is set in rotation and the interface becomes unstable at a critical rotation velocity, triggered by the superfluid Kelvin-Helmholtz instability.