Dynamics of quantum turbulence in axially rotating thermal counterflow

TL;DR

This study investigates how axially rotating thermal counterflow in superfluid helium generates and decays quantum turbulence, revealing the effects of rotation on vortex dynamics and decay behavior.

Contribution

It provides new insights into the effects of rotation on quantum turbulence development, steady states, and decay in superfluid helium, highlighting the transition to two-dimensional turbulence.

Findings

Vortex line density growth is self-similar and linear in time.

Steady state vortex density is unaffected by rotation at high velocities.

Decay exponent decreases with rotation rate, indicating a transition to 2D turbulence.

Abstract

Generation, statistically steady state, and temporal decay of axially rotating thermal counterflow of superfluid $^4$He (He~II) in a square channel is probed using the second sound attenuation technique, measuring the density of quantized vortex lines. The array of rectilinear quantized vortices created by rotation strongly affects the development of quantum turbulence. At relatively slow angular velocities, the type of instability responsible for the destruction of the laminar counterflow qualitatively changes: the growth of seed vortex loops pinned on the channel wall becomes gradually replaced by the growth due to Donnelly-Glaberson instability, which leads to rapid growth of helical Kelvin waves on vortices parallel with applied counterflow. The initial transient growth of vortex line density that follows the sudden start of the counterflow appears self-similar, linear in dimensionless time, $\Omega t$. We show numerically that Kelvin waves of sufficiently strong amplitude reorient the vortices into more flattened shapes, which grow similarly to a free vortex ring. The observed steady state vortex line density at sufficiently high counterflow velocity and its early temporal decay after the counterflow is switched off is not appreciably affected by rotation. It is striking, however, that although the steady state of rotating counterflow is very different from rotating classical grid-generated turbulence, the late temporal decay of both displays similar features: the decay exponent decreases with the rotation rate $\Omega$ from -3/2 towards approximately -0.7, typical for two-dimensional turbulence, consistent with the transition to bidirectional cascade.