Temporal decay of vortex line density in rotating thermal counterflow of He II

TL;DR

This study investigates how rotation affects the decay of vortex line density in superfluid helium-4 counterflow, revealing geometry-dependent effects and the influence of Ekman layers on decay behavior.

Contribution

It provides new insights into the decay dynamics of quantum turbulence under rotation, highlighting the role of geometry and Ekman layers in vortex line density decay.

Findings

Decay exponent decreases with rotation, indicating two-dimensional features.

Rotation geometry influences the impact of Ekman layers on decay.

Faster rotation leads to non-power-law, steeper decay regimes.

Abstract

Horizontally ($\mathbf{\Omega} \perp \mathbf{v}_{\rm{ns}}$) and axially ($\mathbf{\Omega} \parallel \mathbf{v}_{\rm{ns}}$) rotating counterflow of superfluid $^4$He (He~II) generated thermally in a square channel is studied using the second sound attenuation technique, detecting statistically steady state and temporal decay of the density of quantized vortex lines $L(t,\Omega)$. The array of rectilinear quantized vortices created by rotation at angular velocity $\Omega$ strongly affects the transient regimes of quantum turbulence characterized by counterflow velocity $\mathbf{v}_{\rm{ns}}$, differently in both geometries. Two effects are observed, acting against each other and affecting the late temporal decay $L(t,\Omega)$. The first is gradual decrease of the decay exponent $\mu$ of the power law $L(t,\Omega) \propto t^{-\mu}$, associated with the fact that under rotation thermal counterflow acquires two-dimensional features, clearly observed and recently reported by us (Phys. Fluids \textbf{36}, 105121 (2024)) in the $\mathbf{\Omega} \parallel \mathbf{v}_{\rm{ns}}$ geometry. It exists in the $\mathbf{\Omega} \perp \mathbf{v}_{\rm{ns}}$ geometry as well, however, it is screened here by the influence of the effective Ekman layer built within the effective Ekman time of order seconds. For faster rotation rates $L(t,\Omega)$ gradually ceases to display a clear power law. Instead, rounded and ever steeper decays occur, gradually shifted toward shorter and shorter times, significantly shortening the time range for a possible self-similar decay of vortex line density. This effect is not observed in $\mathbf{\Omega} \parallel \mathbf{v}_{\rm{ns}}$ geometry, as here the much longer effective Ekman time of order minutes cannot affect the observed $L(t,\Omega)$ decay appreciably.