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

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.