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

Abstract

Horizontally ($\mathbf{\Omega }\perp {\mathbf{v}}_{\mathrm{ns}}$) and axially ($\mathbf{\Omega }\parallel {\mathbf{v}}_{\mathrm{ns}}$) 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 ${\mathbf{v}}_{\mathrm{ns}}$, 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 $\mathbf{\Omega }\parallel {\mathbf{v}}_{\mathrm{ns}}$ geometry. It exists in the $\mathbf{\Omega }\perp {\mathbf{v}}_{\mathrm{ns}}$ 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 $\mathbf{\Omega }\parallel {\mathbf{v}}_{\mathrm{ns}}$ geometry, as here the much longer effective Ekman time of order minutes cannot affect the observed $L(t,\Omega )$ decay appreciably.

6 pages, 3 figures