Abstract
We report an experimental study of oscillatory thermal counterflow of superfluid $^{4}\mathrm{He}$ and its transition to quantum turbulence inspired by the work of Kotsubo and Swift [Phys. Rev. Lett. 62, 2604 (1989)]. We use a pair of transversally oriented second-sound sensors to provide direct proof that upon exceeding a critical heat flux, quantized vorticity is generated in the antinodes of the longitudinal resonances of the oscillating counterflow. Building on modern understanding of oscillatory flows of superfluid $^{4}\mathrm{He}$ [D. Schmoranzer et al., Phys. Rev. B 99, 054511 (2019)], we re-evaluate the original data together with ours and provide grounds for the previously unexplained temperature dependence of critical velocities. Our analysis incorporates a classical flow instability in the normal component described by the dimensionless Donnelly number, which is shown to trigger quantum turbulence at temperatures below $\ensuremath{\approx}1.7\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. This contrasts with the original interpretation based on the dynamics of quantized vortices, and we show that for oscillatory counterflow, such an approach is valid only at temperatures above $\ensuremath{\approx}1.8\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. Finally, we demonstrate that the instabilities occurring in oscillatory counterflow are governed by the same underlying physics as those in flow due to submerged oscillators and propose a unified description of high Stokes number coflow and counterflow experiments.
Published Version
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