Transition to quantum turbulence in oscillatory thermal counterflow of 4He

We report an experimental study of oscillatory thermal counterflow of superfluid He-4 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 He-4 [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 approximate to 1.7 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 approximate to 1.8 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.