How is superfluid turbulence enhanced by normal-fluid turbulence in counterflow?

Описание: One of the major unresolved problems in quantum hydrodynamics [1] of superfluid 4He is to understand the two-stage transition to turbulence in thermal counterflow — from the T1 state to the T2 state — and the nature of the fully developed turbulence in the T2 state. The T1 state is characterized by turbulence only in the superfluid component, whereas in the T2 state both the superfluid and the normal fluid are believed to become turbulent. However, it remains unclear what role superfluid turbulence (ST) plays in triggering the turbulent transition of the normal fluid in the T2 state.

This two-stage transition has remained a major mystery since the 1970s. Only recently, thanks to remarkable advances in flow visualization experiments [2] and the development of numerical simulations based on fully coupled two-fluid dynamics [3], it has become possible to address this problem quantitatively and systematically.

In this study, we perform numerical simulations based on a fully coupled two-fluid model [4]. In our framework, normal-fluid turbulence (NFT) is not obtained by directly solving the Navier–Stokes equation, but is instead generated and controlled by externally applied forcing, allowing us to systematically tune its turbulent intensity. The dynamics of ST are efficiently computed using the fast multipole method.

Our results show that NFT significantly enhances ST via mutual friction. The vortex line density L of ST obeys the Vinen’s relation L^{1/2}≈γVns, where Vns is the counterflow velocity, and we find that the response coefficient γ is amplified in the presence of NFT. These findings provide new theoretical insight into the mutual interaction between ST and NFT, and offer a step toward understanding the mechanism underlying the T1–T2 transition and the onset of turbulence in the normal fluid.

[1] M. Tsubota, K. Kasamatsu, Quantum Hydrodynamics and Turbulence (Oxford University Press, 2025).

[2] A. Marakov et al., Phys. Rev. B 91, 094503 (2015).

[3] S. Yui et al., Phys. Rev. Lett. 120, 155301 (2018); Phys. Rev. Lett. 124, 155301 (2020), L. Galantucci et al., Eur. Phys. J. Plus 135, 547 (2020); Phys. Rev. Lett. 136, 016601 (2026), Y. Tang et al., Nat. Commun. 14, 2941 (2023).

[4] S. Yui, H. Kobayashi, M. Tsubota, R. Yokota, J. Phys. Soc. Jpn. 94, 043601 (2025).