Quantum hydrodynamics investigates the dynamics of quantum fluids, which emerges owing to quantum condensations at ultralow temperatures, e.g., superfluid ⁴He, superfluid ³He, and atomic Bose-Einstein condensates. An important topic is the turbulent state of quantum fluids, known as quantum turbulence (QT). QT can be realized as the chaotic tangle of quantized vortices, which exhibit definite circulation around the vortex core.

Based on the two-fluid model, superfluid ⁴He is an intimate mixture of an inviscid superfluid and a viscous normal fluid. The two fluids interact through mutual friction via quantized vortices. An interesting topic is QT coupled with normal-fluid turbulence. This coupled dynamics may be related to unsolved experimental phenomena, such as the turbulent-turbulent transition of a superfluid (i.e., the T1-T2 transition).

This study aims to demonstrate that QT can be enhanced by normal-fluid turbulence using coupled numerical simulation. Here, QT is excited by a counterflow between two fluids in superfluid ⁴He. The vortex filament model of the superfluid is coupled with the Navier-Stokes equations of the normal fluid. Normal-fluid turbulence is driven by external forces. Notably, the fast multipole method is introduced to significantly accelerate the calculation of the superfluid velocity.

Our simulations show that QT develops into a statistically steady state. The figure shows that QT comprises a tangle of vortex filaments (blue lines), whereas the normal-fluid vortex tubes (magenta surfaces) are disturbed. Two cases with different forcing amplitudes for the same counterflow velocity are visualized. As the force increases, the vortex tangle becomes denser.

We analyzed the vortex line density L, which is the length of vortex filaments per unit volume. As shown in the figure, the values of L temporally averaged over the statistically steady states increased with the normal-fluid velocity fluctuation I. This suggests that the normal-fluid turbulence enhances the QT through mutual friction and increases . Finally, we investigated an important statistical law of QT: L^1/2=γ(V_ns–V₀). Our simulations confirmed that this law is satisfied even for QT coupled with normal-fluid turbulence. The response coefficient γ has been measured in many experiments. The experimental value of I is approximately 0.35 when the normal fluid is turbulent. We revealed that γ increased with the velocity fluctuation I and that the value is consistent with the experimental value at I=0.35. These results confirmed that QT can be enhanced by normal-fluid turbulence.

(Written by Satoshi Yui on behalf of all authors)

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