Classical Vs. Superfluid Turbulence

L. Skrbek, Steven R. Stalp

Григорий Ефимович Воловик

We argue that turbulence in superfluids is governed by two dimensionless parameters. One of them is the intrinsic parameter q which characterizes the friction forces acting on a vortex moving with respect to the heat bath, with q −1 playing the same role as the Reynolds number Re= UR/ν in classical hydrodynamics. It marks the transition between the “laminar” and turbulent regimes of vortex dynamics. The developed turbulence described by Kolmogorov cascade occurs when Re≫1 in classical hydrodynamics, and q ≪1 in superfluid hydrodynamics. Another parameter of superfluid turbulence is the superfluid Reynolds number Re s = UR/κ , which contains the circulation quantum κ characterizing quantized vorticity in superfluids. This parameter may regulate the crossover or transition between two classes of superfluid turbulence: (i) the classical regime of Kolmogorov cascade where vortices are locally polarized and the quantization of vorticity is not important; (ii) the quantum Vinen turbulence whose properties are determined by the quantization of vorticity. A phase diagram of the dynamical vortex states is suggested.

Григорий Ефимович Воловик

Yuan Tang, Sosuke Inui, Yiming Xing +2 more

Single-body diffusion and two-body dispersion are fundamental processes in classical turbulence, governing particle mixing and transport. However, their behaviors in superfluid turbulence remain largely unexplored. In this study, we numerically investigate the diffusion and relative dispersion of both quantized vortices and superfluid parcels in the 0 K limit in two distinct turbulence regimes: ultraquantum turbulence, characterized by a randomized vortex tangle, and quasiclassical turbulence, in which locally polarized vortices create large-scale flows resembling classical turbulence. Our results reveal that while vortex segments exhibit similar superdiffusion behavior at short times in both regimes, superfluid parcels behave differently—following the same superdiffusion scaling in ultraquantum turbulence but deviating significantly in quasiclassical turbulence. This contrast provides a key clue to the origin of short-time superdiffusion, a puzzle since its recent discovery. Additionally, we show that two-body dispersion of both vortex segments and superfluid parcels exhibits distinct scaling behaviors in ultraquantum and quasiclassical turbulence, highlighting fundamental differences in these two turbulence regimes. Our findings bridge a critical gap in superfluid turbulence research, offering useful insights into turbulent transport in inviscid quantum fluids.

Hiromitsu Takeuchi

ABSTRACT We theoretically study the line density of quantum vortices in a superfluid turbulent wake based on the conjecture of quantum turbulence of a pure superfluid in the zero temperature limit. The conjecture states that a collection of many quantum vortices can mimic a classical eddy in the continuum approximation. By straightforwardly relating the Kolmogorov's similarity to this conjecture, we can estimate that the effective viscosity of a pure superfluid turbulence is comparable to the circulation quantum , the minimum circulation of quantum vortices. This result naturally leads to a definition of the superfluid Reynolds number, with the characteristic size and velocity , supported by the fact that the equation of motion of a pure superfluid reduces to the Euler equation for high . By using the classical description of the rate of energy injection or dissipation, we quantitatively evaluate a characteristic density of vortex lines in a superfluid turbulent wake and its spatial profile of grid turbulence in terms of the superfluid Reynolds number.

C. P. Lorenson