Counterflow Quantum Turbulence Research Articles

Inhomogeneous distribution of particles in coflow and counterflow quantum turbulence

Particles are today the main tool to study superfluid turbulence and visualize quantum vortices. In this work, we study the dynamics and the spatial distribution of particles in co-flow and counterflow superfluid helium turbulence in the framework of the two-fluid Hall-Vinen-Bekarevich-Khalatnikov (HVBK) model. We perform three-dimensional numerical simulations of the HVBK equations along with the particle dynamics that depends on the motion of both fluid components. We find that, at low temperatures, where the superfluid mass fraction dominates, particles strongly cluster in vortex filaments regardless of their physical properties. At higher temperatures, as viscous drag becomes important and the two components become tightly coupled, the clustering dynamics in the coflowing case approach those found in classical turbulence, while under strong counterflow, the particle distribution is dominated by the quasi-two-dimensionalization of the flow.

Energy spectra of counterflow quantum turbulence at different temperatures

The spectrum of the energy generated by a vortex tangle in the counterflow of normal and superfluid components at different temperatures was obtained. The counterflow magnitude was varied from 0.3 cm/s to 1.2 cm/s and the temperature was varied from 1.3 K to 1.9 K. It was shown that at the distances of the order of intervortex separation, E(k) ∼ k−α, where 1.3 < α < 1.4 depending on the temperature. At larger distances, E(k) ∼ k−1. It was established that under the heat flux corresponding to the Gorter–Mellink regime, the density of energy dissipation is proportional to the cube of the counterflow of normal and superfluid components, i.e., the energy dissipation is due to the friction between the normal component of helium and the vortex tangle.

Counterflow quantum turbulence of He-II in a square channel: Numerical analysis with nonuniform flows of the normal fluid

We perform a numerical analysis of counterflow quantum turbulence of superfluid 4He with nonuni- form flows by using the vortex filament model. In recent visualization experiments nonuniform laminar flows of the normal fluid, namely, Hagen-Poiseuille flow and tail-flattened flow, have been observed. Tail-flattened flow is a novel laminar flow in which the outer part of the Hagen-Poiseuille flow becomes flat. In our simulation, the velocity field of the normal fluid is prescribed to be two nonuniform profiles. This work addresses a square channel to obtain important physics not revealed in the preceding numerical works. In the studies of the two profiles we analyze the statistics of the physical quantities. Under Hagen-Poiseuille flow, inhomogeneous quantum turbulence appears as a statistically steady state. The vortex tangle shows a characteristic space-time oscillation. Under tail-flattened flow, the nature of the quantum turbulence depends strongly on that flatness. Vortex line density increases significantly as the profile becomes flatter, being saturated above a certain flatness. The inhomogeneity is significantly reduced in comparison to the case of Hagen-Poiseuille flow. Investigating the behavior of quantized vortices reveals that tail-flattened flow is an intermedi- ate state between Hagen-Poiseuille flow and uniform flow. In both profiles we obtain a characteristic inhomogeneity in the physical quantities, which suggests that a boundary layer of superfluid appears near a solid boundary. The vortex tangle produces a velocity field opposite to the applied superfluid flow, and, consequently, the superfluid flow becomes smaller than the applied one.

Counterflow quantum turbulence in a square channel under the normal fluid with a Poiseuille flow

We perform a numerical analysis of superfluid turbulence produced by thermal counterflow in He II by using the vortex filament model. Counterflow in a low aspect ratio channel is known to show the transition from laminar flow to the two turbulent states TI and TII. The present understanding is that the TI has the turbulent superfluid and the laminar normal fluid but both fluids are turbulent in the TII state. This work studies the vortex tangle in the TI state. Solid boundary condition is applied to walls of a square channel, and the velocity field of the normal fluid is prescribed to be a laminar Poiseuille profile. An inhomogeneous vortex tangle, which concentrates near the solid boundaries, is obtained as the statistically steady state. It is sustained by its characteristic space-time oscillation. The inhomogeneity of the vortex tangle shows the characteristic dependence on temperature, which is caused by two effects, namely the profile of the counterflow velocity and the mutual friction.

Non-classical Velocity Statistics in Counterflow Quantum Turbulence

In this work we analyse the statistical distribution of turbulent superfluid velocity components in a He II counterflow channel, via two-dimensional numerical simulations presented in past studies. The Probability Density Functions (PDFs) of the superfluid velocity components are investigated at lengthscales smaller than the average intervortex spacing, for varying vortex densities and different wall-normal distances. The results obtained confirm the non-classical signature of quantum turbulence already observed in past numerical studies.

Decay of Counterflow Quantum Turbulence in Superfluid 4He

We have simulated the decay of thermal counterflow quantum turbulence from a statistically steady state at T=1.9[K], with the assumption that the normal fluid is at rest during the decay. The results are consistent with the predictions of the Vinen equation (in essence the vortex line density (VLD) decays as t^{-1}). For the statistically steady state, we determine the parameter c_2, which connects the curvature of the vortex lines and the mean separation of vortices. A formula connecting the parameter \chi_2 of the Vinen equation with c_2 is shown to agree with the results of the simulations. Disagreement with experiment is discussed.

Numerical study of velocity statistics in steady counterflow quantum turbulence

We investigate the velocity statistics by calculating the Biot-Savart velocity induced by vortex filaments in steady counterflow turbulence investigated in a previous study [H. Adachi, S. Fujiyama, and M. Tsubota, Phys. Rev. B 81, 104511 (2010).]. The probability density function (PDF) obeys a Gaussian distribution in the low-velocity region and a power-law distribution ${v}^{\ensuremath{-}3}$ in the high-velocity region. This transition between the two distributions occur at the velocity characterized by the mean intervortex distance. Counterflow turbulence causes anisotropy of the vortex tangle, which leads to a difference in the PDF for the velocities perpendicular to and parallel to the counterflow.

Counterflow Quantum Turbulence and the Instability in Two-component Bose-Einstein Condensates

We theoretically study the nonlinear dynamics of the instability of counter-superflow in two miscible Bose-Einstein condensates. The condensates become unstable when the relative velocity exceeds a critical value, which is called counter-superflow instability. We reveal that the counter-superflow instability can lead to quantum turbulence by numerically solving the coupled Gross-Pitaevskii equations. The modes amplified by the instability grow into solitons and decay into quantized vortices.Eventually, the vortices become tangled and quantum turbulence of two superfluids. We show that this process may occur in experiments by investigating the dynamics in a 2D trapped system.