Fully Coupled Two-Fluid Dynamics in Superfluid ${}^4$He: Anomalous Anisotropic Velocity Fluctuations in Counterflow

Abstract

We investigate the thermal counterflow of the superfluid ${}^4$He by numerically simulating three-dimensional fully coupled dynamics of the two fluids, namely quantized vortices and a normal fluid. We analyze the velocity fluctuations of the laminar normal fluid arising from the mutual friction with the quantum turbulence of the superfluid component. The streamwise fluctuations exhibit higher intensity and longer-range autocorrelation, as compared to transverse ones. The anomalous fluctuations are consistent with visualization experiments [Mastracci et al., Phys. Rev. Fluids, Vol. 4, 083305 (2019)], and our results confirm their analysis with simple models on the anisotropic fluctuations. This success validates the model of the fully coupled dynamics and paves the way for solving some outstanding problems in this two-fluid system.

arXiv comment7 pages, 6 figures

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• Bathtub vortex in superfluid ${}^4$He
• Statistical laws and self-similarity of vortex rings emitted from a localized vortex tangle in superfluid ${}^4$He
• Eulerian and Lagrangian second-order statistics of superfluid ${}^4$He grid turbulence
• Reproduction of vortex lattices in the simulations of rotating liquid helium-4 by numerically solving the two-fluid model using smoothed-particle hydrodynamics incorporating vortex dynamics
• Particle approximation of the two-fluid model for superfluid ${}^4$He using smoothed particle hydrodynamics
• Theoretical framework bridging classical and quantum mechanics for the dynamics of cryogenic liquid helium-4 using smoothed-particle hydrodynamics
• Boiling and cavitation caused by transient heat transfer in superfluid helium-4
• Coupled dynamics of quantized vortices and normal fluid in superfluid ${}^4$He based on lattice Boltzmann method
• Numerical model of the Gross-Pitaevskii equation for rotating Bose-Einstein condensates using smoothed-particle hydrodynamics
• Vinen's latest thoughts on the "bump'' puzzle in decaying He II counterflow turbulence
• A hydrodynamic approach to reproduce multiple spinning vortices in horizontally rotating three-dimensional liquid helium-4
• Theory of anisotropic superfluid He-4 counterflow turbulence
• Studies on quantum turbulence with Vinen
• Transient heat transfer of superfluid ${}^4$He in nonhomogeneous geometries -- Part I: Second sound, rarefaction, and thermal layer
• Multi-scale physics of cryogenic liquid helium-4: Inverse coarse-graining properties of smoothed particle hydrodynamics