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

Abstract

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.

arXiv comment13 pages, 18 figures

References in corpus (8)

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Cited by in corpus (14)

• Numerical Studies of Quantum Turbulence
• Fully Coupled Two-Fluid Dynamics in Superfluid ${}^4$He: Anomalous Anisotropic Velocity Fluctuations in Counterflow
• Three-Dimensional Coupled Dynamics of Two-Fluid Model in Superfluid ${}^4$He: Deformed Velocity Profile of Normal Fluid in Thermal Counterflow
• Dissipation in quantum turbulence in superfluid ${}^4$He above 1K
• Coupled normal fluid and superfluid profiles of turbulent helium II in channels
• Spherically symmetric formation of localized vortex tangle around a heat source in superfluid ${}^4$He
• Coupled dynamics for superfluid ${}^4$He in the channel
• Large-scale normal fluid circulation in helium superflows
• Logarithmic velocity profile of quantum turbulence of superfluid ${}^4$He
• Numerical Study on Entrance Length in Thermal Counterflow of Superfluid ${}^4$He
• Coflow turbulence of superfluid ${}^4$He in a square channel: Vortices trapped on a cylindrical attractor
• Dynamics of turbulent plugs in a superfluid ${}^4$He channel counterflow
• Dynamics of the vortex line density in superfluid counterflow turbulence
• Quantum turbulence in coflow of superfluid ${}^4$He