Thermal counterflow in a periodic channel with solid boundaries

Abstract

We perform numerical simulations of finite temperature quantum turbulence produced through thermal counterflow in superfluid ${}^4$He, using the vortex filament model. We investigate the effects of solid boundaries along one of the Cartesian directions, assuming a laminar normal fluid with a Poiseuille velocity profile, whilst varying the temperature and the normal fluid velocity. We analyze the distribution of the quantized vortices, reconnection rates and quantized-vorticity production as a function of the wall-normal direction. We find that the quantized vortex lines tend to concentrate close to the solid boundaries with their position depending only on temperature and not on the counterflow velocity. We offer an explanation of this phenomenon by considering the balance of two competing effects, namely the rate of turbulent diffusion of an isotropic tangle near the boundaries and the rate of quantized-vorticity production at the centre. Moreover, this yields the observed scaling of the position of the peak vortex line density with the mutual friction parameter. Finally we provide evidence that upon the transition from laminar to turbulent normal fluid flow, there is a dramatic increase in the homogeneity of the tangle, which could be used as an indirect measure of the transition to turbulence in the normal fluid component for experiments.

14 pages, 13 figures

References in corpus (4)

• Visualization study of counterflow in superfluid helium-4 using metastable helium molecules
• Vortex line density in counterflowing He II with laminar and turbulent normal fluid velocity profiles
• Vortex density fluctuations in quantum turbulence
• Super Stability of Laminar Vortex Flow in Superfluid 3He-B

Cited by in corpus (18)

• 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
• Counterflow quantum turbulence of He II in a square channel: Numerical analysis with nonuniform flows of the normal fluid
• 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
• On the Nonuniform Quantum Turbulence in Superfluids
• Superfluid turbulence driven by cylindrically symmetric thermal counterflow
• Coupled dynamics for superfluid ${}^4$He in the channel
• Logarithmic velocity profile of quantum turbulence of superfluid ${}^4$He
• Large-scale normal fluid circulation in helium superflows
• 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 the vortex line density in superfluid counterflow turbulence
• Dynamics of turbulent plugs in a superfluid ${}^4$He channel counterflow
• Reconnection dynamics and mutual friction in quantum turbulence
• Modelling turbulent flow of superfluid ${}^4$He past a rough solid wall in the $T=0$ limit