Journal of Low Temperature Physics

, Volume 178, Issue 1–2, pp 35–52 | Cite as

Thermal Counterflow in a Periodic Channel with Solid Boundaries

  • Andrew W. Baggaley
  • Jason Laurie


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 center. 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.


Superfluidity Quantized vortices Thermal counterflow  Transition to turbulence 



We would like to acknowledge Jeremie Bec and Risto Hänninen for helpful discussions. This work was supported by the Carnegie Trust.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUniversity of GlasgowGlasgowUK
  2. 2.Department of Physics of Complex SystemsWeizmann Institute of ScienceRehovotIsrael

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