Superfluid helium is an intimate mixture of a viscous normal fluid, with continuous vorticity, and an inviscid superfluid, where vorticity is constrained to thin, stable topological defects. One mechanism to generate turbulence in this system is through the application of a heat flux, so-called thermal counterflow. Of particular interest is how turbulence in the superfluid responds to both a laminar and turbulent normal fluid in the presence of walls. We model superfluid vortex lines as reconnecting space curves with fixed circulation, and consider both laminar (Poiseuille) and turbulent normal fluid flows in a channel configuration. Using high resolution numerical simulations we show that turbulence in the normal fluid sustains a notably higher vortex line density than a laminar flow with the same mean flow rate. We examine Vinen's relation, , between the steady state vortex line density L and the counterflow velocity vns. Our results support the hypothesis that transition to turbulence in the normal fluid is responsible for the TI to TII transition. We also consider the spectral properties of fluctuations of the superfluid vortices, which show a good agreement with previous experimental results.
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November 2013
Research Article|
November 07 2013
Vortex line density in counterflowing He II with laminar and turbulent normal fluid velocity profiles Available to Purchase
A. W. Baggaley;
A. W. Baggaley
a)
1School of Mathematics and Statistics,
University of Glasgow
, Glasgow G12 8QW, United Kingdom
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A. W. Baggaley
1,a)
S. Laizet
2,b)
1School of Mathematics and Statistics,
University of Glasgow
, Glasgow G12 8QW, United Kingdom
2Turbulence, Mixing and Flow Control Group, Department of Aeronautics,
Imperial College London
, London SW7 2PG, United Kingdom
Physics of Fluids 25, 115101 (2013)
Article history
Received:
August 14 2013
Accepted:
October 22 2013
Citation
A. W. Baggaley, S. Laizet; Vortex line density in counterflowing He II with laminar and turbulent normal fluid velocity profiles. Physics of Fluids 1 November 2013; 25 (11): 115101. https://doi.org/10.1063/1.4828892
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