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Implications of Holm's Finite Temperature Corrections to the HVBK Equations

Authors
  • Henderson, K. L.1
  • Barenghi, C. F.1
  • 1 University of the West of England, School of Mathematical Sciences, Bristol, BS16 1QY, United Kingdom , Bristol
Type
Published Article
Journal
Journal of Low Temperature Physics
Publisher
Kluwer Academic Publishers-Plenum Publishers
Publication Date
Feb 01, 2004
Volume
134
Issue
3-4
Pages
959–972
Identifiers
DOI: 10.1023/B:JOLT.0000013211.05952.c4
Source
Springer Nature
Keywords
License
Yellow

Abstract

The macroscopic equations used to model helium II are the Hall–Vinen–Bekharevich–Khalatnikov (HVBK) equations. Recently Holm suggested a finite-temperature adjustment to these equations, which effects the mutual friction parameters. In this paper we investigate the effect of this adjustment on the linear stability of Couette flow. Using the original HVBK equations, good agreement between the predicted and observed Reynolds number at which Couette flow becomes unstable has been found, particularly at temperatures close to the lambda temperature. Performing the same test on Holm's finite temperature corrections, we find no such agreement. The stability curves all predict that long-wavelength axial disturbances are unstable. We conclude that with the current values of the mutual friction parameters, Holm's finite-temperature corrections do not constitute a good model of helium II. We also discuss the possibility that, since the method of experimentally determining the mutual friction parameters depends on the form of the mutual friction, our interpretation of these parameters needs to be amended.

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