Implications of Holm's finite temperature corrections to the HVBK equations

Henderson, K. L.; Barenghi, C. F.

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. © 2004 Plenum Publishing Corporation.

Citation

Henderson, K. L., & Barenghi, C. F. (2004). Implications of Holm's finite temperature corrections to the HVBK equations. Journal of Low Temperature Physics, 134(3-4), 959-972. https://doi.org/10.1023/B%3AJOLT.0000013211.05952.c4

• Journal Article Type: Article
• Publication Date: Feb 1, 2004
• Journal: Journal Of Low Temperature Physics
• Print ISSN: 0022-2291
• Publisher: Springer Verlag
• Peer Reviewed: Not Peer Reviewed
• Volume: 134
• Issue: 3-4
• Pages: 959-972
• DOI: https://doi.org/10.1023/B%3AJOLT.0000013211.05952.c4
• Keywords: Holm, finite temperature corrections, HVBK equations
• Public URL: https://uwe-repository.worktribe.com/output/1062091
• Publisher URL: http://dx.doi.org/10.1023/B:JOLT.0000013211.05952.c4