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Nonlinear Taylor–Couette flow of helium II

Published online by Cambridge University Press:  26 April 2006

Karen L. Henderson
Affiliation:
Department of Mathematics, University of Newcastle, Newcastle upon Tyne, NE1 7RU, UK
Carlo F. Barenghi
Affiliation:
Department of Mathematics, University of Newcastle, Newcastle upon Tyne, NE1 7RU, UK
Chris A. Jones
Affiliation:
Department of Mathematics, University of Exeter, Exeter, EX4 4QE, UK

Abstract

We solve the nonlinear two-fluid Hall–Vinen–Bekharevich–Khalatnikov equations of motion of helium II for the first time and investigate the configuration of quantized vortex lines in Taylor–Couette flow. The results are interpreted in terms of quantities which can be observed by measuring the attenuation of second sound. Comparison is made with existing experimental results.

Type
Research Article
Copyright
© 1995 Cambridge University Press

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References

Aarts, R. G. K. M. & Waele, A. T. A. M. DE 1994 Physica B 194–196, 725.
Andronikashvili, E. L. & Mamaladze, Yu. G. 1966 Rev. Mod. Phys. 38, 567.
Barenghi, C. F. 1991 J. Comput. Phys. 95, 175.
Barenghi, C. F. 1992 Phys. Rev. B 45, 2290.
Barenghi, C. F., Donnelly, R. J. & Vinen, W. F. 1993 J. Low Temp. Phys. 52, 189.
Barenghi, C. F. & Jones, C. A. 1988 J. Fluid Mech. 197, 551.
Barenghi, C. F., Swanson, C. J. & Donnelly, R. J. 1994 J. Low Temp. Phys. (to appear).
Bekharevich, I. L. & Khalatnikov, I. M. 1961 Sov. Phys. J. Exp. Theor. Phys. 13, 643.
Bendt, P. J. 1967 Phys. Rev. 153, 280.
Bielert, F. 1993PhD. Thesis, University of Göttingen.
Campbell, L. J. & Ziff, R. M. 1978 Phys. Rev. B 20, 1886.
Chandrasekhar, S. 1961 Hydrodynamics and Hydromagnetic Stability. Oxford University Press.
Chandrasekhar, S. & Donnelly, R. J. 1957 Proc. R. Soc. Lond. A 241, 9.
prima, Di R. C., & Swinney, H. L. 1981 In Hydrodynamic Instabilities and Transition to Turbulence (ed. H. I. Swinney & P. Gollub), p. 139. Springer.
Donnelly, R. J. 1991 Quantized Vortices in Helium II, Cambridge University Press.
Donnelly, R. J. & Lamar, M. M. 1988 J. Fluid Mech. 186, 163.
Donnelly, R. J. & Swanson, C. E. 1986 J. Fluid Mech. 173, 387.
Hall, H. E. 1960 Phil. Mag. Suppl. 9, 89.
Hall, H. E., & Vinen, W. F. 1956a Proc. R. Soc. Lond. A 238, 204.
Hall, H. E., & Vinen, W. F. 1956b Proc. R. Soc. Lond. A 238, 215.
Hills, R. N. & Roberts, P. H. 1977 Arch. Rat. Mech. Anal. 66, 43.
Jones, C. A. 1985 J. Comput. Phys. 61, 321.
Khalatnikov, I. M. 1965 An Introduction to the Theory Superfluidity. Benjamin.
Mathieu, P., Placais, B. & Simon, Y. 1984 Phys. Rev. B 29, 2489.
Northby, J. A. & Donnelly, R. J. 1970 Phys. Rev. Lett. 25, 214.
Schwarz, K. W. 1988 Phys. Rev. B 38, 2398.
Snyder, H. A. 1974 Proc. 13th Intl Conf. Low Temp. Phys. LT13, 1, 283. Plenum.
Swanson, C. J. 1992 Appearance of vortices and stability of the Taylor-Couette flow of helium II PhD Thesis, University of Oregon.
Swanson, C. E. & Donnelly, R. J. 1987 J. Low Temp. Phys. 67, 185.
Swanson, C. J. & Donnelly, R. J. 1991 Phys. Rev. Lett. 67, 1578.
Tough, J. T. 1982 Progress of Low Temperature Physics, vol. 8 (ed. D. F. Brewer). North Holland.