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Temperature overshoot due to quantum turbulence during the evolution of moderate heat pulses in He II

Published online by Cambridge University Press:  26 April 2006

W. Fiszdon ,
M. von Schwerdtner ,
G. Stamm  and
W. Poppe
W. Fiszdon
Affiliation:
Max Planck Institut für Strömungsforschung, Bunsenstrasse 10, D-3400, Göttingen, FRG Permanent address: Polish Academy of Sciences and University of Warsaw.
M. von Schwerdtner
Affiliation:
Max Planck Institut für Strömungsforschung, Bunsenstrasse 10, D-3400, Göttingen, FRG
G. Stamm
Affiliation:
Max Planck Institut für Strömungsforschung, Bunsenstrasse 10, D-3400, Göttingen, FRG
W. Poppe
Affiliation:
Max Planck Institut für Strömungsforschung, Bunsenstrasse 10, D-3400, Göttingen, FRG
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Abstract

Transient heat transfer in liquid helium is investigated both experimentally and theoretically in plane and cylindrical geometry in the range of parameters where superfluid turbulence appears to be important. The influence of the main flow parameters – heat flux, pulse duration, and rest time – on the temperature evolution is reported. At high heat inputs the mutual friction force related to the superfluid vortex lines leads to the formation of a temperature overshoot behind the propagating second-sound wave and must be looked upon as a macroscopic effect of microscopic quantum turbulence. The experimental results can be reproduced by a theoretical model when the mutual interaction force is expressed in terms of the vortex line density (VLD), and the Vinen equation, extended to include spatial dependence, is taken into account for its temporal evolution. Fair quantitative agreement between experiment and theory is obtained if the ratio of the temperature overshoot and the shock-wave amplitude is below about 4. At stronger heat inputs the agreement is only qualitative.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 212 , March 1990 , pp. 663 - 684
Copyright
© 1990 Cambridge University Press

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References

Ashton, R. A. & Northby, J. A., 1975 Vortex velocity in turbulent He II counterflow. Phys. Rev. Lett. 35, 1714–1717.Google Scholar
Awschalom, D. D. & Schwarz, K. W., 1984 Observation of remanent vortex line density in superfluid helium. Phys. Rev. Lett. 52, 49–52.Google Scholar
Borner, H., Schmidt, D. W. & Wagner, W. J., 1979 A fast response superconducting thin-film probe for detection of second sound shock waves in superfluid helium. Cryogenics 19, 89–92.Google Scholar
Donnelly, R. J. & Swanson, C. E., 1986 Quantum turbulence. J. Fluid Mech. 173, 387–429.Google Scholar
Feynman, R. P.: 1955 Application of quantum mechanics to liquid helium. In Progress in Low Temperature Physics, Vol 1 (ed. C. J. Gorter), pp. 17–53. North-Holland.
Fiszdon, W. F., Piechna, J. & Poppe, W., 1988 A qualitative numerical analysis of some features of propagation of counterflow temperature waves in superfluid helium. MPI Strömungsforsch. Göttingen, Ber. 9/1988.Google Scholar
Fiszdon, W. F. & Von Schwerdtner, M.: 1989 Influence of quantum turbulence on the evolution of moderate plane second-sound-heat-pulses in helium II. J. Low Temp. Phys. 75, 253–267.Google Scholar
Gorter, C. J. & Mellink, J. H., 1949 On the irreversible processes in liquid helium II. Physica 15, 285–304.Google Scholar
Iznankin, A. Yu. & Mezhov-Deglin, L. P. 1983 Shock waves in liquid helium. Zh. Eksp. Teor. Fiz. 84, pp. 1378–1390 (Soviet Phys. JETP 57, 801–808).Google Scholar
Khalatnikov, I. M.: 1965 Introduction to the Theory of Superfluidity. Benjamin.
Landau, L. D. & Lifschitz, E. M., 1959 Fluid Mechanics, Ch. XVI. Pergamon.
Liepmann, H. W. & Laguna, G. A., 1984 Nonlinear interactions in the fluid mechanics of helium II. Ann. Rev. Fluid Mech. 16, 139–177.Google Scholar
Liepmann, H. W. & Torczynski, J. R., 1986 Shock waves in helium at low temperatures. In Proc. XV. Int. Symp. Shock Waves and Shock Tubes (ed. D. Bershader et al.), pp. 87–96. Stanford University Press.
Nemirovskii, S. K. & Lebedev, V. V., 1983 The hydrodynamics of superfluid turbulence. Zh. Eksp. Teor. Fiz. 84, 1729–1742 (Soviet Phys. JETP 57, 1009–1016).Google Scholar
Putterman, S. J.: 1974 Superfluid Hydrodynamics. North-Holland; Elsevier.
Schwarz, K. W.: 1978 Turbulence in superfluid helium: steady homogeneous counterflow. Phys. Rev. B 18, 245–262.Google Scholar
Schwarz, K. W.: 1988 Three-dimensional vortex dynamics in superfluid 4He: Homogeneous superfluid turbulence. Phys. Rev. B 38, 2398–2417.Google Scholar
von Schwerdtner, M.: 1988 Experimentelle Untersuchung zum transkritischen Wärmetransport in He II. Ph.D. thesis, Mitt. MPI Strömungsforsch. Nr. 90. Göttingen.
von Schwerdtner, M. Stamm, G. & Schmidt, D. W. 1989 The evolution of superfluid vortex line density behind a second-sound pulse in He II. Phys. Rev. Lett. 63, 39–42.Google Scholar
Stamm, G.: 1988 Experimentelle Untersuchung zur zylindersymmetrischen Ausbreitung von Second-Sound-Stoßwellen in He II. M. S. thesis, MPI Strömungsforsch. Ber. 16/1988, Göttingen.
Torczynski, J. R.: 1984 On the interaction of second sound shock waves and vorticity in superfluid helium. Phys. Fluids 27, 2636–2644.Google Scholar
Tough, J. T.: 1982 Superfluid turbulence. In Progress in Low Temperature Physics, vol. 8 (ed. D. F. Brewer), Ch. 3, pp. 133–219. North-Holland.
Turner, T. N.: 1983 Using second sound shock waves to probe the intrinsic critical velocity of liquid helium II. Phys. Fluids 26, 3227–3241.Google Scholar
Vinen, W. F.: 1957 Mutual friction in a heat current in liquid helium II. III. Theory of mutual friction. Proc. R. Soc. Lond. A 242, 493–515.Google Scholar
Wang, R. T., Swanson, C. E. & Donnelly, R. J., 1987 Anisotropy and drift of a vortex tangle in helium II. Phys. Rev. B 36, 5240–5244.Google Scholar