Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-27T13:31:03.650Z Has data issue: false hasContentIssue false
  • English
  • Français

Quantum turbulence

Published online by Cambridge University Press:  21 April 2006

Russell J. Donnelly  and
Charles E. Swanson
Russell J. Donnelly
Affiliation:
Department of Physics, University of Oregon, Eugene, OR 97403, USA
Charles E. Swanson
Affiliation:
Department of Physics, University of Oregon, Eugene, OR 97403, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

We present a review of quantum turbulence, that is, the turbulent motion of quantized vortex lines in superfluid helium. Our discussion concentrates on the turbulence produced by steady, uniform heat flow in a pipe, but touches on other turbulent flows as well. We have attempted to motivate the study of quantum turbulence and discuss briefly its connection with classical turbulence. We include background on the two-fluid model and mutual friction theory, examples of modern experimental techniques, and a brief survey of the phenomenology. We discuss the important recent insights that vortex dynamics has provided to the understanding of quantum turbulence, from simple scaling arguments to detailed numerical simulations. We conclude with a discussion of open questions in this field.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 173 , December 1986 , pp. 387 - 429
Copyright
© 1986 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ahlers, G. 1969 Mutual friction in He II near the lambda transition. Phys. Rev. Lett. 22, 54–56.Google Scholar
Allen, J. F. & Misener, A. D. 1938 Flow of liquid helium II. Nature 141, 75.Google Scholar
Anderson, P. W. 1966 Considerations on the flow of superfluid helium. Rev. Mod. Phys. 38, 298–310.Google Scholar
Arms, R. J. & Hama, F. R. 1965 Localized-induction concept on a curved vortex and motion of an elliptical vortex ring. Phys. Fluids 8, 553–559.Google Scholar
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., Milliken, F. P. & Schwarz, K. W. 1984 Properties of superfluid turbulence in a large channel. Phys. Rev. Lett. 53, 1372–1375.Google Scholar
Baehr, M. L. & Tough, J. T. 1985 Dissipation in combined normal and superfluid flows of He II: A unified description. Phys. Rev. B32, 5632–638.Google Scholar
Baehr, M. L., Opatowsky, L. B. & Tough, J. T. 1983 The transition from dissipationless superflow to homogeneous superfluid turbulence. Phys. Rev. Lett. 51, 2295–2297.Google Scholar
Badash, L. 1985 Kapitza, Rutherford and the Kremlin. Yale University Press.
Barenghi, C. F. 1982 Experiments on quantum turbulence. PhD thesis, University of Oregon.
Barenghi, C. F., Donnelly, R. J. & Vinen, W. F. 1983 Friction on quantized vortices in helium II: a review. J. Low Temp. Phys. 52, 189–247.Google Scholar
Barenghi, C. F., Donnelly, R. J. & Vinen, W. F. 1985 Thermal excitation of waves on quantized vortices. Phys. Fluids 28, 498–504.Google Scholar
Barenghi, C. F., Park, K. & Donnelly, R. J. 1981 Absolute measurement of vortex line density in counterflowing He II. Phys. Lett. 84A, 435–438.Google Scholar
Barenghi, C. F., Swanson, C. E. & Donnelly, R. J. 1982 Induced vorticity fluctuations in counterflowing He II. Phys. Rev. Lett. 48, 1187–1189.Google Scholar
Baym, G. & Chandler, C. 1983 Hydrodynamics of rotating superfluids 1. J. Low Temp. Phys. 50, 57–87.Google Scholar
Bon Mardion, C., Claudet, G. & Seyfert, P. 1978 Steady state heat transport in superfluid helium at 1 bar. In Proc. 7th Intl. Cryogenic Conf. pp. 214–221. IPC Science and Technology Press.
Brewer, D. F. & Edwards, D. O. 1961 Heat conduction in liquid helium II in capillary tubes I Transition to supercritical conduction. Phil. Mag. 6, 775–790.Google Scholar
Carey, R. F., Rooney, J. A. & Smith, C. W. 1978 Ultrasonically generated quantized vorticity in He II. Phys. Lett. 65A, 311–313.Google Scholar
Chase C. E., 1962 Thermal conduction in liquid helium II: I. Temperature dependence. Phys. Rev. 127, 361–370.Google Scholar
Chase C. E., 1963 Thermal conduction in liquid helium II: II. Effects of channel geometry. Phys. Rev. 131, 1898–1903.Google Scholar
Cheng, D. K., Cromar, M. W., & Donnelly R. J. 1973 Influence of an axial heat current on negative ion trapping in rotating He II. Phys. Rev. Lett. 31, 433–436.Google Scholar
Cromar, M. W. 1977 Turbulence in helium II counterflow in wide channels. PhD thesis, University of Oregon.
Cummings, J. C. 1974 Development of a high performance cryogenic shock tube. J. Fluid Mech. 66, 177–187.Google Scholar
Cummings, J. C., Schmidt, D. W. & Wagner, W. J. 1978 Experiments on second sound shock waves in superfluid helium. Phys. Fluids 21, 713–717.Google Scholar
D'Humieres, D. D. & Libchaber, A.1978 Self diffusion of superfluid turbulence through porous media. J. Physique C6 39, 156–157. See also Hulin, J. P., D'Humieres, D. D., Perrin, B. & Libchaber, A. 1974 Critical velocities for superfluid helium flow through a small hole. Phys. Rev. A9, 885–892.Google Scholar
Dimotakis, P. E., & Broadwell J. E. 1973 Local temperature measurements in supercritical counterflow in liquid helium II. Phys. Fluids 16, 1787–1795.Google Scholar
Donnelly, R. J. & Frincis, A. W. 1985 Cryogenic Science and Technology Contributions of Leo I. Dana, Union Carbide Corporation, Danbury.
Donnelly, R. J. & LaMar, M. M. 1986 Flow of liquid helium between concentric cylinders: a review. (in preparation).
Donnelly, R. J. & Roberts, P. H. 1969 Stochastic theory of the interaction of ions and quantized vortices in helium II. Proc. R. Soc. Lond. A312, 519–551.Google Scholar
Feynman, R. P. 1955 Applications of quantum mechanics to liquid helium. In Progress in Low Temperature Physics, vol. 1 (ed. C. J. Gorter), pp. 17–53. North Holland.
Foreman, L. R. & Snyder, H. A. 1979 The penetration of superfluid turbulence through porous filters. J. Low Temp. Phys. 34, 529–538.Google Scholar
Giordano, N. 1984a Vibrating superleak second-sound transducers. Theory and experiment. J. Low Temp. Phys. 55, 495–526.Google Scholar
Giordano, N. 1984b Observations of critical velocity effects in vibrating superleak second sound transducers. In Proc. 17th Intl Conf. on Low Temperature Physics, LR-17, vol. 1, pp. 307–308. North Holland.
Giordano, N. & Musikar, P. 1984 Theory of critical velocity effects in vibrating superleak second sound transducers. In Proc. 17th Intl Conf. on Low Temperature Physics, LT-17, vol. 1, pp. 309–310. North Holland.
Glaberson, W. I. & Donnelly, R. J. 1986 Structure, distributions and dynamics of vortices in helium II. In Progress in Low Temperature Physics, vol. 9 (ed. D. F. Brewer), pp. 1–142. North Holland.
Glaberson, W. I., Johnson, W. W. & Ostermeier, R. M. 1974 Instability of a vortex array in helium II. Phys. Rev. Lett. 33, 1197–1200.Google Scholar
Gorter, C. J. & Mellink, J. H. 1949 On the irreversible processes in liquid helium II. Physica 15, 285–304.Google Scholar
Hall, H. E. & Vinen, W. F. 1956a The rotation of liquid helium II: I. Experiments on the propagation of second sound in uniformly rotating helium II. Proc. R. Soc. Lond. A238, 204–214.Google Scholar
Hall, H. E. & Vinen, W. F. 1956a The rotation of liquid helium II: II. The theory of mutual friction in uniformly rotating helium II. Proc. R. Soc. Lond. A238, 215–234.Google Scholar
Hoch, H., Busse, L. & Moss, F. 1975 Noise from vortex line turbulence in He II. Phys. Rev. Lett. 34, 384–387.Google Scholar
Jones, C. A. & Roberts, P. H. 1982 Motions in a Bose condensate IV Axisymmetric solitary waves. J. Phys. A15, 2599–2619.Google Scholar
Jones, C. A., Putterman, S. J. & Roberts, P. H. 1986 Motions in a Bose condensate. V. Stability of solitary wave solutions of nonlinear Schrodinger Equations in two and three dimensions. J. Phys. A (to appear).Google Scholar
Kapitza, P. 1938 Viscosity of liquid helium below the lambda point. Nature 141, 74.Google Scholar
Kapitza, P. 1941 The study of heat transfer in helium II. J. Phys. USSR 4, 181–220.Google Scholar
Keesom, W. H. & Keesom, A. P. 1936 On the heat conductivity of liquid helium. Physica 3, 359–360.Google Scholar
Keesom, W. H., Keesom, A. P. & Saris, B. F. 1938 A few measurements on the heat conductivity of liquid helium II. Physica 5, 281–285.Google Scholar
Khalatnikov, I. M. 1965 Introduction to the Theory of Superfluidity. Benjamin.
Ladner, D. R., Childers, R. K. & Tough, J. T. 1976 Helium II thermal counterflow at large heat currents. Phys. Rev. B13, 2918–2923.Google Scholar
Laguna, G. 1975 Second-sound attenuation in a supercritical counterflow jet. Phys. Rev. B12, 4874–4881.Google Scholar
Liepmann, H. W. 1952 Deflection and diffusion of a light ray passing through a boundary layer. Douglas Rep. S. M. 14397.Google Scholar
Liepmann, H. W., Cummings, J. C. & Rupert, V. C. 1973 Cryogenic shock tube. Phys. Fluids 16, 332–333.Google Scholar
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
Lorenson, C. P., Griswold, D., Nayak, V. U. & Tough, J. T. 1985 Dynamic features of superfluid turbulence near the second critical heat current. Phys. Rev. Lett. 55, 1494–1497.Google Scholar
Mantese, J., Bischoff, G. & Moss, F. 1977 Vortex line density fluctuations in turbulent superfluid helium. Phys. Rev. Lett. 39, 565–568.Google Scholar
Martin, K. P. & Tough, J. T. 1983 Evolution of superfluid turbulence in thermal counterflow. Phys. Rev. B27, 2788–2799.Google Scholar
Milliken, F. P., Schwarz, K. W. & Smith, C. W. 1982 Free decay of superfluid turbulence. Phys. Rev. Lett. 48, 1204–1207.Google Scholar
Murray, C. A., Woerner, R. L. & Greytak, T. J. 1975 High resolution study of the two-roton bound state. J. Phys. C8, L90–L94.Google Scholar
Oberley, C. E., & Tough J. T. 1972 Evidence for the hydrodynamic origin of critical heat currents in helium II. J. Low Temp. Phys. 7, 223–228.Google Scholar
Onsager, L. 1949 A remark following a paper by Gorter at a conference in Florence. Nuov. Cim. 6, Supp. 2, 249.Google Scholar
Opatowsky, L. B. & Tough, J. T. 1981 Homogeneity of turbulence in pure superflow. Phys. Rev B24, 5420–5421.Google Scholar
Ostermeier, R. M., Cromar, M. W., Kittel, P. & Donnelly, R. J. 1980 Fluctuations in turbulent He II counterflow. Phys. Lett. 77A, 321–324.Google Scholar
Osborne, D. V. 1950 The rotation of liquid helium II. Proc. Phys. Soc. Lond. 63, 909–912.Google Scholar
Osborne, D. V. 1951 Second sound in liquid helium II. Proc. Phys. Soc. Lond. 64, 114–123.Google Scholar
Peshkov, V. P. & Tkachenko, V. K. 1961 Kinetics of the destruction of superfluidity in helium. Zh. Eksp. Teor. Fiz. 41, 1421–1432 [Sov. Phys., J. Exp. Theor. Phys. 14, 1019–1022].Google Scholar
Pfotenhauer, J. M. & Donnelly, R. J. 1985 Heat transfer in liquid helium. In Advances in Heat Transfer, vol. 17 (ed. J. P. Hartnett & T. F. Irvine,), pp. 65–158. Academic.
Pfotenhauer, J. M., Lucas, P. G. J. & Donnelly, R. J. 1984 Stability and heat transfer of rotating cryogens: Part II. Effects of rotation on heat-transfer properties of convection in liquid He4. J. Fluid Mech 145, 239–252.Google Scholar
Roberts, P. H. & Donnelly, R. J. 1973 Dynamics of rotons. Phys. Lett. 43A, 1–2.Google Scholar
Roberts, P. H. & Donnelly, R. J. 1974 Superfluid mechanics. Ann. Rev. Fluid Mech. 6, 179–225.Google Scholar
Roberts, P. H. & Pardee, W. J. 1974 Bound States of the two-roton Schrodinger equation. J. Phys. A1283–1292.Google Scholar
Schwarz, K. W. 1978 Turbulence in superfluid helium: steady homogeneous counterflow. Phys. Rev. B18, 245–262.Google Scholar
Schwarz, K. W. 1982a Free decay of superfluid turbulence. Phys. Rev. Lett. 48, 1204–1207.Google Scholar
Schwarz, K. W. 1982b Generating superfluid turbulence from simple dynamical rules. Phys Rev. Lett. 49, 283–285.Google Scholar
Schwarz, K. W. 1983 Critical velocity for a self-sustaining vortex tangle in superfluid helium. Phys. Rev. Lett. 50, 364–367.Google Scholar
Schwarz, K. W. 1985 Three-dimensional vortex dynamics in superfluid 4He. I. Line—line and line—boundary interactions. Phys. Rev. B31, 5782–5804.Google Scholar
Schwarz, K. W. & Smith, C. W. 1981 Pulsed-ion study of ultrasonically generated turbulence in superfluid 4He. Phys. Lett. 82A, 251–254.Google Scholar
Slegtenhorst, R. P., Marees, G. & van Beelen, H. 1982 Steady flow of helium II in the presence of a heat current. Physica 113B 341–366; also Slegtenhorst, R. P., Marees, G. & van Beelen, H. 1982 Transient effects in superfluid turbulence. Physica 113B, 367–379.Google Scholar
Smith, C. W. & Tejwani, M. J. 1984 Fluctuations of a negative ion current in turbulent He II. Phys. Lett. 104A, 281–284.Google Scholar
Swanson, C. E. 1985 A study of vortex dynamics in counterflowing helium II. PhD thesis, University of Oregon.
Swanson, C. E., Barenghi, C. F. & Donnelly, R. J. 1983 Rotation of a tangle of quantized vortex lines in He II. Phys. Rev. Lett. 50, 190–193.Google Scholar
Swanson, C. E. & Donnelly, R. J. 1985 Vortex dynamics and scaling in turbulent counterflowing helium II. J. Low Temp. Phys. 61, 363–399.Google Scholar
Swanson, C. E., Wagner, W. T., Barenghi, C. F. & Donnelly, R. J. 1986 Calculation of the frequency and velocity dependence mutual friction parameters in helium II. (in preparation).
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. Massachusetts Institute of Technology Press.
Torczynski, J. R. 1984b Converging second sound shock waves in superfluid helium. Phys. Fluids 27, 1138–1141.Google Scholar
Torczynski, J. R. 1984b 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), pp. 133–219. North Holland.
Townsend, A. A. 1961 A continuum theory of the isothermal flow of liquid helium II. J. Fluid Mech. 10, 113–132.Google Scholar
Turner, T. N. 1979 Second sound shock waves and critical velocities in liquid helium II. PhD thesis, California Institute of Technology.
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. 1957a Mutual friction in a heat current in liquid helium II. I. Experiments on steady heat currents. Proc. R. Soc. Lond. A240, 114–127.Google Scholar
Vinen, W. F. 1957b Mutual friction in a heat current in liquid helium II. Experiments on transient effects. Proc. R. Soc. Lond. A240, 128–143.Google Scholar
Vinen, W. F. 1957c Mutual friction in a heat current in liquid helium II. III. Theory of mutual friction. Proc. R. Soc. Lond. A243, 493–515.Google Scholar
Vinen, W. F. 1958 Mutual friction in a heat current in liquid helium II. IV. Critical heat currents in wide channels. Proc. R. Soc. Lond. A243, 400–413.Google Scholar
Vinen W. F. 1966 Vortices in superfluid systems. In Quantum Fluids (ed. D. F. Brewer), pp. 74–108. North Holland.
Wang, R. T., Swanson, C. E. & Donnelly, R. J. 1986 Anisotropy and drift of a quantum vortex tangle. To appear.
Yarmchuk, E. J. & Glaberson, W. I. 1979 Counterflow in rotating superfluid helium. J. Low Temp. Phys. 36, 381–429.Google Scholar