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Emerging issues in helium turbulence

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Abstract

It has been appreciated recently that because helium has the lowest viscosity of any known material, it can be used in reaching the very highest Reynolds numbers and Rayleigh numbers. Critical helium gas, helium I and helium II are all candidates for such uses. Helium gas and helium I are classical fluids and the advantage stems solely from their low kinematic viscosity. Helium II obeys two-fluid equations and their use in turbulence investigations is under study. This article provides a brief introduction and review of this topic, outlining some of the progress already made and questions which need to be resolved as this relatively new field of investigation evolves. A summary of instrumentation available is included.

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References

  1. R. J. Donnelly and C. E. Swanson, Quantum turbulence,J. Fluid Mech. 173, 387–430 (1986).

    Google Scholar 

  2. R. J. Donnelly, Quantum vortices and turbulence in helium II,Annu. Rev. Fluid Mech. 25, 325–371 (1993).

    Google Scholar 

  3. J. T. Tough, Superfluid Turbulence, inProgress in Low Temperature Physics (Vol. 8), D. F. Brewer, ed. (North-Holland, Amsterdam, 1982), pp. 133–219.

    Google Scholar 

  4. R. J. Donnelly,Quantized Vortices in Helium II (Cambridge University Press, Cambridge, 1991).

    Google Scholar 

  5. R. J. Donnelly,High Reynolds Number Flows Using Liquid and Gaseous Helium (Springer-Verlag, New York, 1991).

    Google Scholar 

  6. R. J. Donnelly,Cryogenic Helium Gas Convection Research (Report of the Dept. of Physics, University of Oregon, 1994).

  7. S. Chandrasekhar,Hydrodynamic and Hydromagnetic Stability (Oxford University Press, 1961).

  8. D. C. Threlfall, Free convection in low-temperature gaseous helium,J. Fluid Mech. 67, (part 1), 17–28 (1975).

    Google Scholar 

  9. V. D. Arp and R. D. McCarty, Thermophysical Properties of He-4 from 0.8 K to 1500 K with Pressures to 2000 MPa, Technical Note 1334, NIST (1989).

  10. X. Z. Wu, Along the road to developed turbulence: Free thermal convection in low temperature helium gas, PhD thesis, University of Chicago (1991).

  11. X. Z. Wu and A. Libchaber, Non-Boussinesq effects in free thermal convection,Phys. Rev. A 43, 2833 (1991).

    Google Scholar 

  12. C. F. Barenghi, P. G. J. Lucas, and R. J. Donnelly, Cubic spline fits to thermodynamic and transport parameters of liquid4He above the λ transition,J. Low Temp. Phys. 44, 491–504 (1981).

    Google Scholar 

  13. R. J. Donnelly, R. A. Riegelmann, and C. F. Barenghi, The observed properties of liquid helium at the saturated vapor pressure, Report of the Dept. of Physics, University of Oregon, Eugene, OR (1993).

    Google Scholar 

  14. D. J. Tritton,Physical Fluid Dynamics, 2nd Ed., (Oxford 1988).

  15. J. J. Niemela and R. J. Donnelly, Thermal convection in liquid helium, inHigh Reynolds Number Flows Using Liquid and Gasious Helium, R. J. Donnelly, ed. (Springer-Verlag, New York, 1991), pp. 243–252.

    Google Scholar 

  16. R. P. Behringer, Critical Rayleigh numbers for cryogenic experiments.J. Low Temp. Phys. 78, 231–246 (1990).

    Google Scholar 

  17. H. Schlichting,Boundary-Layer Theory, 7th Ed. Chap. 20 (McGraw-Hill, 1979).

  18. R. J. Donnelly, inExperimental Superfluidity, W. I. Glaberson and P. E. Park, eds. (University of Chicago Press, Chicago, 1967).

    Google Scholar 

  19. M. R. Smith, Evolution and propagation of turbulence in helium II. PhD thesis, University of Oregon (1993).

  20. M. R. Smith, R. J. Donnelly, N. Goldenfeld, and W. F. Vinen, Decay of vorticity in homogeneous turbulence,Phys. Rev. Lett. 71, 2583–2586 (1993).

    Google Scholar 

  21. C. F. Barenghi, R. J. Donnelly, and W. F. Vinen, Friction on quantized vortices in helium II. A Review,J. Low Temp. Phys. 52, 189–247 (1983).

    Google Scholar 

  22. Y. B. You, Remnant vortices of helium II between rotating concentric cylinders, PhD thesis, University of Oregon (1993).

  23. R. J. Donnelly, New thermodynamic potential effects in helium II,Phys. Lett. 17, 109–110 (1965).

    Google Scholar 

  24. I. L. Bekarevich and I. M. Khalatnikov, Phenomenological derivation of the equations of vortex motion in He II,Sov. Phys. JEPT 13, 643 (1961).

    Google Scholar 

  25. E. J. Yarmchuck and W. I. Glaberson, Counterflow in rotating superfluid helium.J. Low Temp. Phys. 36, 381 (1979).

    Google Scholar 

  26. D. Griswold, C. P. Lorenson, and J. T. Tough, Intrinsic fluctuations of the vortex-line density in superfluid turbulence,Phys. Rev. B 35, 3149 (1987).

    Google Scholar 

  27. M. W. Dowley, D. R. Firth, and A. C. Hollis Hallet, 1958 Proceedings of the fifth international conference on low temperature physics, LT-5, pp. 19–21; M. W. Dowley, D. R. Firth, and A. C. Hollis Hallett, 1961 Proceedings of the seventh international conference on low temperature physics, LT-7, pp.464–465; R. A. Laing and H. E. Rorschach, Hydrodynamic drag on spheres moving in liquid helium,Physics of Fluids 4, 564–571 (1961).

  28. P. L. Walstrom, J. G. Weisend H. J. R. Maddocks, and S. W. Van Sciver, Turbulent flow pressure drop in various He II transfer system components,Cryogenics 28, 101–110 (1988).

    Google Scholar 

  29. F. Bielert and G. Stamm, Visualization of Taylor-Couette flow in superfiuid helium,Cryogenics 33, 938 (1993).

    Google Scholar 

  30. K. W. Schwarz and J. R. Rozen, Anomalous decay of turbulence in superfiuid4He,Phys. Rev. Lett. 66, 1898 (1991).

    Google Scholar 

  31. H. E. Hall and W. F. Vinen, The rotation of liquid helium II. II. The theory of mutual friction in uniformly rotating heliumII,Proc. Roy. Soc. A 238, 215 (1956).

    Google Scholar 

  32. R. N. Hills and P. H. Roberts, Superfiuid mechanics for a high density of vortex lines,Arch. Rat. Mech. Anal. 66, 43 (1987).

    Google Scholar 

  33. C. F. Barenghi, Vortices and the Couette flow of helium II,Phys. Rev. B 45, 2290 (1992).

    Google Scholar 

  34. C. F. Barenghi and C. A. Jones, The Stability of the Couette flow of helium II,J. Fluid Mech. 197, 551 (1988).

    Google Scholar 

  35. C. J. Swanson and R. J. Donnelly, Instability of Taylor-Couette flow of helium II,Phys. Rev. Lett. 67, 1578 (1991); F. Bielert and G. Stamm, Influence of quantized vortex lines on the stability of Taylor-Couette flow in He II,Physica B 194, 561 (1994).

    Google Scholar 

  36. C. F. Barenghi and C. A. Jones, On the stability of superfiuid helium between rotating concentric cylinders,Phys. Lett. A 122, 425 (1987).

    Google Scholar 

  37. R. J. Donnelly and M. Ozima, Experiments on the stability of flow between rotating cylinders in the presence of a magnetic field,Proc. Roy. Soc. A 266, 272 (1962).

    Google Scholar 

  38. K. L. Henderson, C. F. Barenghi, and C. A. Jones, Nonlinear Taylor-Couette flow of helium II,J. Fluid Mech. 281, 329 (1995).

    Google Scholar 

  39. K. L. Henderson and C. F. Barenghi, Numerical methods for two fluid hydrodynamics: Applications to the Taylor vortex flow of superfluid helium II,J. Low Temp. Phys. (in press).

  40. K. L. Henderson and C. F. Barenghi, Calculation of torque in nonlinear Taylor vortex flow of helium II,Phys. Lett. A 191, 438 (1994).

    Google Scholar 

  41. K. W. Schwarz, Three-dimensional vortex dynamics in superfluid4He: Homogeneous superfluid turbulence,Phys. Rev. B 38, 2398 (1988).

    Google Scholar 

  42. D. C. Samuels, Velocity matching and Poiseuille pipe flow of superfluid helium,Phys. Rev. B 46, 11714–11724 (1992).

    Google Scholar 

  43. R. G. K. M. Aarts and A.T.A.M. DeWaele, Numerical simulation of superfluid turbulence near the critical velocity,Physica B 194–196, 725 (1994).

    Google Scholar 

  44. K. L. Henderson and C. F. Barenghi, Vortex tension and the stability of Couette flow in helium II,Physica B 194–196, 567 (1994).

    Google Scholar 

  45. D. Stauffer and A. L. Fetter, Distribution of vortices in rotating helium II,Phys. Rev. 168, 156 (1968).

    Google Scholar 

  46. K. W. Schwarz, Three-dimensional vortex dynamics in superfluid4He: Line-line and line-boundary interactions,Phys. Rev. B 31, 5782 (1985).

    Google Scholar 

  47. K. W. Schwarz, Vortex pinning in superfluid helium,Phys. Rev. Lett. 47, 251 (1981).

    Google Scholar 

  48. S. W. Van Sciver, D. S. Holmes, X. Huang, and J. G. Weisend II, He II flowmetering,Cryogenics 31, 75 (1991).

    Google Scholar 

  49. B. Castaing, B. Chabaud, and B. Hébral, Hot wire anemometer operating at cryogenic temperatures,Rev. of Sci. Instr. 63, 4168 (1992).

    Google Scholar 

  50. J. Lipa, B. C. Leslie, and T. C. Walstrom, A very high resolution thermometer for use below 7 K,Physica B 107, 331 (1981).

    Google Scholar 

  51. R. B. Lambert, H. A. Snyder, and S. K. F. Karlsson, Hot thermistor anemometer for finite amplitude stability measurements,Rev. Sci. Inst. 36, 924 (1965).

    Google Scholar 

  52. D. P. Lathrop, J. Fineberg, and H. L. Swinney, Transition to shear-driven turbulence in Couette-Taylor flow,Phys. Rev. A 46, 6390 (1992).

    Google Scholar 

  53. B. Perrin, Emergence of a periodic mode in the so-called turbulent region in a circular Couette flow,J. Phys. Lett. 43, L-5 (1982).

    Google Scholar 

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Barenghi, C.F., Swanson, C.J. & Donnelly, R.J. Emerging issues in helium turbulence. J Low Temp Phys 100, 385–413 (1995). https://doi.org/10.1007/BF00751517

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