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The Use of Cryogenic Helium for Classical Turbulence: Promises and Hurdles

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Fluid turbulence is a paradigm for non-linear systems with many degrees of freedom and important in numerous applications. Because the analytical understanding of the equations of motion is poor, experiments and, lately, direct numerical simulations of the equations of motion, have been fundamental to making progress. In this vein, a concerted experimental effort has been made to take advantage of the unique properties of liquid and gaseous helium at low temperatures near or below the critical point. We discuss the promise and impact of results from recent helium experiments and identify the current technical barriers which can perhaps be removed by low temperature researchers. We focus mainly on classical flows that utilize helium above the lambda line, but touch on those aspects below that exhibit quasi-classical behavior.

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References

  1. Tritton D.J. (1988). Physical Fluid Dynamics. Clarendon Press, Oxford

    MATH  Google Scholar 

  2. Davidson P.A. (2004). Turbulence: An Introduction for Scientists and Engineers. Oxford University Press, Oxford

    MATH  Google Scholar 

  3. Spiegel E.M. (1971). Annu Rev. Astron. Astrophys 9:323

    Article  ADS  Google Scholar 

  4. Glatzmaier G.A., Coe R.C., Hongre L., and Roberts P.H. (1999). Nature 401:885

    Article  ADS  Google Scholar 

  5. Falkovich G., Sreenivasan K.R. (2006). Phy. Today 59:43

    Google Scholar 

  6. Marder M.P. (2000). Condensed Matter Physics. Wiley, New York

    Google Scholar 

  7. Mandelbrot B.B. (1999). Scientific Amer 280:50

    Google Scholar 

  8. National Research Council Report: Condensed Matter and Materials Physics: Basic Research for Tomorrow’s Technology, 308 pages, National Academy Press (1999).

  9. Yakhot V., Sreenivasan K.R. (2005). J. Stat. Phys. 121:823

    Article  MATH  MathSciNet  ADS  Google Scholar 

  10. Oberbeck A. (1879). Annalen der Physik und Chemie 7:271

    MATH  ADS  Google Scholar 

  11. Busse F.H. (1978). Rep. Prog. Phys. 41:1929

    Article  ADS  Google Scholar 

  12. Kolmogorov A.N. (1941). Dokl. Akad. Nauk SSSR 30:9

    Google Scholar 

  13. Monin A.S., Yaglom A.M. (1975). Statistical Fluid Mechanics, vol 2. MIT Press, Cambridge, USA

    Google Scholar 

  14. Sreenivasan K.R. (1995). Phys. Fluids 7:2778

    Article  MATH  MathSciNet  ADS  Google Scholar 

  15. Sreenivasan K.R., Bershadskii A. (2006). J. Fluid. Mech 554: 477

    Article  MATH  ADS  Google Scholar 

  16. Vinen W.F., Niemela J.J. (2002). J. Low Temp. Phys. 128:167

    Article  Google Scholar 

  17. Sreenivasan K.R., Donnelly R.J. (2001). Adv. Appl. Mech. 37:239

    Article  Google Scholar 

  18. Verzicco R. (2004). Phys. Fluids 16:1965

    Article  ADS  Google Scholar 

  19. Brown E., Nikolaenko A., D. Funfschilling and Ahlers G., Phys. Fluids 17, 075108 (2005).

    Google Scholar 

  20. Nikuradse J., NASA TT F-10359 (1966). Translated from the German original Forsch. Arb. Ing.-Wes. No. 356 (1932).

  21. Swanson C.J., Julian B., Ihas G.G., Donnelly R.J. (2002). J. Fluid. Mech. 461:51

    Article  MATH  ADS  Google Scholar 

  22. McKeon B.J., Swanson C.J., Zagarola M.V., Donnelly R.J., Smits A.J. (2004). J. Fluid. Mech 511:41

    Article  MATH  ADS  Google Scholar 

  23. Zagarola M.V., Smits A.J. (1997). Phys. Rev. Lett. 78:239

    Article  ADS  Google Scholar 

  24. Craig P.P., Pellam J.R. (1957). Phys. Rev. 108:1109

    Article  ADS  Google Scholar 

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

    Google Scholar 

  26. Kaimal J.C., Wyngaard J.C., Hsugen D.A., Cote O.R., Izumi Y., Caughey S.J., Readings C.J. (1976). J. Atmos. Sci. 33:2152

    Article  ADS  Google Scholar 

  27. Antonia R.A., Chambers A.J., Rajagopalan S., Sreenivasan K.R., Friehe C.A. (1978). J. Phys. Ocean 8:28

    Article  ADS  Google Scholar 

  28. Sreenivasan K.R., Dhruva B. (1998). Prog. Theo. Phys. Suppl. 130:103

    MATH  MathSciNet  ADS  Google Scholar 

  29. Sreenivasan K.R. (1999). Rev. Mod. Phys. 71:S383

    Article  Google Scholar 

  30. Batchelor G.K., The Theory of Homogeneous Turbulence, Cambridge Univesity Press (1953).

  31. Sreenivasan K.R. (1984). Phys Fluids 27:1048

    Article  ADS  Google Scholar 

  32. Sreenivasan K.R. (1998). Phys. Fluids 10:528

    Article  MathSciNet  ADS  MATH  Google Scholar 

  33. Kaneda Y., Ishihara T., Yokakawa M., Itakura M., Uno A. (2003). Phys Fluids 15:L21

    Article  ADS  Google Scholar 

  34. Tabeling P., Zocchi G., Belin F., Maurer J., Willaime H. (1996). Phys. Rev. E 53:1613

    Article  ADS  Google Scholar 

  35. Arneodo A., Baudet C., Belin F., Benzi R., Castaing B., Chabaud B., Chavarria R., Ciliberto S., Camussi R., Chilla F., Dubrulle B., Gagne Y., Hebral B., Herweijer J., Marchand M., Maurer J., Muzy J.F., Naert A., Noullez A., Peinke J., Roux F., Tabeling P., van de Water W., Willaime H. (1996). Europhys. Lett. 34:411

    Article  ADS  Google Scholar 

  36. Sreenivasan K.R., Antonia R.A. (1997). Annu. Rev. Fluid Mech. 29:435

    Article  MathSciNet  ADS  Google Scholar 

  37. Tennekes H., Lumley J.L. (1971). A First Course in Turbulence. MIT Press, Cambridge, Ma

    MATH  Google Scholar 

  38. Emsellem V., Kadanoff L.P., Lohse D., Tabeling P., Wang Z. (1997). Phys. Rev. E 55:2672

    Article  ADS  Google Scholar 

  39. P. Tabeling and Willaime H., Phys. Rev. E 65, 066301 (2002).

  40. Gylfason A., Ayyalasomayajula A., Warhaft Z. (2004). J. Fluid Mech. 501:213

    Article  MATH  ADS  Google Scholar 

  41. Sreenivasan K.R., Meneveau C. (1988). Phys. Rev. A 38:6287

    Article  ADS  Google Scholar 

  42. Paladin G., Vulpiani A. (1987). Phys. Rev. A 35:1971

    Article  ADS  Google Scholar 

  43. Sreenivasan K.R. (2004). Flow Turbul Combust 72:115

    Article  MATH  Google Scholar 

  44. Yakhot V., Sreenivasan K.R. (2004). Physica A 343:147

    Article  MathSciNet  ADS  Google Scholar 

  45. Schumacher J., Sreenivasan K.R., Yeung P.K. (2005). J Fluid Mech 531:113

    Article  MATH  ADS  MathSciNet  Google Scholar 

  46. Maurer J., Tabeling P. (1998). Europhys Lett 43:29

    Article  ADS  Google Scholar 

  47. Bezaguet A., Dauvergne J.P., Knoops S., Ph. Lebrun, Pezzetti M., O. Pirotte, Bret J.L., Chabaud B., Garde G., Guttin C., Hebral B., S. Pietropinto, Roche P., J. P. Barbier-Neyret, Baudet C., Gagne Y., C. Poulain, Castaing B., Y. Ladam and Vittoz F., AIP Conference Proceedings 613, Cryogenic Engineering Conference, Madison, USA, 16-20/07/2001, 1399 (2002).

  48. Antonia R.A., Satyaprakash B.R., Hussain A.K.M.F. (1982). J. Fluid. Mech 119:55

    Article  ADS  Google Scholar 

  49. Chanal O., Baguenard B., Bethoux O., Chabaud B. (1997). Rev. Sci. Instrum 68:2442

    Article  ADS  Google Scholar 

  50. Threlfall D.C. (1975). J. Fluid. Mech 67:17

    Article  ADS  Google Scholar 

  51. Castaing B., Gunaratne G., Heslot F., Kadanoff L., Libchaber A., Thomae S., Wu X.-Z., Zaleski S., Zanetti G. (1989). J. Fluid. Mech. 204:1

    Article  ADS  Google Scholar 

  52. Wu W.-Z., Ph.D. thesis , University of Chicago, Chicago (1991).

  53. Niemela J.J., Skrbek L., Sreenivasan K.R., Donnelly R.J. (2000). Nature 404:837

    Article  ADS  Google Scholar 

  54. Chavanne X., Chilla F., Chabaud B., Castaing B., Hebral B. (2001). Phys. Fluids 13:1300

    Article  ADS  Google Scholar 

  55. Niemela J.J., Sreenivasan K.R. (2003). J. Fluid Mech. 481:355

    Article  MATH  ADS  Google Scholar 

  56. Sparrow E.M., Husar R.B., Goldstein R.J. (1970). J. Fluid Mech. 41:793

    Article  ADS  Google Scholar 

  57. Theerthan S.A., Arakeri J.H. (1998). J. FLuid Mech. 373:221

    Article  MATH  ADS  Google Scholar 

  58. Du Y.B., Tong P. (2000). J. Fluid Mech. 407:57

    Article  MATH  ADS  Google Scholar 

  59. Malkus W.V.R. (1954). Proc. R Soc. Lond. A 225:196

    Article  MATH  MathSciNet  ADS  Google Scholar 

  60. Howard L.N., in Proc. 11th Intern. Cong. Appl. Mech., H. Gortler (ed.), Springer, Berlin, p. 1109 (1966).

  61. Constantin P., Doering C.R. (1999). J. Stat. Phys. 94:159

    Article  MATH  MathSciNet  Google Scholar 

  62. Kraichnan R.H. (1962). Phys. Fluids 5:1374

    Article  ADS  Google Scholar 

  63. D. Lohse and Toschi F., Phys. Rev. Lett. 90, 034502 (2003).

  64. Grossmann S., Lohse D. (2001). Phys. Rev. Lett. 86:3316

    Article  ADS  Google Scholar 

  65. Niemela J.J., Sreenivasan K.R. (2006). J. Fluid Mech. 557:411

    Article  ADS  MATH  Google Scholar 

  66. Roche P., Castaing B., Chabaud B., Hebral B., Sommeria J. (2001). Euro. Phys. J. 24:405

    ADS  Google Scholar 

  67. Ahlers G., Phys. Rev. E. 63, 015303 (2001).

  68. Verzicco R. (2002). J. Fluid Mech. 473:201

    Article  MATH  ADS  Google Scholar 

  69. Roche P.E., Castaing B., Chabaud B., Hebral B. (2004). J. Low Temp. Phys. 134:1011

    Article  ADS  Google Scholar 

  70. Niemela J.J., Skrbek L., Sreenivasan K.R., Donnelly R.J. (2001). J. Fluid Mech. 449:169

    MATH  ADS  Google Scholar 

  71. Sreenivasan K.R., A. Bershadskii and Niemela J.J., Phys. Rev. E 65, 056306 (2002).

    Google Scholar 

  72. Cioni S., Ciliberto S., Sommeria J. (1997). J. Fluid Mech. 335:111

    Article  MathSciNet  ADS  Google Scholar 

  73. X. L. Qui and Tong P., Phys. Rev. E 64, 036304 (2002).

  74. Villermaux E. (1995). Phys. Rev. Lett. 75:4618

    Article  ADS  Google Scholar 

  75. Sun C., K.-Xia Q., and Tong P., Phys. Rev. E 72, 026302 (2005).

  76. Brown E., A. Nikolaenko and Ahlers G., Phys. Rev. Lett. 95, 084503 (2005).

  77. Sreenivasan K.R., Bershadskii A., Niemela J.J. (2004). Physica A 340:574

    Article  ADS  Google Scholar 

  78. Hwa R.C., Yang C.B., Bershadskii S., J. J. Niemela and K. R. Sreenivasan, Phys. Rev. E 72, 066308 (2005).

    Google Scholar 

  79. Bershadskii A., Niemela J.J., Sreenivasan K.R. (2004). Phys. Lett. A 331:15

    Article  ADS  MATH  Google Scholar 

  80. Roche P.E., Ph.thesis D., l‘Universite Joseph Fourier (2001).

  81. Du Y.B., Tong P. (1998). Phys. Rev. Lett. 81:987

    Article  ADS  Google Scholar 

  82. Gordeev A.V., Chagovets T.V., Soukoup F., Skrbek L. (2005). J. Low Temp. Phys. 138:549

    Article  ADS  Google Scholar 

  83. Finne A.P., Araki T., Blaauwgeers R., Eltsov V.B., Kopnin N.B., Krusius M., Skrbek L., Tsubota M., Volovik G.E. (2003). Nature 424:1022

    Article  ADS  Google Scholar 

  84. V. S. L’vov, S. V. Nazarenko and G. E. Volovik arXiv:nlin.CD/0408048 v3 3 Sep 2004.

  85. White C.M., Karpetis A.N., Sreenivasan K.R. (2002) . J. Fluid Mech. 452:189

    Article  MATH  ADS  Google Scholar 

  86. Smith M.R., Ph.thesis D., University of Oregon, Eugene (1992).

  87. Smith M.R., Donnelly R.J., Goldenfeld N., Vinen W.F. (1993). Phys. Rev. Lett. 71:2583

    Article  ADS  Google Scholar 

  88. Stalp S.R., Ph.thesis D., University of Oregon, Eugene (1998).

  89. Niemela J.J., Donnelly R.J., Sreenivasan K.R. (2005) . J. Low Temp. Phys. 138:537

    Article  ADS  Google Scholar 

  90. Barenghi C.F., S. Hulton and Samuels D.C., Phys. Rev. Lett. 89, 275301 (2002).

    Google Scholar 

  91. Niemela J.J., L. Skrbek and S. Stalp in Quantized Vortex Dynamics and Superfluid Turbulence (Proceedings of a Workshop held at the Isaac Newton Mathematical Institute, August 2000), Barenghi C.F., R. J. Donnelly and W. F. Vinen (eds.), Springer (2001).

  92. Barenghi C.F., Donnelly R.J., Vinen W.F. (1983) . J. Low Temp. Phys. 52:189

    Article  ADS  Google Scholar 

  93. Stalp S.R., Niemela J.J., Vinen W.F., Donnelly R.J. (2002) . Phys. Fluids 14:1377

    Article  ADS  Google Scholar 

  94. Skrbek L., Stalp S.R., Phys. Fluids 12, 1997 (2000).

    Google Scholar 

  95. Stalp S.R., Skrbek L., Donnelly R.J. (1999) . Phys. Rev. Lett. 82: 4831

    Article  ADS  Google Scholar 

  96. Skrbek L., Niemela J.J., Donnelly R.J. (2000). Phys. Rev. Lett. 85: 2973

    Article  ADS  Google Scholar 

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

    Google Scholar 

  98. Donzis D., Sreenivasan K.R., Yeung P.K. (2005) . J. Fluid Mech. 532: 199

    Article  MATH  ADS  MathSciNet  Google Scholar 

  99. Bradley D.I., Clubb D.O., Fisher S.N., Guénault A.M., Haley R.P., Matthews C.J., Pickett G.R., Tselpin V., Zaki K. (2006). Phys. Rev. Lett 96: 035301

    Article  ADS  Google Scholar 

  100. Maurer J., Tabeling P. (1998). Europhys. Lett. 43: 29

    Google Scholar 

  101. Corrsin S., in Handbuch der Physik, S. Flugge and C. Truesdell (eds.), Springer, Berlin, 8, part 2, p. 524 (1963).

  102. Grossmann S., Lohse D. (1993) . Phys. Lett. A 174: 449

    Article  Google Scholar 

  103. Furukawa A., Onuki A. (2002) . Phys. Rev. E 66: 016302

    Article  ADS  Google Scholar 

  104. Meyer H., Kogan A.B. (2002) . Phys. Rev. E 66: 056310

    Article  ADS  Google Scholar 

  105. Raffel M., Willert C., Kompenhaus J. (1998). Particle Image Velocimetry. Springer, Berlin

    Google Scholar 

  106. White C.M., Ph.thesis D., Yale University, New Haven (2001).

  107. Donnelly R.J., Karpetis A.N., Niemela J.J., Sreenivasan K.R., Vinen W.F., White C.M. (2002) . J. Low Temp. Phys. 126: 327

    Article  Google Scholar 

  108. Karpetis A.N., White C.M., Sreenivasan K.R. (2000) . Phys. Rev. E 62: 4421

    Article  ADS  Google Scholar 

  109. Zhang T., Van Sciver S.W. (2005) . J. Low Temp. Phys. 138: 865

    Article  ADS  Google Scholar 

  110. Bewley G.P., Lathrop D.P., Sreenivasan K.R. (2006). Nature 441, 588

    Article  ADS  Google Scholar 

  111. Chopra K.L., Brown J.B. (1957). Phys. Rev. 108, 157

    Article  ADS  Google Scholar 

  112. N. Ichikawa and M. Murakami in High Reynolds Number Flows Using Liquid and Gaseous Helium, R. J. Donnelly (ed.), Springer-Verlag (1991).

  113. Poole D.R., Barenghi C.F., Sergeev Y.A., Vinen C.F. (2005). Phys. Rev. B 71, 064514

    Article  ADS  Google Scholar 

  114. A. L. Woodcraft, P. G. J. Lucas, R. G. Matley and W. Y. T. Wong, in Proc. Intern. Workshop on Ultra-High Reynolds Number Flows, R. J. Donnelly and K. R. Sreenivasan (eds.), Springer-Verlag p. 436 (1999).

  115. Matley R.G., Wong W.Y.T., Thurlow M.S., Lucas P.G.J., Lees M.J., Griffiths O.J., Woodcraft A.L. (2001). Phys. Rev. E 63, 045301

    Article  ADS  Google Scholar 

  116. Siefer S., Steinberg V. (2004) . Phys. Fluids 16:1587

    Article  ADS  Google Scholar 

  117. Baudet C., Ciliberto S., Pinton J.-F. (1991). Phys. Rev. Lett. 67, 193

    Article  ADS  Google Scholar 

  118. U. Frisch, Turbulence: the Legacy of A. N. Kolmogorov, Cambridge University Press (1995).

  119. Muriel A., Novopashin S., J. Esguerra and Gutierrez E., Science Diliman 11, http://www.ovcrd.upd.edu.ph/vol

  120. White C.M., Sreenivasan K.R. (1998). Phys. Lett. A 238, 323

    Article  ADS  Google Scholar 

  121. Amati G., Koal K., Massaioli F., Sreenivasan K.R., Verzicco R. (2005). Phys. Fluids 17, 121710

    Article  ADS  Google Scholar 

  122. Schwarz K.W. (1985). Phys. Rev. B, 31, 5782

    Google Scholar 

  123. Schwarz K.W. (1988). Phys. Rev. B, 38:2398

    Article  ADS  Google Scholar 

  124. C. F. Barenghi, in Quantized Vortex Dynamics and Superfluid Turbulence C. F. Barenghi, R. J. Donnelly and W. F. Vinen (eds.), Springer, Berlin, pp. 4-14 (2001).

  125. D. C. Samuels, in Quantized Vortex Dynamics and Superfluid Turbulence, C. F. Barenghi, R. J. Donnelly and W. F. Vinen (eds.), Springer, Berlin pp. 97-112, (2001).

  126. Koplik J., Levine H. (1993). Phys. Rev. Lett. 71:1375

    Article  ADS  Google Scholar 

  127. Nore C., Abid M., Brachet M.E. (1997). Phys. Rev. Lett. 78:3896

    Article  ADS  Google Scholar 

  128. Kerr R.M. (2000). J. Fluid Mech. 419, 325

    Article  MATH  MathSciNet  ADS  Google Scholar 

  129. D. N. McKinsey, W. H. Lippincott, J. Nikkel and W. Rellergert, arXiv:nucl-ex/0503006 v1 11 Mar 2005.

  130. Niemela J.J. (2004). J. Low Temp. Phys. 134, 447

    Article  ADS  Google Scholar 

  131. R. du Puits, C. Resagk, A. Tilgner, F. H. Busse and A. Thess “Structure of thermal boundary layers in turbulent Rayleigh Benard convection” (to be published in J. Fluid Mech).

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Niemela, J.J., Sreenivasan, K.R. The Use of Cryogenic Helium for Classical Turbulence: Promises and Hurdles. J Low Temp Phys 143, 163–212 (2006). https://doi.org/10.1007/s10909-006-9221-9

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