Issues

 / 

2009

 / 

September

  

Methodological notes


Hydrodynamic and hydromagnetic stability of the Couette flow


Ioffe Institute, ul. Polytekhnicheskaya 26, St. Petersburg, 194021, Russian Federation

The stability of the dissipative Couette flow is examined in the linear approximation. The onset conditions and flow instability properties are studied, with special emphasis placed on the instability properties in the presence of a magnetic field and density stratification. Theoretical and experimental results on instability parameters are found to be in good agreement (within a few percent).

Fulltext pdf (342 KB)
Fulltext is also available at DOI: 10.3367/UFNe.0179.200909d.0971
PACS: 47.20.Qr, 47.65.−d, 52.30.Cv (all)
DOI: 10.3367/UFNe.0179.200909d.0971
URL: https://ufn.ru/en/articles/2009/9/d/
000274047000004
2-s2.0-76149134667
2009PhyU...52..915S
Citation: Shalybkov D A "Hydrodynamic and hydromagnetic stability of the Couette flow" Phys. Usp. 52 915–935 (2009)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Шалыбков Д А «Гидродинамическая и гидромагнитная устойчивость течения Куэтта» УФН 179 971–993 (2009); DOI: 10.3367/UFNr.0179.200909d.0971

References (107) ↓ Cited by (18) Similar articles (20)

  1. Mallock A Proc. R. Soc. London A 45 126 (1888)
  2. Couette M Ann. Chim. Phys. 21 433 (1890)
  3. Mallock A Philos. Trans. R. Soc. London A 187 41 (1896)
  4. Lord Rayleigh Proc. R. Soc. London A 93 148 (1917)
  5. Synge J L Proc. R. Soc. Can. 27 1 (1933)
  6. Synge J L Proc. R. Soc. London A 167 250 (1938)
  7. Chandrasekhar S Hydrodynamic And Hydromagnetic Stability (Oxford: Clarendon Press, 1961)
  8. Taylor G J Philos. Trans. R. Soc. London A 223 289 (1923)
  9. Dutcher C S, Muller S J Phys. Rev. E 75 047301 (2007)
  10. Drazin P G, Reid W H Hydrodynamic Stability (Cambridge: Cambridge Univ. Press, 1981)
  11. DiPrima R C, Swinney H L In Hydrodynamic Instabilities And The Transition To Turbulance (Topics In Applied Physics, Vol. 45, Eds H L Swinney, J P Gollub) (Berlin: Springer-Verlag, 1981) p. 139
  12. Tagg R Nonlin. Sci. Today 4 (3) 1 (1994)
  13. Chossat P, Iooss G The Couette - Taylor Problem (New York: Springer-Verlag, 1994)
  14. 15th Intern. Couette - Taylor Workshop, 9 - 12 July 2007, LMPG, Le Havre Univ., France; J. Phys. Conf. Ser. 137 (2008)
  15. Brevdo L, Bridges T J Proc. R. Soc. London A 453 1345 (1997)
  16. Taylor G I Proc. R. Soc. London A 157 546 (1936)
  17. Dubrulle B et al. Phys. Fluids 17 095103 (2005)
  18. Ji H et al. Nature 444 343 (2006)
  19. Schultz-Grunow F Z. Angew. Math. Mech. 39 101 (1959)
  20. Hollerbach R, Fournier A AIP Conf. Proc. 733 114 (2004)
  21. Andereck C D, Liu S S, Swinney H L J. Fluid Mech. 164 155 (1986)
  22. Wendl M C Phys. Rev. E 60 6192 (1999)
  23. Landau L D, Lifshits E M Gidrodinamika (M.: Nauka, 1986) p. 143; Landau L D, Lifshitz E M Fluid Mechanics (Oxford: Pergamon Press, 1987)
  24. Leblanc S, Le Duc A J. Fluid Mech. 537 433 (2005)
  25. Billant P, Gallaire F J. Fluid Mech. 542 365 (2005)
  26. Howard L N, Gupta A S J. Fluid Mech. 14 463 (1962)
  27. Blaes O M, Glatzel W Mon. Not. R. Astron. Soc. 220 253 (1986)
  28. Goldreich P, Narayan R Mon. Not. R. Astron. Soc. 213 7P (1985)
  29. Kubotani H et al. Prog. Theor. Phys. 82 523 (1989)
  30. Roberts P "Appendix to paper Donnelly and Schwarz" Proc. R. Soc. London A 283 550 (1965)
  31. Langford W F et al. Phys. Fluids 31 776 (1988)
  32. Herron I H, Ali H N Quart. Appl. Math. 61 279 (2003)
  33. Fricke K J, Smith R C Astron. Astrophys. 15 329 (1971)
  34. Jenny M, Nsom B Phys. Fluids 19 108104 (2007)
  35. Manela A, Frankel I J. Fluid Mech. 588 59 (2007)
  36. Boubnov B M, Gledzer E B, Hopfinger E J J. Fluid Mech. 292 333 (1995)
  37. Caton F, Janiaud B, Hopfinger E J J. Fluid Mech. 419 93 (2000)
  38. Thorpe S A In Notes On 1966 Summer Geophysical Fluid Dynamics (Woods Hole, MA: Woods Hole Oceanographic Institute, 1966) p. 80
  39. Hua B L, Le Gentil S, Orlandi P Phys. Fluids 9 365 (1997)
  40. Withjack E M, Chen C F J. Fluid Mech. 66 725 (1974)
  41. Molemaker M J, McWilliams J C, Yavneh I Phys. Rev. Lett. 86 5270 (2001)
  42. Yavneh I, McWilliams J C, Molemaker M J J. Fluid Mech. 448 1 (2001)
  43. Shalybkov D, Rüdiger G Astron. Astrophys. 438 411 (2005)
  44. Le Bars M, Le Gal P Phys. Rev. Lett. 99 064502 (2007)
  45. Rüdiger G, Shalybkov D A Astron. Astrophys. 493 375 (2009)
  46. Velikhov E P Zh. Eksp. Teor. Fiz. 36 1398 (1959); Velikhov E P Sov. Phys. JETP 9 995 (1959)
  47. Balbus S A, Hawley J F Astrophys. J. 376 214 (1991)
  48. Balbus S A, Hawley J F Rev. Mod. Phys. 70 1 (1998)
  49. Balbus S A Annu. Rev. Astron. Astrophys. 41 555 (2003)
  50. Mahajan S M, Krishan V Astrophys. J. 682 602 (2008)
  51. Donnelly R J, Ozima M Phys. Rev. Lett. 4 497 (1960)
  52. Donnelly R J, Ozima M Proc. R. Soc. London A 266 272 (1962)
  53. Donnelly R J, Caldwell D R J. Fluid Mech. 19 257 (1964)
  54. Brahme A Phys. Scr. 2 108 (1970)
  55. Sisan D R et al. Phys. Rev. Lett. 93 114502 (2004)
  56. Chang T S, Sartory W K Proc. R. Soc. London A 301 451 (1967)
  57. Hassard B D, Chang T S, Ludford G S S Proc. R. Soc. London A 327 269 (1972)
  58. Soundalgekar V M, Ali M A, Takhar H S Int. J. Energy Res. 18 689 (1994)
  59. Chen C-K, Chan M H J. Fluid Mech. 366 135 (1998)
  60. Kurzweg U H J. Fluid Mech. 17 52 (1963)
  61. Goodman J, Ji H J. Fluid Mech. 462 365 (2002)
  62. Rüdiger G, Shalybkov D Phys. Rev. E 66 016307 (2002)
  63. Rüdiger G, Schultz M, Shalybkov D Phys. Rev. E 67 046312 (2003)
  64. Wang Z et al. Phys. Plasmas 15 102109 (2008)
  65. Willis A P, Barenghi C F Astron. Astrophys. 388 688 (2002)
  66. Velikhov E P et al. Phys. Lett. A 356 357 (2006)
  67. Shalybkov D A, Rüdiger G, Schultz M Astron. Astrophys. 395 339 (2002)
  68. Michael D H Mathematika London 1 45 (1954)
  69. Kadomtsev B B v Sb. Voprosy Teorii Plazmy Vol. 2 (Pod red. M A Leontovicha) (M.: Gosatomizdat, 1963) p. 132
  70. Edmonds F N (Jr.) Phys. Fluids 1 30 (1958)
  71. Shalybkov D Phys. Rev. E 73 016302 (2006)
  72. Shalybkov D Phys. Rev. E 75 047302 (2007)
  73. Shalybkov D Phys. Rev. E 76 027302 (2007)
  74. Tayler R J J. Nucl. Energy C 3 266 (1961)
  75. Tayler R J Mon. Not. R. Astron. Soc. 161 365 (1973)
  76. Rüdiger G et al. Phys. Rev. E 76 056309 (2007)
  77. Ogilvie G I, Pringle J E Mon. Not. R. Astron. Soc. 279 152 (1996)
  78. Rüdiger G et al. Mon. Not. R. Astron. Soc. 377 1481 (2007)
  79. Rüdiger G et al. Astron. Nachr. 328 1158 (2007)
  80. Bernstein I B et al. Proc. R. Soc. London A 244 17 (1958)
  81. Frieman E, Rotenberg M Rev. Mod. Phys. 32 898 (1960)
  82. Lundquist S Phys. Rev. 83 307 (1951)
  83. Newcomb W A Ann. Physics 10 232 (1960)
  84. Suydam B R in Proc. Second United Nat. Intern. Conf. on the Peaceful uses of Atomic Energy Vol. 31 (Geneva, 1958) p. 157; Saidem B v Sb. Trudy Vtoroi Mezhdunar. Konf. Po Mirnomu Ispol’zovaniyu Atomnoi Energii. Izbrannye Dokl. Inostrannykh Uchenykh. Fizika Goryachei Plazmy i Termoyadernye Reaktsii (Pod red. V F Kadinina) (M.: Izd-vo Glavnogo upr. po ispol’zovaniyu atomnoi energii pri SM SSSR, 1959) p. 89
  85. Bondeson A, Iacono R, Bhattacharjee A Phys. Fluids 30 2167 (1987)
  86. Wang C et al. J. Plasma Phys. 70 651 (2004)
  87. Tayler R J Rev. Mod. Phys. 32 907 (1960)
  88. Tayler R J, Hopgood F R A J. Nucl. Energy C 5 355 (1963)
  89. Longaretti P-Y Phys. Lett. A 320 215 (2003)
  90. Hollerbach R, Rüdiger G Phys. Rev. Lett. 95 124501 (2005)
  91. Rüdiger G et al. Astron. Nachr. 326 409 (2005)
  92. Rüdiger G, Shalybkov D Phys. Rev. E 69 016303 (2004)
  93. Wardle M Mon. Not. R. Astron. Soc. 307 849 (1999)
  94. Balbus S A, Terquem C Astrophys. J. 552 235 (2001)
  95. Sano T, Stone J M Astrophys. J. 570 314 (2002)
  96. Sano T, Stone J M Astrophys. J. 577 534 (2002)
  97. Rüdiger G, Kitchatinov L L Astron. Astrophys. 434 629 (2005)
  98. Rüdiger G et al. Astron. Nachr. 330 12 (2009)
  99. Chanmugam G Mon. Not. R. Astron. Soc. 187 769 (1979)
  100. Umurhan O M Mon. Not. R. Astron. Soc. 365 85 (2006)
  101. Dubrulle B et al. Astron. Astrophys. 429 1 (2005)
  102. Rüdiger G et al. Astrophys. J. Lett. 649 L145 (2006)
  103. Stefani F et al. Phys. Rev. Lett. 97 184502 (2006)
  104. Stefani F et al. Astron. Nachr. 329 652 (2008)
  105. Liu W, Goodman J, Ji H Phys. Rev. E 76 016310 (2007)
  106. Liu W Phys. Rev. E 77 056314 (2008)
  107. Mikhailovskii A B et al. Phys. Plasmas 15 014504 (2008)

© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions