RSS feeds
РусскийEnglish
Issue 11, 2024
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

2005

 / 

December

←  →



On the mechanical prototypes of fundamental hydrodynamic invariants and slow manifolds


Arnol’d’s group-theoretical concept of generalized rigid body includes the Euler equations of motion of the classical gyroscope and ideal homogeneous fluid as particular representatives. Here, this concept is extended to motion in force fields with a scalar or vector potential and in a Coriolis force field. The concepts of generalized heavy top and generalized MHD system are introduced. As particular cases, they include, on the one hand, the Euler-Poisson equations of the classical heavy top and the Kirchhoff equations of motion of a solid body in a potential flow of an ideal incompressible fluid and, on the other hand, the Oberbeck-Boussinesq equations of motion of a heavy fluid and MHD equations. On this basis, mechanical prototypes are constructed for all known fundamental hydrodynamic invariants and global geophysical flows, including a prototype of the general atmospheric circulation.

Fulltext pdf (700 KB)
Fulltext is also available at DOI: 10.1070/PU2005v048n12ABEH002375
PACS: 02.40.−k, 45.40.−f, 92.10.−c, 92.60.−e (all)
DOI: 10.1070/PU2005v048n12ABEH002375
URL: https://ufn.ru/en/articles/2005/12/a/
000236670800001
2005PhyU...48.1205D
Citation: Dolzhanskii F V "On the mechanical prototypes of fundamental hydrodynamic invariants and slow manifolds" Phys. Usp. 48 1205–1234 (2005)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Должанский Ф В «О механических прообразах фундаментальных гидродинамических инвариантов и медленных многообразий» УФН 175 1257–1288 (2005); DOI: 10.3367/UFNr.0175.200512a.1257

References (63) ↓ Cited by (17)

  1. Greenhill A G Proc. Camb. Philos. Soc. 3 233 (1879)
  2. Zhukovskii N E Zhurn. Russk. Fiz.-khim. Obshch. 17/1 81 (1885); Zhukovskii N E Zhurn. Russk. Fiz.-khim. Obshch. 17/1 145 (1885); Zhukovskii N E Zhurn. Russk. Fiz.-khim. Obshch. 17/1 431 (1885)
  3. Hough S S Philos. Trans. R. Soc. London A 186 (1) 469 (1895)
  4. Poincaré H Bull. Astron. 27 321 (1910)
  5. Moiseev N N, Rumyantsev V V Dinamika Tel s Polostyami, Soderzhashchimi Zhidkost’ (M.: Nauka, 1965)
  6. Arnold V Ann. Inst. Fourier 16 (1) 319 (1966)
  7. Arnol’d V I Matematicheskie Metody Klassicheskoi Mekhaniki (M.: Nauka, 1979)
  8. Arnold V I, Khesin B A Topological Methods In Hydrodynamics (Appl. Math. Sci., Vol. 125) (New York: Springer, 1999)
  9. Kirchhoff G R Vorlesungen über Mathematische Physik (Leipzig: B.G. Teubner, 1876)
  10. Dolzhanskii F V Izv. RAN. Ser. Fiz. Atm. Okeana 37 446 (2001)
  11. Rossby C G et al. J. Marine Res. 2 38 (1939)
  12. Ertel H Meteorol. Z. 59 (9) 277 (1942)
  13. Obukhov A M Izv. AN SSSR. Ser. Geograf. Geofiz. 13 281 (1949)
  14. Landau L D, Lifshits E M Gidrodinamika (M.: Nauka, 1986)
  15. Moreau J J C.R. Acad. Sci. 252 2810 (1961)
  16. Moffatt H K J. Fluid Mech. 35 117 (1969)
  17. Woltjer L Proc. Natl. Acad. Sci. USA 44 489 (1958); Woltjer L Proc. Natl. Acad. Sci. USA 44 833 (1958)
  18. Lorenz E N J. Atm. Sci. 37 1685 (1980)
  19. Lorenz E N J. Atm. Sci. 43 1547 (1986)
  20. Lorenz E N, Krishnamurthy V J. Atm. Sci. 44 2940 (1987)
  21. Reznik G M, Zeitlin V, Ben Jelloul M J. Fluid Mech. 445 93 (2001)
  22. Lorenz E N J. Atm. Sci. 20 130 (1963)
  23. Landau L D, Lifshits E M Mekhanika (M.: Nauka, 1973)
  24. Kochin N E, Kibel’ I A, Roze N V Teoreticheskaya Gidromekhanika Vol. 1 (M.: Fizmatgiz, 1963)
  25. Lamb H Hydrodynamics (Cambridge: Cambridge Univ. Press, 1993)
  26. Gledzer E B, Dolzhanskii F V, Obukhov A M Sistemy Gidrodinamicheskogo Tipa i Ikh Primenenie (M.: Nauka, 1981)
  27. Dolzhanskii F V Izv. AN SSSR. Ser. Fiz. Atm. Okeana 8 661 (1972)
  28. Dolzhanskii F V Izv. AN SSSR. Ser. Fiz. Atm. Okeana 13 201 (1977)
  29. Vishik S M, Dolzhanskii F V Dokl. Akad. Nauk SSSR 238 1032 (1978)
  30. Vishik S M v Kn. Kochin N E, Kibel’ I A, Roze N V, Teoreticheskaya Gidromekhanika Vol. 1 (M.: Fizmatgiz, 1963), Prilozhenie 2
  31. Pedlosky J Geophysical Fluid Dynamics (Heidelberg: Springer, 1979); Pedloski Dzh Geofizicheskaya Gidrodinamika (M.: Mir, 1984)
  32. Moran F Publ. Inst. Nac. Geofis. (Madrid) 21 (1942)
  33. Charney J G Geophys. Publ. 17 (2) 1 (1948)
  34. Obukhov A M v Sb. N.E. Kochin i Razvitie Mekhaniki (Otv. red. A Yu Ishlinskii, sost. N N Kochina) (M.: Nauka, 1984)
  35. Zakharov V E, Kuznetsov E A Usp. Fiz. Nauk 167 1137 (1997); Zakharov V E, Kuznetsov E A Phys. Usp. 40 1087 (1997)
  36. Salmon R AIP Conf. Proc. 88 127 (1982)
  37. Salmon R J. Fluid Mech. 132 431 (1983)
  38. Salmon R Annu. Rev. Fluid Mech. 20 225 (1988)
  39. Obukhov A M Meteorol. Gidrol. (2) 3 (1964)
  40. Hoskins B J, McIntyre M E, Robertson A W Quart. J. R. Meteorol. Soc. 111 877 (1985)
  41. Obukhov A M, Kurganskii M V, Tatarskaya M S Meteorol. Gidrol. (8) 111 (1988)
  42. Haynes P H, McIntyre M E J. Atm. Sci. 47 2021 (1990)
  43. Viúdez Á J. Atm. Sci. 56 507 (1999)
  44. Ogorodnikova N P, Putin G F Dokl. Akad. Nauk SSSR 269 1065 (1983)
  45. Dolzhanskii F V, Ponomarev V M Izv. RAN. Ser. Fiz. Atm. Okeana 38 316 (2002)
  46. Arnol’d V I i dr. v Sb. Itogi Nauki i Tekhniki (Ser. Sovremennye problemy matematiki. Fundamental’nye napravleniya) Vol. 5 (Pod red. V I Arnol’da, R V Gamkrelidze) (M.: VINITI, 1986)
  47. Eady E T Tellus 1 33 (1949)
  48. Glukhovskii A B, Dolzhanskii F V Izv. AN SSSR. Ser. Fiz. Atm. Okeana 16 451 (1980)
  49. Ziglin S L Tr. Mosk. Mat. Obshch. 41 287 (1980)
  50. Gledzer A E Izv. RAN. Ser. Fiz. Atm. Okeana 39 466 (2003)
  51. Dolzhanskii F V, Myamlina L A Izv. AN SSSR. Ser. Fiz. Atm. Okeana 12 3 (1976)
  52. Dolzhanskii F V, Pleshanova L A v Sb. Fizika Atmosfery i Problema Klimata (Otv. red. G S Golitsyn, A M Yaglom) (M.: Nauka, 1980)
  53. Lorenz E N The Nature And Theory Of The General Circulation Of The Atmosphere (Geneva: World Meteorological Organization, 1967); Lorents E N Priroda i Teoriya Obshchei Tsirkulyatsii Atmosfery (L.: Gidrometeoizdat, 1970)
  54. Starr V P Physics Of Negative Viscosity Phenomena (New York: McGraw-Hill, 1968); Starr V Fizika Yavlenii s Otritsatel’noi Vyazkost’yu (M.: Mir, 1971)
  55. Hide R, Mason P T Adv. Phys. 24 (1) 47 (1975)
  56. Dolzhanskii F V, Golitsyn G S Izv. AN SSSR. Ser. Fiz. Atm. Okeana 13 550 (1977)
  57. Dolzhanskii F V Izv. AN SSSR. Ser. Fiz. Atm. Okeana 17 563 (1981)
  58. Lorenz E N J. Atm. Sci. 19 39 (1962)
  59. Lorenz E N J. Atm. Sci. 20 448 (1963)
  60. Gledzer A E i dr. Izv. RAN. Ser. Fiz. Atm. Okeana, v pechati
  61. Hill M J M Philos. Trans. R. Soc. London A 185 (1894)
  62. Batchelor G K An Introduction To Fluid Dynamics (Cambridge: Univ. Press, 1967); Betchelor Dzh Vvedenie v Dinamiku Zhidkosti (M.: Mir, 1973)
  63. Saffman P G Vortex Dynamics (Cambridge: Cambridge Univ. Press, 1992); Seffmen F Dzh Dinamika Vikhrei (M.: Nauchnyi mir, 2000)
© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions