Skip to main content
Log in

Hydrodynamic stability and stellar oscillations

  • Published:
Pramana Aims and scope Submit manuscript

Abstract

Chandrasekhar’s monograph on Hydrodynamic and hydromagnetic stability, published in 1961, is a standard reference on linear stability theory. It gives a detailed account of stability of fluid flow in a variety of circumstances, including convection, stability of Couette flow, Rayleigh–Taylor instability, Kelvin–Helmholtz instability as well as the Jean’s instability for star formation. In most cases he has extended these studies to include effects of rotation and magnetic field. In a later paper he has given a variational formulation for equations of non-radial stellar oscillations. This forms the basis for helioseismic inversion techniques as well as extension to include the effect of rotation, magnetic field and other large-scale flows using a perturbation treatment.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. S Chandrasekhar, Hydrodynamic and hydromagnetic stability (Clarendon, Oxford, 1961)

    MATH  Google Scholar 

  2. S Chandrasekhar, Astrophys. J. 139, 664 (1964)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. L Rayleigh, Phil. Mag. 32, 529 (1916)

    Google Scholar 

  4. H Bénard, Ann. Chimie Phys. 23, 62 (1901)

    Google Scholar 

  5. Å Nordlund and R F Stein, Comp. Phys. Comm. 59, 119 (1990)

    Article  ADS  MATH  Google Scholar 

  6. R F Stein and Å Nordlund, Astrophys. J. 499, 914 (1998)

    Article  ADS  Google Scholar 

  7. M Steffen, H-G Ludwig and B Freytag, Astron. Nach. Supp. 3, 174 (2003)

    ADS  Google Scholar 

  8. H H Plasket, Mon. Not. R. Astron. Soc. 114, 251 (1954)

    ADS  Google Scholar 

  9. M Asplund, N Grevesse and A J Sauval, in Cosmic abundances as records of stellar evolution and nucleosynthesis edited by T G Barnes, F N Bash, ASP Conf. Ser. 336, 25 (2005)

  10. S Basu and H M Antia, Phys. Rep. 457, 217 (2008)

    Article  ADS  Google Scholar 

  11. E Caffau, H-G Ludwig, M Steffen, B Freytag and P Bonifacio, Solar Phys. 268, 255 (2011), arXiv:1003.1190

    Article  ADS  Google Scholar 

  12. M C Cross and P Hohenberg, Rev. Mod. Phys. 65, 851 (1993)

    Article  ADS  Google Scholar 

  13. M C Begelman, R D Blandford and M J Rees, Rev. Mod. Phys. 56, 255 (1984)

    Article  ADS  Google Scholar 

  14. J S Langer, Rev. Mod. Phys. 52, 1 (1980)

    Article  ADS  Google Scholar 

  15. E N Parker, Astrophys. J. 145, 811 (1966)

    Article  ADS  Google Scholar 

  16. S H Lubow and F Shu, Astrophys. J. 198, 383 (1975)

    Article  ADS  Google Scholar 

  17. V M Canuto and I Mazzitelli, Astrophys. J. 370, 295 (1991)

    Article  ADS  Google Scholar 

  18. S Basu and H M Antia, J. Astrophys. Astron. 15, 143 (1994)

    Article  ADS  Google Scholar 

  19. P H Scherrer et al, Solar Phys. 162, 129 (1995)

    Article  ADS  Google Scholar 

  20. J Schou, A G Kosovichev, P R Goode and W A Dziembowski, Astrophys. J. 489, L197 (1997)

    Article  ADS  Google Scholar 

  21. H M Antia, Astron. Astrophys. 330, 336 (1998)

    ADS  Google Scholar 

  22. W H Press and S A Teukolsky, Astrophys. J. 213, 183 (1977)

    Article  MathSciNet  ADS  Google Scholar 

  23. A Fabian, J Pringle and M J Rees, Mon. Not. R. Astron. Soc. 172, 15 (1975)

    ADS  Google Scholar 

  24. J L Friedman, J R Ipser and L Parker, Astrophys. J. 304, 115 (1986)

    Article  ADS  Google Scholar 

  25. D Lynden-Bell and J P Ostriker, Mon. Not. R. Astron. Soc. 136, 293 (1967)

    ADS  MATH  Google Scholar 

  26. M J Clement, Astrophys. J. 140, 1045 (1964)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. D O Gough and M J Thompson, in Solar interior and atmosphere edited by A N Cox, W C Livingston and M Matthews, Space Science Series (University of Arizona Press) p. 519

  28. F Hill et al, Science 272, 1292 (1996)

    Article  ADS  Google Scholar 

  29. A S Brun, H M Antia, S M Chitre and J-P Zahn, Astron. Astrophys. 391, 725 (2002)

    Article  ADS  Google Scholar 

  30. M Asplund, N Grevesse, A J Sauval, C Allende Prieto and D Kiselman, Astron. Astrophys. 417, 751 (2004); Erratum, Astron. Astrophys. 435, 339 (2005)

  31. J N Bahcall and M H Pinsonneault, Phys. Rev. Lett. 92, 121301 (2004)

    Article  ADS  Google Scholar 

  32. H M Antia and S Basu, Astrophys. J. 620, L129 (2005)

    Article  ADS  Google Scholar 

  33. M H Ritzwoller and E M Lavely, Astrophys. J. 369, 557 (1991)

    Article  ADS  Google Scholar 

  34. J Schou, J Christensen-Dalsgaard and M J Thompson, Astrophys. J. 433, 389 (1994)

    Article  ADS  Google Scholar 

  35. E A Spiegel and J-P Zahn, Astron. Astrophys. 265, 106 (1992)

    ADS  Google Scholar 

  36. F P Pijpers, Mon. Not. R. Astron. Soc. 297, L76 (1998)

    Article  ADS  Google Scholar 

  37. R H Dicke, J R Kuhn and K G Libbrecht, Nature 316, 687 (1985)

    Article  ADS  Google Scholar 

  38. D O Gough and M J Thompson, Mon. Not. R. Astron. Soc. 242, 25 (1990)

    ADS  MATH  Google Scholar 

  39. H M Antia, S M Chitre and M J Thompson, Astron. Astrophys. 360, 335 (2000)

    ADS  Google Scholar 

  40. C S Baldner, H M Antia, S Basu and T P Larson, Astrophys. J. 705, 1704 (2009)

    Article  ADS  Google Scholar 

  41. E M Lavely and M H Ritzwoller, Phil. Tran. Phys. Sci. Eng. 339, 431 (1992)

    Article  ADS  Google Scholar 

  42. P Chatterjee and H M Antia, Astrophys. J. 707, 208 (2009)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to H M ANTIA.

Rights and permissions

Reprints and permissions

About this article

Cite this article

ANTIA, H.M. Hydrodynamic stability and stellar oscillations. Pramana - J Phys 77, 3–18 (2011). https://doi.org/10.1007/s12043-011-0107-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12043-011-0107-2

Keywords

PACS Nos

Navigation