Skip to main content
SpringerLink
Log in

Chandrasekhar–Kendall functions in astrophysical dynamos

  • Published:
Pramana Aims and scope Submit manuscript

Abstract

Some of the contributions of Chandrasekhar to the field of magnetohydrodynamics are highlighted. Particular emphasis is placed on the Chandrasekhar–Kendall functions that allow a decomposition of a vector field into right- and left-handed contributions. Magnetic energy spectra of both contributions are shown for a new set of helically forced simulations at resolutions higher than what has been available so far. For a forcing function with positive helicity, these simulations show a forward cascade of the right-handed contributions to the magnetic field and nonlocal inverse transfer for the left-handed contributions. The speed of inverse transfer is shown to decrease with increasing value of the magnetic Reynolds number.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. E N Parker, J. Astrophys. Astron. 17, 147 (1996)

    Article  ADS  Google Scholar 

  2. W Heisenberg, Z. Phys. 124, 628 (1948)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. J S Hall, Science 109, 166 (1949)

    Article  ADS  Google Scholar 

  4. W A Hiltner, Astrophys. J. 109, 471 (1949)

    Article  ADS  Google Scholar 

  5. S Chandrasekhar and E Fermi, Astrophys. J. 118, 113 (1953)

    Article  MathSciNet  ADS  Google Scholar 

  6. D Falceta-Goncalves, A Lazarian and G Kowal, Astrophys. J. 679, 537 (2008)

    Article  ADS  Google Scholar 

  7. H W Babcock and H D Babcock, Astrophys. J. 121, 349 (1955)

    Article  ADS  Google Scholar 

  8. H W Babcock, Astrophys. J. 105, 105 (1947)

    Article  ADS  Google Scholar 

  9. T G Cowling, Mon. Not. R. Astron. Soc. 94, 39 (1933)

    ADS  MATH  Google Scholar 

  10. S Chandrasekhar, Astrophys. J. 124, 232 (1956)

    Article  MathSciNet  ADS  Google Scholar 

  11. A Herzenberg, Proc. R. Soc. London 250A, 543 (1958)

    MathSciNet  ADS  Google Scholar 

  12. S Chandrasekhar, Astrophys. J. 124, 244 (1956)

    Article  MathSciNet  ADS  Google Scholar 

  13. E N Parker, Astrophys. J. 122, 293 (1955)

    Article  MathSciNet  ADS  Google Scholar 

  14. E Bullard and H Gellman, Phil. Trans. R. Soc. London, Ser. A247, 213 (1954)

    Article  MathSciNet  ADS  Google Scholar 

  15. W M Elsasser, Am. J. Phys. 23, 590 (1955)

    Article  ADS  MATH  Google Scholar 

  16. W M Elsasser, Am. J. Phys. 24, 85 (1956)

    Article  ADS  Google Scholar 

  17. S Chandrasekhar, Hydrodynamic and hydromagnetic stability (Dover Publ., New York, 1961)

    MATH  Google Scholar 

  18. S Chandrasekhar and P C Kendall, Astrophys. J. 126, 457 (1957)

    Article  MathSciNet  ADS  Google Scholar 

  19. U Frisch, A Pouquet, J Léorat and A Mazure, J. Fluid Mech. 68, 769 (1975)

    Article  ADS  MATH  Google Scholar 

  20. A Pouquet, U Frisch and J Léorat, J. Fluid Mech. 77, 321 (1976)

    Article  ADS  MATH  Google Scholar 

  21. A Brandenburg, ÅNordlund, R F Stein and I Torkelsson, Astrophys. J. 446, 741 (1995)

    Article  ADS  Google Scholar 

  22. O Gressel, D Elstner, U Ziegler and G Rüdiger, Astron. Astrophys. 486, L35 (2008)

    Article  ADS  Google Scholar 

  23. A Brandenburg, K Enqvist and P Olesen, Phys. Rev. D54, 1291 (1996)

    ADS  Google Scholar 

  24. M Christensson, M Hindmarsh and A Brandenburg, Phys. Rev. E64, 056405 (2001)

    ADS  Google Scholar 

  25. R Lüst and A Schlüter, Z. Astrophys. 34, 263 (1954)

    MathSciNet  MATH  Google Scholar 

  26. S Chandrasekhar, Proc. Natl. Acad. Sci. 42, 1 (1956)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. B C Low, Astrophys. J. 212, 234 (1977)

    Article  ADS  Google Scholar 

  28. J B Taylor, Phys. Rev. Lett. 58, 741 (1986)

    Google Scholar 

  29. V Krishan, Solar Phys. 97, 183 (1985)

    Article  ADS  Google Scholar 

  30. E C Morse, J. Math. Phys. 48, 083504 (2007)

    Article  MathSciNet  Google Scholar 

  31. M G Linton, R B Dahlburg, G H Fisher and D W Longcope, Astrophys. J. 507, 404 (1998)

    Article  ADS  Google Scholar 

  32. F Alladio, A Mancuso, P Micozzi and F Rogier, Phys. Plasmas 12, 112502 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  33. F Waleffe, Phys. Fluids A5, 677 (1993)

    ADS  Google Scholar 

  34. A Brandenburg, W Dobler and K Subramanian, Astron. Nachr. 323, 99 (2002)

    Article  ADS  MATH  Google Scholar 

  35. H K Moffatt, J. Fluid Mech. 35, 117 (1969)

    Article  ADS  MATH  Google Scholar 

  36. A Brandenburg and K Subramanian, Phys. Rep. 417, 1 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  37. D Balsara and A Pouquet, Phys. Plasmas 6, 89 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  38. A Brandenburg, Astrophys. J. 550, 824 (2001)

    Article  ADS  Google Scholar 

  39. http://pencil-code.googlecode.com

  40. R Durrer and C Caprini, J. Cosmol. Astropart. Phys. 0311, 010 (2003)

    Article  ADS  Google Scholar 

  41. M Berger, Geophys. Astrophys. Fluid Dynam. 30, 79 (1984)

    Article  ADS  Google Scholar 

  42. N I Kleeorin and A A Ruzmaikin, Magnetohydrodynamics 18, 116 (1982)

    Google Scholar 

  43. G B Field and E G Blackman, Astrophys. J. 572, 685 (2002)

    Article  ADS  Google Scholar 

  44. E G Blackman and A Brandenburg, Astrophys. J. 579, 359 (2002)

    Article  ADS  Google Scholar 

  45. K Subramanian, Bull. Astron. Soc. India 30, 715 (2002)

    ADS  Google Scholar 

  46. M K Verma, Phys. Plasmas 8, 3945 (2001)

    Article  ADS  Google Scholar 

  47. W-C Müller and S K Malapaka, in: Numerical modeling of space plasma flows edited by N V Pogorelov, E Audit and G P Zank (Astron. Soc. Pac., San Francisco, 2010) p. 28

  48. S Chandrasekhar, Phil. Trans. R. Soc. London, Ser. A216, 293 (1953)

    MathSciNet  ADS  Google Scholar 

  49. E P Velikhov, Sov. Phys. JETP 36, 1398 (1959)

    Google Scholar 

  50. S Chandrasekhar, Proc. Natl. Acad. Sci. 46, 253 (1960)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  51. S A Balbus and J F Hawley, Astrophys. J. 376, 214 (1991)

    Article  ADS  Google Scholar 

  52. V S Safronov, Evolution of the protoplanetary cloud and formation of the Earth and the planets, Israel Program for Scientific Translation, Jerusalem (1972)

  53. N I Shakura and R A Sunyaev, Astron. Astrophys. 24, 337 (1973)

    ADS  Google Scholar 

  54. S H Hong, Z. Angew. Math. Phys. 27, 483 (1976)

    Article  MATH  Google Scholar 

  55. J M Stone, J F Hawley, C F Gammie and S A Balbus, Astrophys. J. 463, 656 (1996)

    Article  ADS  Google Scholar 

  56. U Ziegler and G Rüdiger, Astron. Astrophys. 378, 668 (2001)

    Article  ADS  Google Scholar 

  57. O Gressel, Mon. Not. R. Astron. Soc. 405, 41 (2010)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. NORDITA, AlbaNova University Center, Roslagstullsbacken 23, SE 10691, Stockholm, Sweden

    AXEL BRANDENBURG

  2. Department of Astronomy, Stockholm University, SE 10691, Stockholm, Sweden

    AXEL BRANDENBURG

Authors
  1. AXEL BRANDENBURG
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to AXEL BRANDENBURG.

Rights and permissions

Reprints and permissions

About this article

Cite this article

BRANDENBURG, A. Chandrasekhar–Kendall functions in astrophysical dynamos. Pramana - J Phys 77, 67–76 (2011). https://doi.org/10.1007/s12043-011-0112-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12043-011-0112-5

Keywords

PACS Nos

Search

Navigation