Abstract
Energy cascade rates and Kolmogorov’s constant for non-helical steady magnetohydrodynamic turbulence have been calculated by solving the flux equations to the first order in perturbation. For zero cross helicity and space dimensiond = 3, magnetic energy cascades from large length-scales to small length-scales (forward cascade). In addition, there are energy fluxes from large-scale magnetic field to small-scale velocity field, large-scale velocity field to small-scale magnetic field, and large-scale velocity field to large-scale magnetic field. Kolmogorov’s constant for magnetohydrodynamics is approximately equal to that for fluid turbulence (≈ 1.6) for Alfvén ratio 05 ≤r A ≤ ∞. For higher space-dimensions, the energy fluxes are qualitatively similar, and Kolmogorov’s constant varies asd 1/3. For the normalized cross helicity σc →1, the cascade rates are proportional to (1 − σc)/(1 + σc , and the Kolmogorov’s constants vary significantly with σcc.
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References
R H Kraichnan,Phys. Fluids 8, 1385 (1965)
P S Iroshnikov,Sov. Astron. I. 7, 566 (1964)
E Marsch, inReviews in modern astronomy edited by G Klare (Springer-Verlag, Berlin, 1990) p. 43
W H Matthaeus and Y Zhou,Phys. Fluids B1, 1929 (1989)
Y Zhou and W H Matthaeus,J. Geophys. Res. 95, 10291 (1990)
M K Vermaet al, J. Geophys. Res. 101, 21619 (1996)
P Frick and D Sokoloff,Phys. Rev. E57, 4155 (1998)
W C Müller and D Biskamp,Phys. Rev. Lett. 84, 475 (2000)
D Biskamp and W C Müller,Phys. Plasma 7, 4889 (2000)
M K Verma,Phys. Plasma 6, 1455 (1999)
S Sridhar and P Goldreich,Astrophys. J. 432, 612 (1994)
P Goldreich and S Sridhar,Astrophys. J. 438, 763 (1995)
M K Verma,Phys. Rev. E64, 26305 (2001)
M K Verma,Phys. Plasma 8, 3945 (2001)
M Hnatich, J Honkonen and M Jurcisin, nlin.CD/0106043 (2001)
A Pouquet, U Frisch and J Léorat,J. Fluid Mech. 77, 321 (1976)
A Pouquet and G S Patterson,J. Fluid Mech. 85, 305 (1978)
M K Verma,Pramana — J. Phys. (submitted); nlin.CD/0107069 (2002)
G Dar, M K Verma and V Eswaran,Physica D157, 207 (2001)
A Ishizawa and Y Hattori,J. Phys. Soc. Jpn. 67, 441 (1998)
J Cho and E T Vishniac,Astrophys. J. 538, 217 (2000)
M M Stanisić,Mathematic theory of turbulence (Springer-Verlag, New York, 1988)
D C Leslie,Development in the theory of turbulence (Clarendon, Oxford University Press, 1973)
J D Fournier and U Frisch,Phys. Rev. A17, 747 (1979)
M K Verma, D A Roberts and M L Goldstein,J. Geophys. Res. 100, 19839 (1995)
C-Y Tu,J. Geophys. Res. 93, 7 (1988)
M K Verma,Int. J. Mod. Phys. B (submitted); nlin.CD/0103033 (2001)
G Dar, Ph.D. thesis, IIT Kanpur, 2000
W H Matthaeus and M L Goldstein,J. Geophys. Res. 87, 6011 (1982)
E Marsch and C-Y Tu,J. Geophys. Res. 95, 8211 (1990)
M K Verma and J K Bhattacharjee,Europhys. Lett. 31, 195 (1995)
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Verma, M.K. Field theoretic calculation of energy cascade rates in non-helical magnetohydrodynamic turbulence. Pramana - J Phys 61, 577–594 (2003). https://doi.org/10.1007/BF02705480
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DOI: https://doi.org/10.1007/BF02705480