General second-rank correlation tensors for homogeneous magnetohydrodynamic turbulence

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 56, Issue 3, 1997, Pages 2875-2888

  Oughton, S ^a   Radler K H ^b   Matthaeus, W H ^c  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

^b ASTROPHYSIKALISCHES INSTITUT POTSDAM   (Germany)

^c UNIVERSITY OF DELAWARE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0005835845     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.56.2875     Document Type: Article

References (51)

1. H. P. Robertson, Proc. Camb. Philos. Soc. 36, 209 (1940).PCPSA4
2. G. I. Taylor, Proc. R. Soc. London, Ser. A 151, 421 (1935).PRLAAZ
3. T. von Kármán and L. Howarth, Proc. R. Soc. London, Ser. A 164, 192 (1938).PRLAAZ
4. G. K. Batchelor, The Theory of Homogeneous Turbulence (Cambridge University Press, Cambridge, 1970).
5. A. Monin and A. Yaglom, Statistical Fluid Mechanics (MIT Press, Cambridge, MA, 1971), Vol. 1;ibid. (MIT Press, Cambridge, MA, 1975), Vol. 2.
6. G. K. Batchelor, Proc. R. Soc. London, Ser. A 186, 480 (1946).PRLAAZ
7. S. Chandrasekhar, Philos. Trans. R. Soc. London, Ser. A 242, 557 (1950).PTRMAD
8. W. H. Matthaeus and C. Smith, Phys. Rev. A 24, 2135 (1981).PLRAAN
9. S. Chandrasekhar, Proc. R. Soc. London, Ser. A 204, 435 (1951).PRLAAZ
10. S. Chandrasekhar, Proc. R. Soc. London, Ser. A 207, 301 (1951).PRLAAZ
11. F. Krause and K.-H. Rädler, Mean-Field Magnetohydrodynamics and Dynamo Theory (Akademie-Verlag, Berlin, 1980).
12. H. K. Moffatt, Magnetic Field Generation in Electrically Conducting Fluids (Cambridge University Press, New York, 1978).
13. U. Frisch, A. Pouquet, J. Léorat, and A. Mazure, J. Fluid Mech. 68, 769 (1975).JFLSA7
14. W. H. Matthaeus and D. Montgomery, Ann. (N.Y.) Acad. Sci. 357, 203 (1980).ANYAA9
15. W. H. Matthaeus, M. L. Goldstein, and C. W. Smith, Phys. Rev. Lett. 48, 1256 (1982).PRLTAO
16. S. Chandrasekhar, Proc. R. Soc. London, Ser. A 203, 358 (1950).PRLAAZ
17. G. Rüdiger, Differential Rotation and Stellar Convection (Gordon and Breach, New York, 1989).
18. W. H. Matthaeus, J. W. Bieber, and G. P. Zank, Rev. Geophys. Suppl. 33, 609 (1995).
19. E. Marsch and C.-Y. Tu, J. Plasma Phys. 41, 479 (1989).JPLPBZ
20. Y. Zhou and W. H. Matthaeus, J. Geophys. Res. 95, 10 291 (1990a).JGREA2
21. permits only limited information about the full correlations to be obtained because it is generally not possible to obtain measurements corresponding to the full range of (Formula presented) (see Sec. VIII).
22. S. A. Orszag, Stud. Appl. Math. 48, 275 (1969).SAPMB6
23. R. Betchov, Phys. Fluids 4, 925 (1961).PFLDAS
24. J. W. Belcher and L. Davis, Jr., J. Geophys. Res. 76, 3534 (1971).JGREA2
25. H. K. Moffatt and M. R. E. Proctor, Geophys. Astrophys. Fluid Dyn. 21, 265 (1982).GAFDD3
26. H. K. Moffatt, J. Fluid Mech. 35, 117 (1969).JFLSA7
27. M. A. Berger and G. B. Field, J. Fluid Mech. 147, 133 (1984).JFLSA7
28. D. C. Montgomery and L. Turner, Phys. Fluids 24, 825 (1981).PFLDAS
29. M. Lesieur, Turbulence in Fluids (Nijhoff, Dordrecht, The Netherlands, 1990).
30. For example, (Formula presented) and (Formula presented)(Formula presented)
31. See the remark in the paragraph below Eq. (19) for an explanation of the nonequivalence of Eq. (22) and the Fourier transform of Eq. (21).
32. R. Aris, Vectors, Tensors, and the Basic Equations of Fluid Mechanics (Dover, Mineola, NY, 1989).
33. Some care is necessary here since the notation is dense with “(Formula presented)” functions. Unlike the other (Formula presented)’s, (Formula presented) is not a scalar function associated with the antisymmetric part of a “(Formula presented)” tensor but the cross helicity.
34. D. C. Montgomery, Phys. Scr. T2/1, 83 (1982).PHSTBO
35. G. P. Zank and W. H. Matthaeus, J. Plasma Phys. 48, 85 (1992a).JPLPBZ
36. J. V. Shebalin, W. H. Matthaeus, and D. Montgomery, J. Plasma Phys. 29, 525 (1983).JPLPBZ
37. M. Hossain, G. Vahala, and D. Montgomery, Phys. Fluids 28, 3074 (1985).PFLDAS
38. V. Carbone and P. Veltri, Geophys. Astrophys. Fluid Dyn. 52, 153 (1990).GAFDD3
39. S. Oughton, E. R. Priest, and W. H. Matthaeus, J. Fluid Mech. 280, 95 (1994b).JFLSA7
40. J. W. Bieber, W. Wanner, and W. H. Matthaeus, J. Geophys. Res. 101, 2511 (1996).JGREA2
41. E. Marsch and C. Y. Tu, in Proceedings of Solar Wind 7, COSPAR Colloquium Series, edited by E. Marsch and R. Schwenn (Pergamon, Oxford, 1992), Vol. 3, p. 505.
42. C.-Y. Tu, E. Marsch, and K. M. Thieme, J. Geophys. Res. 94, 11 739 (1989a).JGREA2
43. This technicality may be sidestepped by working with velocity and magnetic fields whose integrals over all space are bounded, but which differ from the perfectly homogeneous fields only in physically unimportant ways. For example, take (Formula presented) and (Formula presented) to be periodic with very large wavelengths and use Fourier series; alternatively, suppose (Formula presented) and (Formula presented) are zero outside a very large box, permitting use of the standard Fourier integrals. In any case, for our purposes the distinction is unimportant and we hereafter drop the (Formula presented) functions in such equations and use shorthand forms such as (Formula presented).
44. R. H. Kraichnan and D. C. Montgomery, Rep. Prog. Phys. 43, 547 (1980).RPPHAG
45. W. H. Matthaeus and M. L. Goldstein, J. Geophys. Res. 87, 6011 (1982a).JGREA2
46. A. C. Ting, W. H. Matthaeus, and D. Montgomery, Phys. Fluids 29, 3261 (1986).PFLDAS
47. T. Stribling and W. H. Matthaeus, Phys. Fluids B 3, 1848 (1991).PFBPEI
48. R. H. Kraichnan, J. Fluid Mech. 59, 745 (1973).JFLSA7
49. A. Pouquet, U. Frisch, and J. Léorat, J. Fluid Mech. 77, 321 (1976).JFLSA7
50. R. Grappin, U. Frisch, J. Léorat, and A. Pouquet, Astron. Astrophys. 105, 6 (1982).AAEJAF
51. R. Grappin, A. Pouquet, and J. Léorat, Astron. Astrophys. 126, 51 (1983). AAEJAF