Transition from two-dimensional to three-dimensional magnetohydrodynamic turbulence

Journal of Fluid Mechanics

Volumn 579, Issue , 2007, Pages 383-412

  Thess, André ^a   Zikanov, Oleg ^b  

^a ILMENAU UNIVERSITY OF TECHNOLOGY   (Germany)

^b Department of Electrical and Computer Engineering   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DIRECT NUMERICAL SIMULATION; LINEAR STABILITY ANALYSIS; REYNOLDS NUMBER; THREE DIMENSIONAL; TURBULENCE; TWO DIMENSIONAL; VORTEX FLOW; VORTICITY;

ECCENTRICITY; TRIAXIAL ELLIPSOID; UNBOUNDED FLOWS;

MAGNETOHYDRODYNAMICS;

DIRECT NUMERICAL SIMULATION; LINEAR STABILITY ANALYSIS; MAGNETOHYDRODYNAMICS; REYNOLDS NUMBER; THREE DIMENSIONAL; TURBULENCE; TWO DIMENSIONAL; VORTEX FLOW; VORTICITY;

MAGNETIC FIELD; MAGNETOHYDRODYNAMICS; NUMERICAL MODEL; REYNOLDS NUMBER; TURBULENCE;

EID: 34548153565     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112007005277     Document Type: Article

References (47)

1. ALEMANY, A., MOREAU, R., SULEM, P. L. & FRISCH, U. 1979 Influence of external magnetic field on homogeneous MHD turbulence. J. Méc. 18, 280-313.
2. BALBUS, S. A. & HAWLEY, J. F. 1991 A powerful local shear instability in weakly magnetized disks. I. Linear analysis. Astrophys. J. 376, 214-233.
3. BALBUS, S. A. & HAWLEY, J. F. 1998 Instability, turbulence, and enhanced transport in accretion disks. Rev. Mod. Phys. 70, 1-53.
4. BAYLY, B. J. 1986 Three-dimensional instability of elliptical flow. Phys. Rev. Lett. 57, 2160-2163.
5. BETCHOV, R. & SZEWCZYK, A. 1963 Stability of a shear layer between parallel streams. Phys. Fluids 6, 1391-1396.
6. CAPERAN, P. & ALEMANY, A. 1985 Homogeneous low-magnetic-Reynolds-number MHD turbulence - Study of the transition to the quasi-two-dimensional phase and characterization of its anisotropy. J. Méc. 4, 175-200.
7. CHANDRASEKHAR, S. 1960 The stability of non-dissipative Couette flow in hydromagnetics. Proc. Natl Acad. Sci. USA 46, 253-257.
8. DAVIDSON, P. A. 1997 Magnetic damping of jets and vortices. J. Fluid Mech. 336, 123-150.
9. DAVIDSON, P. A. 1999 Magnetohydrodynamics in Materials Processing. Annu. Rev. Fluid Mech. 31, 273-300.
10. DAVIDSON, P. A. 2001 An Introduction to Magnetohydrodynamics Cambridge University Press.
11. DORMY, E., CARDIN, P. & JAULT, D. 1998 MHD flow in a slightly differentially rotating spherical shell, with conducting inner core, in a dipolar magnetic field. Earth Planet. Sci. Lett. 160, 15-30.
12. DORMY, E., JAULT, D. & SOWARD, A. M. 2002 A super-rotating shear layer in magnetohydrodynamic spherical Couette flow. J. Fluid Mech. 452, 263-291.
13. DRAZIN, P. G. 1960 Stability of parallel flow in a magnetic field at small magnetic Reynolds number. J. Fluid Mech. 8, 130-142.
14. DUBRULLE, B. & KNOBLOCH, E. 1992 On the local stability of accretion disks. Astron. Astrophys. 256, 673-678.
15. DUBRULLE, B. & KNOBLOCH, E. 1993 On instabilities in magnetized accretion disks. Astron. Astrophys. 274, 667-674.
16. GLEDZER, E. B., DOLZHANSKY, F. V. & OBUKHOV, A. M. 1981 Systems of Hydrodynamic Type and their Applications. Nauka, Moscow (in Russian).
17. GLEDZER, E. B. & PONOMAREV, V. M. 1977 Finite dimensional approximations of the motions of an incompressible fluid in an ellipsoidal cavity. Isv. Atmos. Ocean. Phys. 13, 565-569.
18. GREENSPAN, H. P. 1968 The Theory of Rotating Fluids. Breukelen Press, Brookline.
19. GOODMAN, J. & JI, H. 2002 Magnetorotational instability of dissipative Couette flow. J. Fluid Mech. 462, 365-382.
20. JIMENEZ, J. 1990 Transition to turbulence in two-dimensional Poiseuille flow. J. Fluid Mech. 281, 295-297.
21. HINZE, J. O. 1959 Turbulence. McGraw-Hill.
22. HOLLERBACH, R. & SKINNER, S. 2001 Instabilities of magnetically induced shear layers and jets. Proc. R. Soc. Lond. A 457, 785-802.
23. HUNT, J. C. R. 1966 On the stability of parallel flows with parallel magnetic fields. Proc. R. Soc. Lond. A 293, 342.
24. KERSWELL, R. R. 2002 Elliptical instability. Annu. Rev. Fluid Mech. 34, 83-113.
25. KNAEPEN, B. & MOIN, P. 2004 Large-eddy simulation of conductive flows at low magnetic Reynolds number. Phys. Fluids 16, 1255-1261.
26. KRAICHNAN, R. H. & MONTGOMERY, D. 1980 Two-dimensional turbulence. Rep. Prog. Phys. 43, 547-619.
27. LAHJOMRI, J., CAPERAN, P. & ALEMANY, A. 1993 The cylinder wake in a magnetic field aligned with the velocity. J. Fluid Mech. 253 421-448.
28. LESIEUR, M. 1990 Turbulence in Fluids. Kluwer.
29. LUNDGREN, T. S. & MANSOUR, N. N. 1996 Transition to turbulence in an elliptic vortex J. Fluid Mech. 307, 43-62.
30. MOFFATT, H. K. 1967 On the suppression of turbulence by a uniform magnetic field. J. Fluid Mech. 28, 571-592.
31. MOFFATT, H. K. 1978 Magnetic Field Generation in Electrically Conducting Fluids. Cambridge University Press.
32. MOREAU, R. 1990 Magnetohydrodynamics. Kluwer.
33. MUTSCHKE, G., GERBETH G., SHAIROV, V. & TOMBOULIDES, A. 2001 The scenario of three-dimensional instabilities of the cylinder wake in an external magnetic field: A linear stability analysis. Phys. Fluids 13, 723-734.
34. NAKAUCHI, N., OSHIMA, H. & SAITO, Y. 1992 Two-dimensionality in low-magnetic Reynolds number magnetohydrodynamic turbulence subjected to a uniform external magnetic field and randomly stirred two-dimensional force. Phys. Fluids A 4, 2906-2914.
35. PATNAIK, P. C., SHERMAN, F. S. & CORCOS, G. M. 1976 A numerical simulation of Kelvin-Helmholtz waves of finite amplitude. J. Fluid Mech. 73, 215-240.
36. ROBERTS, P. H. 1967 An Introduction to Magnetohydrodynamics. Elsevier.
37. SCHUMANN, U. 1976 Numerical simulation of the transition from three- to two-dimensional turbulence under a uniform magnetic field. J. Fluid Mech. 74, 31-58.
38. SOMMERIA, J. 1986 Experimental study of the two-dimensional inverse energy cascade in a square box. J. Fluid Mech. 170, 139-168.
39. SOMMERIA, J. & MOREAU, R. 1982 Why, how, and when, MHD turbulence becomes two-dimensional. J. Fluid Mech. 118, 507-518.
40. TSINOBER, A. 1990 MHD flow drag reduction. In Viscous Drag Reduction in Boundary Layers (ed. D. M. Bushnell & J. N. Hefner, pp. 327-349.
41. TSINOBER, A. 2001 An Informal Introduction to Turbulence. Kluwer.
42. VELJKHOV, E. P. 1959 Stability of an ideally conducting liquid flowing between cylinders rotating in a magnetic field. Sov. Phys. JETP 36 (9), 995-998.
43. VOROBEV, A. & ZIKANOV, O. 2007 Instability and transition to turbulence in a free shear layer affected by a parallel magnetic field. J. Fluid Mech. 574, 131-154.
44. VOROBEV, A., ZIKANOV, O., DAVIDSON, P. A. & KNAEPEN, B. 2005 Anisotropy of magnetohydrodynamic turbulence at low magnetic Reynolds number. Phys. Fluids 17, 125105.
45. WALEFFE, F. A. 1990 On the three-dimensional instability of strained vortices. Phys. Fluids 2, 76-80.
46. ZIKANOV, O., SLINN, D. N. & DHANAK, M. 2003 Large-eddy simulations of the wind-induced turbulent Ekman layer. J. Fluid Mech. 495 343-368.
47. ZIKANOV, O. & THESS, A. 1998 Direct numerical simulation of forced MHD turbulence at low magnetic Reynolds number. J. Fluid Mech. 358, 299-333.