A geostrophic-like model for large-Hartmann-number flows

Journal of Fluid Mechanics

Volumn 521, Issue , 2004, Pages 125-154

  Alboussière, Thierry ^a  

^a UNIVERSITÉ GRENOBLE ALPES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY LAYERS; CREEP; ELECTRIC CONDUCTIVITY OF LIQUIDS; INTEGRODIFFERENTIAL EQUATIONS; MAGNETIC FIELD EFFECTS; REYNOLDS NUMBER; SURFACE ACTIVE AGENTS;

ELECTRICALLY CONDUCTING FLUIDS; HARTMANN LAYERS; SHEAR LAYERS; TRANSVERSE MAGNETIC FIELDS;

FLOW OF FLUIDS;

BOUNDARY LAYER; ELECTRICAL CONDUCTIVITY; MAGNETOHYDRODYNAMICS;

EID: 12144281186     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112004001740     Document Type: Article

References (39)

1. Alboussière, T. 2001 Quasi characteristic MHD flows. C. R. Acad. Sci. Paris 329 (11b), 767-773.
2. Alboussière, T., Garandet, J. & Moreau, R. 1996 Asymptotic analysis and symmetry in MHD convection. Phys. Fluids 8, 2215-2226.
3. Branover, G. 1967 Resistance of magnetohydrodynamic channels. Magnetohydrodynamics 3 (4), 1-11.
4. Branover, G. & Shcherbinin, E. 1966 Magnetohydrodynamic jet flow in a bounded space. Magnetohydrodynamics 2 (3), 32-37.
5. Calderon, A. & Walker, J. 1977 Steady flow in rapidly rotating variable-area rectangular ducts. Part 2. Small divergences. J. Fluid Mech. 81, 353-368.
6. Cardin, P., Brito, D., Nataf, H. & Masson, J. 2002 Towards a rapidly rotating liquid metal sodium dynamo experiment. Magnetohydrodynamics 38 (1-2), 177-189.
7. Chang, C. & Lundgren, T. 1961 Duct flow in magnetohydrodynamics. Z. Angew. Math. Phys. 12, 100-114.
8. Elsasser, W. 1950 The hydromagnetic equations. Phys. Rev. 79 183.
9. Greenspan, H. 1968 The Theory of Rotating Fluids. Cambridge University Press.
10. Hartmann, J. & Lazarus, F. 1937a Hg-dynamics I. Theory of the laminar flow of an electrically conductive liquid in a homogeneous magnetic field. K. Dan. Vidensk. Selsk. Mat.-Fys. Medd. 15 (6), 1-28.
11. Hartmann, J. & Lazarus, F. 1937b Hg-dynamics II. Experimental investigations on the flow of mercury in a homogeneous magnetic field. K. Dan. Vidensk. Selsk. Mat.-Fys. Medd. 15 (7), 1-45.
12. Holroyd, R. 1979 An experimental study of the effects of wall conductivity, non-uniform magnetic fields and variable area ducts on liquid metal flows at high Hartmann numbers. Part 1. Ducts with non-conducting walls. J. Fluid Mech. 93, 609-630.
13. Holroyd, R. 1980 MHD flow in a rectangular duct with pairs of conducting and non-conducting walls in the presence of a non-uniform magnetic field. J. Fluid Mech. 96, 335-353.
14. Holroyd, R. & Walker, J. 1978 A theoretical study of the effect of wall conductivity, non-uniform magnetic fields and variable-area ducts on liquid-metal flows at high Hartmann numbers. J. Fluid Mech. 84 471-495.
15. Hua, T. & Walker, J. 1989 Three-dimensional MHD flow in insulating circular ducts in non-uniform transverse magnetic fields. Intl J. Engng Sci. 27, 1079-1091.
16. Hunt, J. 1965 Magnetohydrodynamic flow in rectangular ducts. J. Fluid Mech. 21, 577-590.
17. Hunt, J. & Shercliff, J. 1971 Magnetohydrodynamics at high Hartmann number. Annu. Rev. Fluid Mech. 3, 37-62.
18. Koleskinov, Y. 1972 Two-dimensional turbulent flow in a channel with inhomogeneous electrical conductivity. Magnetohydrodynamics 8 (3), 308-312.
19. Kulikovskii, A. 1968 Slow steady flows of a conducting fluid at high Hartmann numbers. Isv. Akad. Nauk. SSSR Mekh. Zhidk. Gaza 3, 3-10.
20. Kulikovskii, A. 1973 Flows of a conducting incompressible liquid in an arbitrary region with a strong magnetic field. Isz. Akad. Nauk. SSSR Mekh. Zhidk. Gaza 3, 144-150.
21. Lehnert, B. 1955 An instability of laminar flow of mercury caused by an external magnetic field. Proc. R. Soc. Lond. A 233, 299-302.
22. Molokov, S. & Bühler, L. 1994 Liquid metal flow in a U-bend in a strong uniform magnetic field. J. Fluid Mech. 267, 325-352.
23. Munk, W. 1950 On the wind-driven ocean circulation. J. Met. 7 (2), 79-93.
24. Murgatroyd, W. 1953 Experiments on magneto-hydrodynamic channel flow. Phil. Mag. 44, 1348-1354.
25. Pironneau, O., Hecht, F., Bernardi, D., Ohtsuka, K. & Lachand-Robert, T. 2001 Freefem+. http://www-rocq1.inria.fr/gamma/cdrom/www/freefem/frap.htm.
26. Roberts, P. 1967 Singularities of hartmann layers. Proc. R. Soc. Lond. A 300, 94-107.
27. Sellers, C. & Walker, J. 1999 Liquid-metal flow in an electrically insulated rectangular duct with a non-uniform magnetic field. Intl J. Engng Sci. 37, 541-552.
28. Shercliff, J. 1953 Steady motion of conducting fluids under transverse magnetic fields. Proc. Camb. Phil. Soc. 49, 136-144.
29. Slyusarev, N., Shilova, E. & Shcherbinin, E. 1970 Experimental study of MHD flows in convergent and divergent channels. Magnetohydrodynamics 6 (4), 497-502.
30. Sommeria, J. & Moreau, R. 1982 Why, how, and when, MHD turbulence becomes two-dimensional. J. Fluid Mech. 118, 507-518.
31. Stewartson, K. 1957 On almost rigid rotations. J. Fluid Mech. 3 17-26.
32. Stewartson, K. 1966 On almost rigid rotations. Part 2. J. Fluid Mech. 26, 131-144.
33. Stommel, H. 1948 The westward intensification of wind-driven ocean currents. Trans. Am. Geophys. Union 29, 202-206.
34. Todd, L. 1968 Magnetohydrodynamic flow along cylindrical pipes under non-uniform transverse magnetic fields. J. Fluid Mech. 31, 321-342.
35. Walker, J. 1974 Steady flow in rapidly rotating circular expansions. J. Fluid Mech. 66, 657-671.
36. Walker, J. 1975 Steady flow in rapidly rotating variable-area rectangular ducts. J. Fluid Mech. 69, 209-227.
37. Walker, J. & Ludford, G. 1972 Three-dimensional MHD duct flows with strong transverse magnetic fields. Part 4. Fully insulated, variable-area rectangular ducts with small divergences. J. Fluid Mech. 56, 481-496.
38. Walker, J. & Ludford, G. 1974 MHD flow in insulated circular expansions with strong transverse magnetic fields. Intl J. Engng Sci. 12 1045-1061.
39. Walker, J., Ludford, G. & Hunt, J. 1972 Three-dimensional MHD duct flows with strong transverse magnetic fields. Part 3. variable-area rectangular ducts with insulating walls. J. Fluid Mech. 56, 121-141.