On the onset of oscillatory convection in molten gallium

Journal of Fluid Mechanics

Volumn 515, Issue , 2004, Pages 391-413

  Hof, B ^a   Juel, A ^a   Zhao, L ^b   Henry, D ^b   Ben Hadid, H ^b   Mullin, T ^a  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

^b ECOLE CENTRALE DE LYON   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); COMPUTER SIMULATION; FLOW OF FLUIDS; MATHEMATICAL MODELS; MOLTEN MATERIALS;

HOPF BIFURCATION; MOLTEN GALLIUM;

GALLIUM;

CONVECTION; FLUID MECHANICS; GALLIUM; LIQUID METAL;

EID: 5444253156     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112004000527     Document Type: Article

References (35)

1. AFRID, M. & ZEBIB, A. 1990 Oscillatory three-dimensional convection in rectangular cavities and enclosures. Phys. Fluids A 2, 1318-1327.
2. BEN HADID, H. & HENRY, D. 1997 Numerical study of convection in the horizontal Bridgman configuration under the action of a constant magnetic field. Part 2: Three-dimensional flow. J. Fluid Mech. 333, 57-83.
3. BRANDES, E. A. & BROOK, G. B. (ed.) 1992 Smithells Metals Reference Book. 7th edn. Butterworths/ Heinemann.
4. BRAUNSFURTH, M. G. & MULLIN, T. 1996 An experimental study of oscillatory convection in liquid gallium. J. Fluid Mech. 327, 199-219.
5. BRAUNSFURTH, M. G., SKELDON, A. C., JUEL, A., MULLIN, T. & RILEY, D. 1997 Free convection in liquid gallium. J. Fluid Mech. 342, 295-314.
6. GILL, A. E. 1974 A theory of thermal oscillations in liquid metals. J. Fluid Mech. 64, 577-588.
7. HART, J. E. 1972 Stability of thin non-rotating Hadley circulations. J. Atmos. Sci. 29, 687-697.
8. HART, J. E. 1983 A note on the stability of low-Prandtl-number Hadley circulations. J. Fluid Mech. 132, 271-281.
9. HART, J. E. & PRATTE, J. M. 1990 A laboratory study of oscillations in differentially heated layers of mercury. In Numerical Simulation of Oscillatory Convection in Low-Pr Fluids (ed. B. Roux), GAMM Workshop. Notes on Numerical Fluid Mechanics, vol. 27. Vieweg.
10. HENRY, D. & BUFFAT, M. 1998 Two- and three-dimensional numerical simulations of the transition to oscillatory convection in low-Prandtl number fluids. J. Fluid Mech. 374, 145-171.
11. HOF, B., JUEL, A. & MULLIN, T. 2003 Magnetohydrodynamic damping of convective flows in molten gallium. J. Fluid Mech. 482, 163-179.
12. HOF, B. & MULLIN, T. 2001 Critical dynamics in oscillatory convection. Magnetohydrodynamics 37, 119-126.
13. HUNG, M. C. & ANDERECK, C. D. 1988 Transitions in convection driven by a horizontal temperature gradient. Phys. Lett. A 132, 253-258.
14. HUNG, M. C. & ANDERECK, C. D. 1990 Subharmonic transition in a moderately shallow cavity. In Numerical Simulation of Oscillatory Convection in Low-Pr Fluids (ed. B. Roux), GAMM Workshop. Notes on Numerical Fluid Mechanics, vol. 27. Vieweg.
15. HURLE, D. T. J. 1966 Temperature oscillations in molten metals and their relationship to growth striae in melt-grown crystals. Phil. Mag. 13, 305-310.
16. HURLE, D. T. J., JAKEMAN, E. & JOHNSON, C. P. 1974 Convective temperature oscillations in molten gallium. J. Fluid Mech. 64, 565-576.
17. JUEL, A., MULLIN, T., BEN HADID, H. & HENRY, D. 2001 Three-dimensional free convection in molten gallium. J. Fluid Mech. 436, 267-281.
18. KAMOTANI, Y. & SAHRAOUI, T. 1990 Oscillatory natural convection in rectangular enclosures filled with mercury. J. Heat Transfer 112, 235-255.
19. KARNIADAKIS, G. E., ISRAELI, M. & ORSZAG, S. A. 1991 High-order splitting method for the incompressible Navier-Stokes equations. J. Comput. Phys. 97, 414-443.
20. KAYE, G. W. & LABY, T. H. 1982 Tables of Physical and Chemical Constants, 14th Edn. Longman.
21. KUO, H. P. & KORPELA, S. A. 1988 Stability and finite amplitude natural convection in a shallow cavity with insulating top and bottom and heated from a side. Phys. Fluids 31, 33-42.
22. LAURE, P. 1987 Etude des mouvements de convection dans une cavité rectangulaire soumise à un gradient de température horizontal. J. Méc. Théor. Appl. 6, 351-382.
23. LAURE, P. & ROUX, B. 1990 Linear and nonlinear analysis of the Hadley circulation. In Numerical Simulation of Oscillatory Convection in Low-Pr Fluids (ed. B. Roux), GAMM Workshop. Notes on Numerical Fluid Mechanics, vol. 27. Vieweg.
24. MARCH, N. H. 1968 Liquid Metals. Pergamon.
25. MILLS, K., MONAGHAN, B. & KEENE, B. 1996 Thermal conductivities of molten metals: Part 1 pure metals. Intl Materials Rev. 41, 209-242.
26. MÜLLER, G. & OSTROGORSKY, A. 1993 Convection in melt growth. In Handbook of Crystal Growth: Growth Mechanisms and Dynamics, vol. 2b (ed. D. T. J. Hurle). North-Holland.
27. PRATTE, J. M. & HART, J. E. 1990 Endwall driven, low Prandtl number convection in a shallow rectangular cavity. J. Cryst. Growth 102, 54-68.
28. ROUX, B. (ed.) 1990 Numerical Simulation of Oscillatory Convection in Low-Pr Fluids, GAMM Workshop. Notes on Numerical Fluid Mechanics, vol. 27. Vieweg.
29. SKELDON, A. C., RILEY, D. C. & CLIFFE, K. A. 1996 Convection in a low Prandtl number fluid. J. Cryst. Growth 162, 95-106.
30. SMITHELLS, C. J. & BRANDES, E. A. (ed.) 1976 Metals Reference Book, 5th edn. Butterworths.
31. STROGATZ, S. H. 1994 Nonlinear Dynamics and Chaos. Addison-Wesley.
32. TOULOUKIAN, Y. S., POWELL, R. W., HO, C. Y. & KLEMANS, P. G. (ed.) 1979 Thermophysical Properties of Matter, Vol.1: Thermal Conductivity: Metallic Elements and Alloys. IFI/Plenum.
33. WAKITANI, S. 2001 Numerical study of three-dimensional oscillatory natural convection at low Prandtl number in rectangular enclosures. J. Heat Transfer 123, 77-83.
34. WANG, T. M. & KORPELA, S. A. 1989 Convection rolls in a shallow cavity heated from a side. Phys. Fluids A 1, 947-953.
35. WINTERS, K. H. 1988 Oscillatory convection in liquid metals in a horizontal temperature gradient. Intl J. Numer. Meth. Engng 25, 401-414.