On the onset of low-Prandtl-number convection in rotating spherical shells: Non-slip boundary conditions

Journal of Fluid Mechanics

Volumn 601, Issue , 2008, Pages 317-337

  Net, Marta ^a   Garcia, Ferran ^a   Sánchez, Juan ^a  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; COMPUTATIONAL FLUID DYNAMICS; EIGENVALUES AND EIGENFUNCTIONS; HEAT CONVECTION; NUMERICAL METHODS;

AZIMUTHAL WAVENUMBER; EKMAN NUMBER; RAYLEIGH NUMBER; THERMAL CONVECTION;

PRANDTL NUMBER;

BOUNDARY CONDITIONS; COMPUTATIONAL FLUID DYNAMICS; EIGENVALUES AND EIGENFUNCTIONS; HEAT CONVECTION; NUMERICAL METHODS; PRANDTL NUMBER;

BOUNDARY CONDITION; RAYLEIGH NUMBER; ROTATING FLOW; SPHERE; THERMAL CONVECTION;

EID: 42349111521     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S002211200800061X     Document Type: Article

References (34)

1. AL-SHAMALI, F., HEIMPEL, M. & ARNOU, J. 2004 Varying the spherical shell geometry in rotating thermal convection. Geophys. Astrophys. Fluid Dyn. 98, 153-169.
2. ARDES, M., BUSSE, F. H. & WICHT, J. 1997 Thermal convection in rotating spherical shells. PEPI 99, 55-67.
3. AUBERT, J., BRITO, D., NATAF, H.-C., CARDIN, P. & MASSON, J. P. 2001 A systematic experimental study of rapidly rotating spherical convection in water and liquid gallium. Phys. Earth Planet. Inter. 128, 51-74.
4. BATISTE, O., MERCADER, I., NET, M. & KNOBLOCH E. 1999 Onset of oscillatory binary fluid convection in finite containers. PRE 59, 6730-6741.
5. BUSSE, F. H. 1970 Thermal instabilities in rapidly rotating systems. J. Fluid Mech. 44, 441-460.
6. BUSSE, F. H. & SIMITEV, R. 2004 Inertial convection in rotating fluid spheres. J. Fluid Mech. 498, 23-30.
7. DORMY, E., SOWARD, A. M., JONES, C. A., JAULT, D. & CARDIN, P. 2004 The onset of thermal convection in rotating spherical shells. J. Fluid Mech. 501, 43-70.
8. ECKE, R. E., ZHONG, F. & KNOBLOCH E. 1992 Hopf bifurcation with broken reflection symmetry in rotating Rayleigh Bénard convection. Europhys. Lett. 19, 177-182.
9. FINLAY, C. C. & JACKSON, A. 2003 Equatorially dominated magnetic field change at the surface of the Earth's core. Science 300 (5628), 2084-2086.
10. GILLET, N., BRITO, D., JAULT, D. & NATAF, H.-C. 2007 Experimental and numerical studies of convection in a rapidly rotating spherical shell. J. Fluid Mech. 580, 83-121.
11. HERRMANN, J. & BUSSE, F. H. 1997 Convection in a rotating cylindrical annulus. Part 4. Modulations and transitions to chaos at low Prandtl numbers. J. Fluid Mech. 350, 209-229.
12. JALETZKY, M. 1999 Experimental study of rotating cylindrical annulus convection. PhD thesis, University of Bayreuth.
13. JONES, C. A., SOWARD, A. M. & MUSSA, A. I. 2000 The onset of thermal convection in a rapidly rotating sphere. J. Fluid Mech. 405, 157-179.
14. LEHOUCQ, R. B., SORENSEN, D. C. & YANG, C. 1998 ARPACK User's Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods. SIAM.
15. LI, L., ZHANG, P., LIAO, X. & ZHANG, K. 2005 Multiplicity of nonlinear thermal convection in a spherical shell. Phys. Rev. E 71, 016301(1)-016301(9).
16. PINO, D., MERCADER, I. & NET, M. 2000 Thermal and inertial modes of convection in a rapidly rotating annulus. Phys. Rev. E 61 1507-1517.
17. PINO, D., NET, M., SÁNCHEZ, J. & MERCADER, I. 2001 Thermal Rossby waves in a rotating annulus: Their stability. Phys. Rev. E 63, 056312(1)-056312(14).
18. PLAUT, E. & BUSSE, F. H. 2002 Low-Prandtl-number convection in a rotating annulus. J. Fluid Mech. 464, 345-363.
19. PLAUT, E. & BUSSE, F. H. 2005 Multicellular convection in rotating annuli. J. Fluid Mech. 528, 119-133.
20. ROBERTS, P. H. 1968 On the thermal instability of a rotating fluid sphere containing heat sources. Phil. Trans. R. Soc. Lond. A 263, 93-117.
21. SCHNAUBELT, M. & BUSSE, F. H. 1992 Convection in a rotating cylindrical annulus. Part 3. Vacillating and spatially modulated flow. J. Fluid Mech. 245, 155-173.
22. SECCO, R. A. & SCHLOESSIN, H. H. 1989 The electrical resistivity of solid and liquid Fe at pressures up to 7 GPa. J. Geophy. Res. B 94, 5887-5894.
23. SIMITEV, R. & BUSSE, F. H. 2003 Patterns of convection in rotating spherical shells. New J. Phys. 5, 97.1-97.20.
24. SOWARD, A. M. 1977 On the finite amplitude thermal instability in a rapidly rotating fluid sphere. Geophys. Astrophys. Fluid Dyn. 9, 19-74.
25. WIJS, G. A. D., KRESSE, G., VOČADLO, L., DOBSON, D., ALFÈ, D., GILLAN, M. J. & PRICE, G. D. 1998 The viscosity of liquid iron at the physical conditions of the Earth's core. Nature 392, 805-807.
26. YANO, J. I. 1992 Asymptotic theory of thermal convection in a rapidly rotating system. J. Fluid Mech. 243, 103-131.
27. ZHANG, K. 1992 Spiralling columnar convection in rapidly rotating spherical fluid shells. J. Fluid Mech. 236, 535-556.
28. ZHANG, K. 1993 On equatorially trapped boundary inertial waves. J. Fluid Mech. 248, 203-217.
29. ZHANG, K. 1994 On coupling between the Poincaré equation and the heat equation. J. Fluid Mech. 268, 211-229.
30. ZHANG, K. 1995 On coupling between the Poincaré equation and the heat equation: Non-slip boundary condition. J. Fluid Mech. 284, 239-256.
31. ZHANG, K. & BUSSE, F. H. 1987 On the onset of convection in rotating spherical shells. Geophys. Astrophys. Fluid Dyn. 39 119-147.
32. ZHANG, K. & JONES, C. A. 1993 The influence of Ekman boundary layers on rotating convection. Geophys. Astrophys. Fluid Dyn. 71, 145-162.
33. ZHANG, K. & LIAO, X. 2004 A new asymptotic method for the analysis of convection in a rapidly rotating sphere. J. Fluid Mech. 518 319-346.
34. ZHANG, K., LIAO, X. & BUSSE, F. 2007 Asymptotic solutions of convection in rapidly rotating non-slip spheres. J. Fluid Mech. 578, 371-380.