The onset of thermal convection in rotating spherical shells

Journal of Fluid Mechanics

Volumn 501, Issue , 2004, Pages 43-70

  Dormy, E ^a   Soward, A M ^b   Jones, C A ^b   Jault, D ^c   Cardin, P ^c  

^a CNRS   (France)

^b UNIVERSITY OF EXETER   (United Kingdom)

^c UNIVERSITÉ GRENOBLE ALPES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; BOUNDARY CONDITIONS; COMPUTER SIMULATION; GRAVITATION; HEAT CONVECTION; PROBLEM SOLVING; ROTATION; SHELLS (STRUCTURES); STRESS ANALYSIS;

SPHERICAL SHELLS; THERMAL CONVECTION;

FLUID MECHANICS;

CONVECTION; INSTABILITY; MATHEMATICAL ANALYSIS; MODELING; ROTATING FLOW; THERMAL CONDUCTIVITY;

EID: 1842533162     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112003007316     Document Type: Article

References (35)

1. ARDES, M., BUSSE, F. H. & WICHT, J. 1997 Thermal convection in rotating spherical shells. Phys. Earth Planet. Inter. 99, 55-67.
2. BUSSE, F. H. 1970 Thermal instabilities in rapidly rotating systems. J. Fluid Mech. 44, 441-460.
3. BUSSE, F. H. 1975 A model of the geodynamo. Geophys. J. R. Astron. Soc. 42, 437-459.
4. BUSSE, F. H. 1994 Convection driven zonal flows and vortices in the major planets. Chaos 4, 123-134.
5. BUSSE, F. H. 2002 Convective flows in rapidly rotating spheres and their dynamo action. Phys. Fluids 14, 1301-1314.
6. BUSSE, F. H. & CARRIGAN, C. R. 1976 Laboratory simulation of thermal convection in rotating planets and stars. Science 191, 81-83.
7. BUSSE, F. H. & CUONG, P. G. 1977 Convection in rapidly rotating spherical fluid shells. Geophys. Astrophys. Fluid Dyn. 8, 17-44.
8. CARRIGAN, C. R. & BUSSE, F. H. 1983 An experimental and theoretical investigation of the onset of convection in rotating spherical shells. J. Fluid Mech. 126, 287-305.
9. CHAMBERLAIN, J. A. & CARRIGAN, C. 1986 An experimental and theoretical investigation of convection in a rotating sphere subject to time varying thermal boundary conditions. Geophys. Astrophys. Fluid Dyn. 35, 303-327.
10. CHANDRASHKHAR, S. 1961 Hydrodynamic and Hydromagnetic Stability. Clarendon.
11. CHRISTENSEN, U., AUBERT, J., CARDIN, P. ET AL., 2001 A numerical dynamo benchmark. Phys. Earth Planet. Inter. 128, 25-34.
12. CORDERO, S. & BUSSE, F. H. 1992 Experiments on convection in rotating hemispherical shells: transition to a quasi-periodic state. Geophys. Res. Lett. 19, 733-736.
13. DORMY, E. 1997 Modélisation numérique de la dynamo terrestre. IPGP PhD thesis.
14. 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.
15. GILMAN, P. A. 1975 Linear simulations of Boussinesq convection in a deep rotating spherical shell. J. Atmos. Sci. 32, 1331-1352.
16. GREENSPAN, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
17. HART, J. E., GLATZMAIER, G. A. & TOOMRE, J. 1986 Space-laboratory and numerical simulations of thermal convection in it rotating hemispherical shell with radial gravity. J. Fluid Mech. 173, 519-544.
18. HUERRE, P. & MONKEWITZ, P. A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 14, 473-537.
19. ISHIHARA, N. & KIDA, S. 2002 Dynamo mechanism in a rotating spherical shell: competition between magnetic field and convection vortices. J. Fluid Mech. 465, 1-32.
20. JONES, C. A., MUSSA, A. I. & WORLAND, S. J. 2003 Magnetoconvection in a rapidly rotating sphere: the weak field case. Proc. R. Soc. Lond, A 459, 773-797.
21. 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 (referred to herein as JSM).
22. LAKSHMIVARAHAN, S. & DHALL, S. 1990 Analysis and Design of Parallel Algorithms. Mc Graw-Hill.
23. MEUNIER, N., PROCTOR, M. R. E., SOKOLOFF, D. D., SOWARD, A. M. & TOBIAS, S. M. 1997 Asymptotic properties of a nonlinear αω-dynamo wave: period, amplitude and latitudinal dependence. Geophys. Astrophys. Fluid Dyn. 86, 249-285.
24. ROBERTS, P. H. 1965 On the thermal instability of a highly rotating fluid sphere. Astrophys. J. 141, 240-250.
25. 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.
26. SONWARD, A. M. 1977 On the finite amplitude thermal instability of a rapidly rotating fluid sphere. Geophys. Astrophys. Fluid Dyn. 9, 19-74.
27. SOWARD, A. M. 2003 Thin aspect ratio αΩ-dynamos in galactic discs and spherical shells. In Advances in Nonlinear Dynamo Theory (ed. M. Nún̄ez & A. Ferriz-Mas), vol. 9, pp. 224-268. Taylor & Francis.
28. YANO, J.-I. 1992 Asymptotic theory of thermal convection in rapidly rotating systems. J. Fluid Mech. 243, 103-131.
29. ZHANG, K. 1991 Convection in a rapidly rotating spherical shell at infinite Prandtl number; steadily drifting rolls. Phys. Earth Planet. Inter. 68, 156-169.
30. ZHANG, K. 1992 Spiralling columnar convection in rapidly rotating spherical fluid shells. J. Fluid Mech. 236, 535-556.
31. ZHANG, K. 1995 On coupling between the Poincaré equation and the heat equation: non-slip boundary conditions. J. Fluid Mech. 284, 239-256.
32. ZHANG, K.-K. & BUSSE, F. H. 1987 On the onset of convection in rotating spherical shells. Geophys. Astrophys. Fluid Dyn. 39, 119-147.
33. ZHANG, K. & JONES, C. A. 1993 The influence of Ekman boundary layers on rotating convection in spherical fluid shells. Geophys. Astrophys. Fluid Dyn. 71, 145-162.
34. ZHANG, K. & ROBERTS, P. H. 1997 Thermal inertial waves in a rotating fluid layer: exact and asymptotic solutions. Phys. Fluid 9, 1980-1987.
35. ZHANG, K. & ROBERTS, P. H. 1998 A note on stabilising and destabilising effects of Ekman boundary layers. Geophys. Astrophys. Fluid Dyn. 88, 215-223.