Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-19T02:48:06.240Z Has data issue: false hasContentIssue false
  • English
  • Français

Finite-amplitude convection in rotating spherical fluid shells

Published online by Cambridge University Press:  10 February 1997

A. Tilgner  and
F. H. Busse
A. Tilgner
Affiliation:
Institute of Physics, University of Bayreuth, D-95440 Bayreuth, Germany
F. H. Busse
Affiliation:
Institute of Physics, University of Bayreuth, D-95440 Bayreuth, Germany
Get access Rights & Permissions [Opens in a new window]

Extract

Finite-amplitude convection in rotating spherical fluid shells is considered for a variety of Prandtl numbers P and Rayleigh numbers Ra up to about 10 times the critical value. Convection at low Rayleigh numbers in the form of azimuthally periodic or weakly aperiodic drifting waves is characterized by relatively low heat transport, especially for P ≲ 1. The transition to strongly time-dependent convection leads to a rapid increase of the heat transport with increasing Rayleigh numbers. Onset of convection in the polar regions is delayed, but contributes a disproportionate fraction of the heat transport at high Rayleigh number. The differential rotation generated by convection, the distributions of helicity, and the role of asymmetry with respect to the equatorial plane are also studied.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 332 , February 1997 , pp. 359 - 376
Copyright
Copyright © Cambridge University Press 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Backus, G. E. 1958 A class of self sustaining dissipative spherical dynamos. Ann. Phys. 4, 372–447.Google Scholar
Busse, F. H. 1970a Thermal instabilities in rapidly rotating systems. J. Fluid Mech. 44, 441–460.Google Scholar
Busse, F. H. 19706 Differential rotation in stellar convection zones. Astrophys. J. 159, 629–639.Google Scholar
Busse, F. H. 1973 Differential rotation in stellar convection zones II. Astron. Astrophys. 28, 27–37.Google Scholar
Busse, F. H. 1975 A model of the geodynamo. Geophys. J. R. Astron. Soc. 42, 437–459.Google Scholar
Busse, F. H. 1976 A simple model of convection in the Jovian atmosphere. Icarus 20, 235–260.Google Scholar
Busse, F. H. 1982 Thermal convection in rotating systems. Proc. Ninth US Natl Congr. of Applied Mechanics, pp. 29–305. ASME.Google Scholar
Busse, F. H. 1983 A model of mean zonal flow in the major planets. Geophys. Astrophys. Fluid Dyn. 23, 153–174.Google Scholar
Busse, F. H. & CUONG, P. G. 1977 Convection in rapidly rotating spherical fluid shells. Geophys. Astrophys. Fluid Dyn. 8, 17–44.CrossRefGoogle Scholar
Clever, R. M. & Busse, F. H. 1979 Nonlinear properties of convection rolls in a horizontal layer rotating about a vertical axis. J. Fluid Mech. 94, 609–627.CrossRefGoogle Scholar
Oilman, P. A. 1977 Nonlinear dynamics of Boussinesq convection in deep rotating spherical shells - I. Geophys. Astrophys. Fluid Dyn. 8, 93–136.Google Scholar
Gilman, P. A. 1978a Nonlinear dynamics of Boussinesq convection in deep rotating spherical shells - II: Effects of temperature boundary conditions. Geophys. Astrophys. Fluid Dyn. 11, 157–179.Google Scholar
Gilman, P. A. 1978a Nonlinear dynamics of Boussinesq convection in deep rotating spherical shells - Ill: Effects of velocity boundary conditions. Geophys. Astrophys. Fluid Dyn. 11, 181–203.CrossRefGoogle Scholar
Glatzmaier, G. A. 1984 Numerical simulations of stellar convective dynamos. I. The model and the method. J. Comput. Phys. 55, 461–484.Google Scholar
OR, A. C. & BUSSE, F. H. 1987 Convection in a rotating cylindrical annulus. Part 2. Transitions to asymmetric and vacillating flow. J. Fluid Mech. 174, 313–326.Google Scholar
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.Google Scholar
Roberts, P. H. 1972 Kinematic dynamo models. Phil. Trans. R. Soc. Lond. A 272, 663–698.Google Scholar
Sarson, G. R. & GUBBINS, D. 1996 Three-dimensional kinematic dynamos at high magnetic Reynolds number. J. Fluid Mech. 306, 223–245.Google Scholar
Schnaubelt, M. & BUSSE, F. H. 1992 Convection in a rotating cylindrical annulus. Part 3. Vacillating and spatially modulated flows. J. Fluid Mech. 245, 155–173.CrossRefGoogle Scholar
Sun, Z.-R, Schubert, G. & Glatzmaier, G. A. 1993a Transitions to chaotic thermal convection in a rapidly rotating spherical fluid shell. Geophys. Astrophys. Fluid Dyn. 69, 95–131.Google Scholar
Sun, Z.-R, Schubert, G. & Glatzmaier, G. A. 1993b Banded surface flow maintained by convection in a model of the rapidly rotating Giant Planets. Science 260, 661–664.CrossRefGoogle Scholar
Sun, Z.-R, Schubert, G. & Glatzmaier, G. A. 1994 Numerical simulations of thermal convection in a rapidly rotating spherical shell cooled inhomogeneously from above. Geophys. Astrophvs. Fluid Dyn. 75, 199–226.Google Scholar
Veronis, G. 1968 Large-amplitude Benard convection in a rotating fluid. J. Fluid Mech. 31, 113–139.CrossRefGoogle Scholar
Zhang, K. 1991 Vacillatory convection in a rotating spherical fluid shell at infinite Prandtl number. J. Fluid Mech. 228, 607–628.Google Scholar
Zhang, K. 1992 Convection in a rapidly rotating spherical shell at infinite Prandtl number: transition to vacillating flows, Phys. Earth Planet. Inter. 72, 236–248.Google Scholar
Zhang, K. 1994 On coupling between the Poincare equation and the heat equation. J. Fluid Mech. 268, 211–229.CrossRefGoogle Scholar
Zhang, K. & BUSSE, F. H. 1987 On the onset of convection in rotating spherical shells. Geophys. Astrophys. Fluid Dyn. 39, 119–147.Google Scholar