Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-05T11:56:28.986Z Has data issue: false hasContentIssue false
  • English
  • Français

An experimental and theoretical investigation of the onset of convection in rotating spherical shells

Published online by Cambridge University Press:  20 April 2006

C. R. Carrigan  and
F. H. Busse
C. R. Carrigan
Affiliation:
Department of Earth and Space Sciences, Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90024 Permanent address: Sandia National Laboratories, Geophysics Research Division (5541), Albuquerque, NM 87185.
F. H. Busse
Affiliation:
Department of Earth and Space Sciences, Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90024
Get access Rights & Permissions [Opens in a new window]

Abstract

Convection in a rapidly rotating spherical layer with constant-temperature boundary conditions is studied in a laboratory experiment. The asymptotic theory of Busse (1970) is extended to permit a comparison with the observations of the onset of convection and its properties. It is found that the prediction of the power-law dependences of the critical buoyancy number and the critical wavenumber on the rotation rate are borne out, although discrepancies in the actual values of these quantities do exist. Calculations on the basis of equations proposed by Roberts (1968) show that a thermal wind that is present in the basic state of the model has a stabilizing influence on the onset of convection. Stewartson layers not taken into account in the asymptotic analysis for vanishing Ekman number E appear to be responsible for the remaining disagreement between theoretical predictions and observations at finite values of E.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 126 , January 1983 , pp. 287 - 305
Copyright
© 1983 Cambridge University Press

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

Busse, F. H. 1970 Thermal instabilities in rapidly rotating systems J. Fluid Mech. 44, 441–460.Google Scholar
Busse, F. H. & Carrigan, C. R. 1974 Convection induced by centrifugal buoyancy J. Fluid Mech. 62, 579–592.Google Scholar
Busse, F. H. & Carrigan, C. R. 1976 Laboratory simulation of thermal convection in rotating planets and stars Science 191, 81–83.Google Scholar
Busse, F. H. & Cuong, P. G. 1977 Convection in rapidly rotating spherical fluid shells Geophys. Astrophys. Fluid Dyn. 8, 17–44.Google Scholar
Cuong, P. G. 1979 Thermal convection and magnetic field generation in rotating spherical shells. Ph.D. dissertation, University of California, Los Angeles.
Gilman, P. A. 1976 Theory of convection in a deep rotating spherical shell and its application to the Sun. In Proc. IAU Symp. no. 71. Basic Mechanisms of Solar Activity (ed. V. Bumba & J. Kleczek), pp. 207–228. Reidel.
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
Soward, A. M. 1977 On the finite amplitude thermal instability of a rapidly rotating fluid sphere Geophys. Astrophys. Fluid Dyn. 9, 19–74.Google Scholar
Sparrow, E. M., Goldstein, R. J. & Jonsson, V. H. 1964 Thermal instability in a horizontal fluid layer: effect of boundary conditions and nonlinear temperature profile. J. Fluid Mech. 18, 513–528.Google Scholar