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Space-laboratory and numerical simulations of thermal convection in a rotating hemispherical shell with radial gravity

Published online by Cambridge University Press:  21 April 2006

John E. Hart ,
Gary A. Glatzmaier  and
Juri Toomre
John E. Hart
Affiliation:
Department of Astrophysical, Planetary and Atmospheric Sciences, University of Colorado, Boulder, CO 80309, USA
Gary A. Glatzmaier
Affiliation:
Earth and Space Sciences Division, MS F665, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Juri Toomre
Affiliation:
Joint Institute for Laboratory Astrophysics, and Department of Astrophysical, Planetary and Atmospheric Sciences, University of Colorado, Boulder, CO 80309, USA
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Abstract

The Sun and the giant planets rotate and possess deep shells of convection. Some basic aspects of prototypical global convection have been studied with a laboratory model operated in the microgravity environment of Spacelab 3 that flew on the space shuttle Challenger in May 1985. This experiment studied thermally driven circulations within a rotating hemispherical shell of fluid across which are imposed radial and latitudinal temperature gradients. The radial force of gravity is modelled by imposing a strong electric field across the shell, with dielectric polarization forces producing radial accelerations proportional to temperature. When the influence of rotation is large, the experiments yield north-south oriented columnar convection in equatorial and subequatorial regions. As the differential heating is increased, these roll-like cells interact with mid-latitude waves, ultimately being destroyed by turbulent, horizontally isotropic convection that moves down from the pole. When a significant equator-to-pole temperature difference is imposed on the boundaries, spiral waves develop on top of a strong meridional circulation. Intricate, non-axisymmetric, convective patterns that propagate in longitude and evolve in time are described. Schlieren visualizations of these laboratory flows are compared with three-dimensional nonlinear simulations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 173 , December 1986 , pp. 519 - 544
Copyright
© 1986 Cambridge University Press

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References

Atten, P. & LaCroix, J. C. 1979 Nonlinear hydrodynamic stability of liquids subject to unipolar injection. J. Méc. 18, 469–510.Google Scholar
Busse, F. H. 1970 Thermal instabilities in rotating systems. J. Fluid Mech. 44, 441–460.Google Scholar
Busse, F. H. 1973 Differential rotation in stellar convection zones II. Astron. Astrophys. 28, 27–37.Google Scholar
Busse, F. H. 1983 A model of mean zonal flows in the major planets. Geophys. Astrophys. Fluid Dyn. 23, 153–174.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, 17–41.Google Scholar
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.Google Scholar
Chandra, B. & Smylie, D. E. 1972 A laboratory model of thermal convection under a central force field. Geophys. Fluid Dyn. 3, 211–224.Google Scholar
Charney, J. G. 1947 The dynamics of long waves in a baroclinic westerly current. J. Met. 4 135–163.Google Scholar
Charney, J. G. & Drazin, P. G. 1961 Propagation of planetary scale disturbances from the lower into the upper atmosphere. J. Geophys. Res. 66, 83–109.Google Scholar
Durney, B. R. 1970 Nonaxisymmetric convection in a rotating spherical shell. Astrophys J. 161, 1115–1127.Google Scholar
Finlayson, B. A. 1970 Convective instability of ferromagnetic fluids. J. Fluid Mech. 40, 753–767.Google Scholar
Gilman, P. A. 1973 Convection in a rotating annulus uniformly heated from below. Part 2. Nonlinear results. J. Fluid Mech. 57, 381–400.Google Scholar
Gilman, P. A. 1975 Linear simulations of Boussinesq convection in a deep rotating spherical shell. J. Atmos. Sci. 32, 1331–1352.Google Scholar
Gilman, P. A. 1977 Nonlinear dynamics of Boussinesq convection in a deep rotating spherical shell. I. Geophys. Astrophys. Fluid Dyn. 8, 93–135.Google Scholar
Gilman, P. A. 1978 Nonlinear dynamics of Boussinesq convection in a deep rotating spherical shell. III. Effects of velocity boundary conditions. Geophys. Astrophys. Fluid Dyn. 11, 181–203.Google Scholar
Gilman, P. A. 1986 The solar dynamo: observations and theories of solar convection, global circulations and magnetic fields. Physics of the Sun (ed. P. A. Sturrock), vol. 1, chap. 5, pp. 95–160. Reidel.
Glatzmaier, G. A. 1983 Numerical simulations of stellar convective dynamos. I. The model and method. J. Comp. Phys. 55, 461–484.Google Scholar
Glatzmaier, G. A. 1985 Numerical simulations of stellar convective dynamos. II. Field propagation in the convection zone. Astrophys. J. 291, 300–307.Google Scholar
Glatzmaier, G. A. & Gilman, P. A. 1981 Compressible convection in a rotating spherical shell. II. A linear anelastic model. Astrophys. J. Suppl. 45, 351–380.Google Scholar
Hart, J. E. 1976 Studies of Earth simulation experiments. NASA Rep. CR-2753, 66 pp.
Hart, J. E. & Toomre, J. 1977 Geophysical fluid dynamics with dielectric polarization forces. Rep. 2, NASA Contract NAS-8–31958, 65 pp. (available from JEH or JT).
Hart, J. E., Toomre, J., Deane, A. E., Hurlburt, N. E., Glatzmaier, G. A., Fichtl, G. H., Leslie, F., Fowlis, W. W. & Gilman, P. A. 1986 Laboratory experiments on planetary and stellar convection performed on Spacelab 3. Science (to appear September 1986).Google Scholar
Ingersol, A. P. 1976 Pioneer 10 and 11 observations and the dynamics of Jupiter's atmosphere. Icarus 29, 245–251.Google Scholar
Ingersol, A. P., Revercomb, H. E., Sromovsky, L. A., Krauss, J. R., Santek, D. A., Sovmi, V. E., Collins, S. A. & Aris, C. C. 1980 Interaction of eddies and mean zonal flow on Jupiter as inferred from Voyager 1 and Voyager 2 images. J. Geophys. Res. 86, 8733–8743.Google Scholar
Markiewicz, W. J. & Aldridge, K. D. 1982 Dielectrophoretic thermal instability in a spherical shell of fluid. Geophys. Astrophys. Fluid Dyn. 21, 225–236.Google Scholar
Melcher, J. R. & Taylor, G. I. 1969 Electrohydrodynamics: A review of the role of interfacial shear stress. Ann. Rev. Fluid Mech. 1, 111–146.Google Scholar
Moffatt, H. K. 1978 Magnetic Field Generation in Electrically Conducting Fluids. Cambridge University Press.
Ostrach, S. 1982 Low-gravity fluid flows. Ann. Rev. Fluid Mech. 14, 313–345.Google Scholar
Panofsky, W. H. K. & Phillips, M. 1955 Classical Electricity and Magnetism. Addison-Wesley.
Parker, E. N. 1979 Cosmical Magnetic Fields: Their Origin and Activity. Oxford University Press.
Proudman, J. 1916 On the motion of solids in a liquid possessing vorticity. Proc. R. Soc. Lond. A 92, 408–424.Google Scholar
Roberts, P. H. 1969 Electrohydrodynamic convection. Q. J. Mech. Appl. Math 22, 211–220.Google Scholar
Smylie, D. E. 1966 Thermal convection in dielectric liquids and modelling in geophysical fluid dynamics. Earth Planet. Sci. Lett. 1, 339–340.Google Scholar
Stratton, J. A. 1941 Electromagnetic Theory. McGraw-Hill.
Taylor, G. I. 1921 Experiments with rotating fluids. Proc. R. Soc. Lond. A 100, 114–121.Google Scholar
Turnbull, R. J. 1971 Instability of a thermal boundary layer in a constant electric field. J. Fluid Mech. 47, 231–239.Google Scholar
Turnbull, R. J. & Melcher, J. R. 1969 Electrohydrodynamic Rayleigh-Taylor bulk instability. Phys. Fluids 12, 1160–1166.Google Scholar
Worraker, W. J. & Richardson, A. T. 1981 A nonlinear electrohydrodynamic stability analysis of a thermally stabilized plane layer of dielectric liquid. J. Fluid Mech. 109, 217–237.Google Scholar