Editorial Type:
Article
Article Type:
Research Article

Linear Penetrative Spherical Rotating Convection

Keke Zhang Institute of Geophysics and Planetary Physics, University of California, Los Angeles, Los Angeles, California

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Gerald Schubert Institute of Geophysics and Planetary Physics, University of California, Los Angeles, Los Angeles, California

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Print Publication:
01 Nov 1997
DOI:
https://doi.org/10.1175/1520-0469(1997)054<2509:LPSRC>2.0.CO;2
Page(s):
2509–2518
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Abstract

The onset of penetrative convection in a rotating, gravitationally unstable spherical fluid layer bounded above or below by a stable spherical corotating layer is investigated. Rapid rotation and spherical geometry produce new phenomena in the context of penetrative convection that are fundamentally different from what has been observed in the well-studied plane-layer model. In a slowly rotating or nonrotating spherical system, the character of penetration is qualitatively similar to that in plane fluid layers. In a rapidly rotating spherical system with a spherical layer of stable fluid bounded above by an unstable spherical layer, the stable fluid prevents penetration of convection across the interface between the stable and unstable spherical layers. In the reciprocal situation, however, when a spherical layer of stable fluid is bounded below by an unstable spherical layer, convective motions penetrate from the unstable layer all the way through the outermost stable layer with nearly the same amplitude as in the underlying unstable layer. The phenomena can be explained as a direct consequence of the combined effects of rapid rotation and spherical layer geometry.

*thinsp;Current affiliation: Department of Mathematics, University of Exeter, Exeter, United Kingdom.

+ Also affiliated: Department of Earth and Space Sciences.

Corresponding author address: Dr. Keke Zhang, Department of Mathematics, University of Exeter, Exeter, EX4 4QJ, United Kingdom.

Abstract

The onset of penetrative convection in a rotating, gravitationally unstable spherical fluid layer bounded above or below by a stable spherical corotating layer is investigated. Rapid rotation and spherical geometry produce new phenomena in the context of penetrative convection that are fundamentally different from what has been observed in the well-studied plane-layer model. In a slowly rotating or nonrotating spherical system, the character of penetration is qualitatively similar to that in plane fluid layers. In a rapidly rotating spherical system with a spherical layer of stable fluid bounded above by an unstable spherical layer, the stable fluid prevents penetration of convection across the interface between the stable and unstable spherical layers. In the reciprocal situation, however, when a spherical layer of stable fluid is bounded below by an unstable spherical layer, convective motions penetrate from the unstable layer all the way through the outermost stable layer with nearly the same amplitude as in the underlying unstable layer. The phenomena can be explained as a direct consequence of the combined effects of rapid rotation and spherical layer geometry.

*thinsp;Current affiliation: Department of Mathematics, University of Exeter, Exeter, United Kingdom.

+ Also affiliated: Department of Earth and Space Sciences.

Corresponding author address: Dr. Keke Zhang, Department of Mathematics, University of Exeter, Exeter, EX4 4QJ, United Kingdom.

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Journal of the Atmospheric Sciences

  • Atkinson, D. H., J. B. Pollack, and A. Seiff, 1996: Galileo Doppler measurements of the deep zonal winds in Jupiter. Science,272, 842–843.

  • Baker, R. D., G. Schubert, and P. W. Jones, 1997: Cloud-level penetrative compressible convection in Venus’ atmosphere. J. Atmos. Sci., in press.

  • Busse, F. H., 1970: Thermal instabilities in rapidly rotating systems. J. Fluid Mech.,44, 441–460.

  • Chandrasekhar, S., 1961: Hydrodynamic and Hydromagnetic Stability. Clarendon Press.

  • Glatzmaier, G. A., and P. Olson, 1993: Highly supercritical thermal convection in a rotating spherical shell: Centrifugal versus radial gravity. Geophys. Astrophys. Fluid Dyn.,70, 113–125.

  • Gubbins, D., C. J. Thomson, and K. A. Whaler, 1982: Stable regions in the earth’s liquid core. Geophys. J. Roy. Astron. Soc.,68, 241–251.

  • Guillot, T., D. Gautier, G. Chabrier, and B. Mooser, 1994a: Are the giant planets fully convective? Icarus,112, 337–353.

  • ——, ——, P. Morel, and D. Gautier, 1994b: Nonadiabatic models of Jupiter and Saturn. Icarus,112, 354–367.

  • Hart, J. E., G. A. Glatzmaier, and J. Toomre, 1986: Space-laboratory and numerical simulations of thermal convection in a rotating hemispherical shell with radial gravity. J. Fluid Mech.,173, 519–544.

  • Hurlburt, N. E., J. Toomre, and J. M. Massaguer, 1986: Nonlinear compressible convection penetrating into stable layers and producing internal gravity waves. Astrophys. J.,311, 563–577.

  • Ingersoll, A. P., R. F. Beebe, S. A. Collins, G. E. Hunt, J. L. Mitchell, J. P. Muller, B. A. Smith, and R. J. Terrile, 1981: Zonal velocity and texture in the Jovian atmosphere inferred from Voyager images. Nature,280, 773–775.

  • Jackson, A., J. Bloxham, and D. Gubbins, 1992: Time dependent flow at the core surface and conservation of angular momentum in the coupled core-mantle system. “Dynamics of the Earth’s Deep Interior and Earth Rotation,” Geophysical Monogr., Amer. Geophys. Union.

  • Jacobs, J. A., 1975: The Earth’s Core. Academic Press.

  • Julien, K., S. Legg, J. McWilliams, and J. Werne, 1996: Penetrative convection in rapidly rotating flows: Preliminary results from numerical simulation. Dyn. Atmos. Oceans,24, 237–249.

  • LeMouël, J.-L., C. Gire, and T. Madden, 1985: Motions of the core surface in the geostrophic approximation. Phys. Earth Planet. Int.,39, 270–287.

  • Malkus, W. V. R., 1960: Considerations on localized velocity fields in stellar atmospheres. Aerodynamic Phenomena in Stellar Atmospheres, IAU Symp. 12, Bologna, Italy.

  • Matthews, P. C., 1988: A model for the onset of penetrative convection. J. Fluid Mech.,188, 571–583.

  • Moore, D. R., and N. O. Weiss, 1973: Nonlinear penetrative convection. J. Fluid Mech.,61, 553–581.

  • Roberts, P. H., 1965: On the thermal instability of a highly rotating fluid sphere. Astrophys. J.,141, 240–250.

  • ——, 1968: On the thermal instability of a self-gravitating fluid sphere containing heat sources. Philos. Trans. Roy. Soc. London,A263, 93–117.

  • Seiff, A., and Coauthors, 1996: Measurements of structure of the atmosphere of Jupiter obtained by the Galileo probe. Science,272, 844–846.

  • Straughan, B., 1993: Mathematical Aspects of Penetrative Convection. Longman Scientific and Technical.

  • Sun, Z.-P., and G. Schubert, 1995: Numerical simulation of thermal convection in a rotating spherical shell at high Taylor and Rayleigh numbers. Phys Fluids.,7, 2686–2699.

  • Townsend, A. A., 1964: Natural convection in water over an ice surface. Quart. J. Roy. Meteor. Soc.,90, 248–259.

  • Veronis, G., 1963: Penetrative convection. Astrophys. J.,137, 641–663.

  • Whaler, K., 1982: Geomagnetic secular variation and fluid motion at the core surface. Philos. Trans. Roy. Soc. London,A306, 235–246.

  • Zhang, K., 1992: Spiralling columnar convection in rapidly rotating spherical fluid shells. J. Fluid Mech.,236, 535–556.

  • ——, 1994: On coupling between the Poincaré equation and the heat equation. J. Fluid Mech.,268, 211–229.

  • ——, and C. A. Jones, 1993: The influence of Ekman boundary layers on rotating convection. Geophys. Astrophys. Fluid Dyn.,71, 145–162.

  • ——, and G. Schubert, 1996: Penetrative convection and zonal flow on Jupiter. Science,273, 941–943.

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