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Mathematical Geophysics pp 265–290Cite as

Infinite Prandtl number spherical-shell convection

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Part of the book series: Modern Approaches in Geophysics ((MAGE,volume 3))

Abstract

This work presents an overview of numerical simulations of thermal convection for constant viscosity, infinite Prandtl number fluids in a spherical shell, with mantle convection being the main application. Using high-resolution grids on a supercomputer Cray-2, we have monitored the transitions from steady state to the onset of oscillatory time-dependent convection. This occurs at a Rayleigh number which is around 30 times the critical for an inner to outer radii of.62. Additional bifurcations are found with increasing strength of convection. This process culminates in chaotic convection. Analysis of the spatial correlation function of the time-dependent signals shows that the dimensionality of this chaotic attractor, at about 60 times the critical, is around 2.8 and resembles a low dimensional fractal. A large scale circulation, dominated by the degree n =2 component, is found to coexist with aperiodic boundary layer instabilities, mainly starting from the bottom. Spectral analysis of the power associated with the thermal anomalies reveals an upward cascade of energy from n=2 to n=4 to 6 at the bottom boundary. This last signature agrees well with recent seismic findings at the core-mantle boundary.

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Authors and Affiliations

  1. GRGS/CNES, 18 Avenue E.Belin, 31055, Toulouse, France

    Philippe Machetel

  2. Minnesota Supercomputer Institute and Department of Geology and Geophysics, University of Minnesota, Minneapolis, MN, 55455, USA

    David A. Yuen

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  1. Philippe Machetel
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  2. David A. Yuen
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Editors and Affiliations

  1. University of Utrecht, The Netherlands

    N. J. Vlaar , G. Nolet , M. J. R. Wortel  & S. A. P. L. Cloetingh , ,  & 

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Machetel, P., Yuen, D.A. (1988). Infinite Prandtl number spherical-shell convection. In: Vlaar, N.J., Nolet, G., Wortel, M.J.R., Cloetingh, S.A.P.L. (eds) Mathematical Geophysics. Modern Approaches in Geophysics, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2857-2_12

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  • DOI: https://doi.org/10.1007/978-94-009-2857-2_12

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7785-9

  • Online ISBN: 978-94-009-2857-2

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