Infinite Prandtl number spherical-shell convection

  • Philippe Machetel
  • David A. Yuen
Chapter
Part of the Modern Approaches in Geophysics book series (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.

Keywords

Nusselt Number Rayleigh Number Spherical Shell Thermal Convection Lower Mantle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© D. Reidel Publishing Company 1988

Authors and Affiliations

  • Philippe Machetel
    • 1
  • David A. Yuen
    • 2
  1. 1.GRGS/CNESToulouseFrance
  2. 2.Minnesota Supercomputer Institute and Department of Geology and GeophysicsUniversity of MinnesotaMinneapolisUSA

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