The onset of time‐dependent convection in spherical shells as a clue to chaotic convection in the Earth's mantle
作者:
Philippe Machetel,
David A. Yuen,
期刊:
Geophysical Research Letters
(WILEY Available online 1986)
卷期:
Volume 13,
issue 13
页码: 1470-1473
ISSN:0094-8276
年代: 1986
DOI:10.1029/GL013i013p01470
数据来源: WILEY
摘要:
This work presents a detailed numerical study of the dynamical behavior of convection in a spherical shell, as applied to mantle convection. From both 2‐dimensional (120 radial and 360 tangential points) and 3‐dimensional (60 radial levels and spherical harmonics up to order and degreel=33, m=33), we show that for a spherical shell (with inner to outer radii ratio η=.62) convection becomes time‐dependent, withl=2 dominating, at a Rayleigh number of about 31 times supercritical for a constant viscosity, base‐heated configuration. This secondary instability is characterized by oscillatory time‐dependence, with higher frequencies involved, at slightly higher Rayleigh numbers. In the process of illustrating the onset of time‐dependence, we extend our analysis to show that the onset of weak turbulence in spherical‐shell convection takes place at about 60 times the critical Rayleigh number via a quasi
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