Physics
Scientific paper
Dec 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986georl..13.1470m&link_type=abstract
Geophysical Research Letters (ISSN 0094-8276), vol. 13, Dec. 1986, p. 1470-1473.
Physics
27
Chaos, Convection, Earth Mantle, Spherical Shells, Incompressible Fluids, Nusselt Number, Rayleigh Number, Spherical Harmonics, Time Dependence
Scientific paper
This work presents a detailed numerical study of the dynamical behavior of convection in a spherical shell, as applied to mantle convection. From both two-dimensional (120 radial and 360 tangential points) and three-dimensional (60 radial levels and spherical harmonics up to order and degree L = 33, m = 33), it is shown that for a spherical shell (with inner-to-outer radii ratio eta = 0.62) convection becomes time-dependent, with l = 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 illustrating the onset of time dependence, the analysis is extended 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-periodic mode.
Machetel Philippe
Yuen David
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