Two-dimensional, time-dependent convection with a Newtonian temperature-dependent viscosity has been investigated in wide aspect-ratio boxes. Large-scale circulations have been found in the regime with volumetrically averaged Rayleigh numbers, Rav ranging between O(105) and O(108). Viscosity contrasts up to 1000 have been examined. The horizontally averaged temperature in the interior, 〈T〉 1 2, does not vary much within the above range of Rav for large-aspect-ratio boxes. The horizontal Fourier spectra of the viscosity field show a decrease of magnitude in the viscosity with shorter wavelength. The viscosity spectra decay differently with decreasing wavelength than the corresponding thermal spectra. Lithospheric processes, such as lubrication of subduction and lithospheric thinning, are facilitated by high Rav. The vertical correlation function for the temperature anomalies used recently for comparing convection calculations with tomographic models is found to be strongly time-dependent for Rav ≤ O(106). The temporal fluctuations of the vertical correlation function decrease for higher Rayleigh numbers. Correlation functions for low Ra are broad and smooth, while those for high Ra, greater than 107, are narrow and fragmented.
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We thank Dr. S. Balachandar and Dr. U. Hansen for stimulating conversations and advice. We are grateful to B.S, Schroeder for technical assistance. This research was supported by Department of Energy, NSF Geochemistry program, Army High Performance Computing and Research Center (under ARO contract DAAL03-89-C-0038), and the Danish Research Academy.