Dynamics of thermal convection with Newtonian temperature-dependent viscosity at high Rayleigh number

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, Ra_v 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 Ra_v 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 Ra_v. 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 Ra_v ≤ 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.