V. V. Rykov and V. P. Trubitsyn


We present a new numerical approach for modeling three-dimensional mantle flows as these interact with moving continents. Flows are modeled in a square $3\times 3\times 1$ region. The mantle is considered as a viscous incompressible fluid heated from below. Continents consist of a thin heat-conducting crust and a lithospheric region of high viscosity. The numerical algorithm was applied to the square region and allowed for thermomechanical interaction of the mantle and continents. Impenetrability and free-slip conditions were assigned at the upper boundary outside the continents. Impenetrability and no-slip conditions were prescribed at the bottom of the crust. A numerical analysis illustrated the aggregation of two continents into a supercontinent of Pangea type and its subsequent breakup. A linear temperature distribution with a small artificial perturbation was taken as the initial condition. The perturbation structure was similar to the onset of thermal convection. The Rayleigh number 10$^5$ was assumed. As an initial condition, the two continents were placed on opposite sides of a central downwelling. Because of the viscous flow, the continents approached one another and aggregated into a large continent. This resulted in heating of the mantle under the supercontinent due to reduction in heat loss across it. Hence an upwelling developed in place of the former downwelling. The continents diverged from the left and remained partially converged from the right, thus forming a configuration of the North and South America type. A global subduction of the West Pacific type developed to the right of the continents. With time, this belt was buried under continents seaward-moving. The numerical results for Ra = 10$^5$ were extrapolated to a higher value of $10^8$ for the whole mantle convection. The relevant cycle time so obtained for continental drift was of order 1 billion years.

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Computational Seismology, Vol. 3.