Effects of Rayleigh number, length and thickness of continent on time of mantle flow reversal

Numerical experiments are carried out to study the effects of continents on the structure of thermal convection in the mantle. The mantle is modelled by a viscous fluid occupying a horizontally extended rectangular 2-D region of aspect ratio 10:1. Continents are treated as thick rigid heat-conductin g plates placed in the mantle, with free-slip and with no-slip conditions. Continents restrict the heat release from the underlying mantle; the mantle material heats up and becomes lighter; as a result, a hot upwelling flow r eplaces downwelling. We calculate the characteristic time tau of this restr ucturing for various values of model parameters and obtain analytical appro ximations for tau as function of Rayleigh number Ra, plate length L, and pl ate thickness d. For commonly accepted mean parameters of the Earth's mantl e, giving Ra = 10(7), with continental plate thickness about 300 km and len gth about 6000 km, the restructuring time tau is estimated as 2.10(8) a. As the continents are not fixed, but drift, the possibility of forming an asc ending mantle flow exists if the continent does not significantly shift dur ing an interval of about tau relative to the mantle by more than half of it s length. Hence, under a continent drifting relative to the mantle with spe ed less than 1 cm/a an ascending mantle flow is expected, whereas under rap idly moving continents such an ascending flow has not enough time to develo p. (C) 1998 Elsevier Science Ltd. All rights reserved.