Influence of subduction on the structure of thermal gravitational flows beneath a continent

The problem on the cooling of asthenospheric layer beneath a continent by d escending lithosphere within a subduction zone has been stated and solved. The asthenospheric layer beneath a continent is considered as a horizontal low-viscosity fluid layer, heated from the lower boundary at a depth of 400 km and cooled from the side (at the submerging plate) and from the upper b oundary (asthenosphere-continental lithosphere). In this case, a flat cellu lar flow appears in the asthenospheric layer, its extent is much more than the thickness of the asthenosphere. A roll layer appears near the heated lo wer surface owing to unstable stratification: The axes of convection roils are parallel to the main now. Using the method of successive approximations , the laws of variations in temperature, velocity, friction, and heat trans fer at the horizontal boundaries of the asthenosphere have been determined, as well as the horizontal extent x(1) of the convective now in the astheno sphere. It has been found that the local shear stress at the asthenospheric boundar ies is directly proportional to the square root of kinematic viscosity and thermal diffusivity. The total friction force F = integral(0)(x1) tau dx ac ting on the continent is directed toward the subduction zone and is proport ional to the thermal gravitational force resulting from horizontal temperat ure gradient in the asthenospheric layer. The criterion obtained, rho beta g Delta Tl-2 / F = (3.3-5) . 10(-2), defines the relationship between frict ion force F, temperature drop Delta T, and asthenosphere thickness l.