Convection in a mantle with variable viscosity

Abstract

Studies are made on typical features of convection current in a thin viscous layer on a deep layer of high viscosity. The streamlines in this case are concentrated but not closed in the upper thin layer. The horizontal velocity is one sign in the upper layer and the other sign in the lower. The horizontal mass flux in the upper layer is balanced by the counter-horizontal mass flux in the lower layer. The aspect ratio of the critical perturbation, referred to the whole layer thickness, is not so different from that in the homogeneous layer case. The aspect ratio, referred to the thickness of the thin upper layer in which the current is concentrated, is large, about 30 in a case studied in the present paper. The result will give a theoretical justification for the existence of very flat convection cells supposed to exist in the mantle. The free surface of the fluid is low (high) where the temperature is lower (higher) and the vertical velocity is downward (upward). This may explain the formations of guyots in the Pacific. A quantitative check of this idea and estimations of physical parameters involved in the problem are made.