Temperature Distribution at the Border Astenosphere–Lithosphere (Mathematical Model)

Abstract

The convection of matter in the Earth's upper mantle is considered, which in the Oberbeck–Boussinesq approximation is due to thermogravitational differentiation. Within the framework of this approximation, a 2-D numerical simulation of convective flows of the medium matter was performed. The equation for temperature follows from the entropy balance relation, where, due to taking into account the variable viscosity in the system, there is an effect of energy dissipation. The boundary conditions correspond to the assignment of the temperature generally accepted at the boundary of the upper and lower mantles, and for the lateral boundaries - their thermal insulation. At the asthenosphere–lithosphere boundary, assumptions were made that the heat dynamics is determined by its flow from the asthenosphere layer closest to the boundary, part of the heat dissipation along the boundary, and heat consumption for melting the lithosphere matter. Numerical solution of the constitutive equations is carried out in variables stream function - vorticity. An iterative scheme for their solution is given. The issues of software implementation of the numerical simulation apparatus are discussed. It is shown that under such boundary conditions, a quasi-periodic regime of heat oscillations is formed in the system under consideration.