A conservative form of the deep convection equations and the efficiency of heat energy conversion in a polytropic mantle model |
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| Authors: | G S Golitsyn A N Vul’fson |
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| Institution: | (1) Oboukhov Institute of Atmospheric Physics, Russian Academy of Sciences, Pyzhevskii per. 3, Moscow, 119017, Russia;(2) Oil and Gas Research Institute, Russian Academy of Sciences, ul. Gubkina 3, Moscow, 119991, Russia |
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| Abstract: | A wide class of equations is defined for a high pressure and subcritical temperature range of a fluid state whose thermodynamic properties enable the construction of a polytropic model of the mantle. A variant of deep convection equations of the Ogura and Phillips type is substantiated in terms of the polytropic mantle model. The proposed system of the deep convection equations includes fluctuation of the generalized potential temperature, has a quasi-incompressible form, and is transformed into Mihaljan’s system of shallow convection equations with a decrease in the layer depth. This circumstance is of great importance because it validates the use of the same dimensionless parameters as in the shallow convection model. The advantage of the proposed variant of the deep convection equations is its complete conservatism, which allows one to gain constraints on the efficiency of energy conversion in deep mantle processes and the thermal energy power expended on the generation rate of the convection kinetic energy and associated processes. This power is shown to be of the order of half the geothermal flux measured on the Earth’s surface. |
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