Abstract
In this paper, the classical Rayleigh–Bénard convection model is considered and solved numerically for extremely large viscosity variations (i.e., up to 10^{30}) across the mantle at a high Rayleigh number. The Arrhenius form of viscosity is defined as a cut-off viscosity function. The effects of viscosity variation and viscous dissipation on convection with temperature-dependent viscosity and also temperature- and pressure-dependent viscosity are shown through the figures of temperature profiles and streamline contours. The values of Nusselt number and root mean square velocity indicate that the convection becomes significantly weak as viscosity variation and viscous dissipation are increased at a fixed pressure dependence parameter.
Highlights
Convection in mantle is responsible for most of the physical and chemical phenomena happening on the surface and in the interior of the Earth, and it is caused by the heat transfer from the interior to the Earth’s surface
Even though there are some debates, it is quite well established that convection in the mantle is the driving mechanism for plate tectonics, seafloor spreading, volcanic eruptions, earthquakes, etc
Leng and Zhong [19] concluded that the dissipation occurring in a subduction zone is 10–20% of the total dissipation for cases with only temperature-dependent viscosity, whereas Morgan et al [20] declared that when slabs subduct, about 86% of the gravitational energy for the whole mantle flow is mostly transformed into heat by viscous dissipation
Summary
Convection in mantle is responsible for most of the physical and chemical phenomena happening on the surface and in the interior of the Earth, and it is caused by the heat transfer from the interior to the Earth’s surface. Even though there are some debates, it is quite well established that convection in the mantle is the driving mechanism for plate tectonics, seafloor spreading, volcanic eruptions, earthquakes, etc. The mechanism of mantle convection is still an unsolved mystery since the rheology of mantle rocks is extremely complicated [2,3,4]. Temperature, pressure, stress, radiogenic elements, creep, and many other factors influence the mantle’s behavior on a large scale. One of its significant but complex characteristics is its viscosity, which is dependent mainly on temperature, pressure, and stress [5]. In earlier studies of mantle convection, scientists assumed constant viscosity Studies with purely temperature-dependent viscosity cannot portray the true convection
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