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MIT12_009S11_lec2_5 - 2 Plate tectonics The volcanic source...

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2 Plate tectonics: volcanic source Earth’s biological carbon cycle derives its energy from the sun, which fuels photosynthesis. A small portion of the organic carbon that is fixed is buried as rock. Likewise, some inorganic carbon is buried as carbonate. If this burial were to continue without replacement, all the carbon in the atmosphere and oceans would be gone within about 10 6 yr. There must therefore be a resupply of CO 2 from geologic sources. This resupply of CO 2 comes via volcanism. The relative magnitude of its flux is small [3]: source volcanism other degassing combustion respiration flux (Gt C/yr) 0.1 0.1 7 100 Volcanism is nevertheless hugely significant at evolutionary time scales: with- out it, the carbon cycle would have long ago grinded to a halt, and life as we know it would not exist! In this way the biological carbon cycle is inextricably tied to the geological carbon cycle, or “rock cycle.” The rock cycle is fueled by the heat flux that comes out of the Earth. We proceed to describe an important manifestation of this heat flux: plate tec- tonics . We then use mathematical and physical reasoning to quantitatively evaluate predictions of plate tectonics. 13 The
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2.1 Thermal convection and plate tectonics There are two internal sources of heat: Heat accumulated during the process of planetary accretion, i.e., the gravitational energy dissipated by the formation of the Earth 4.5 Ga. Heat generated by the radioactive decay of uranium, thorium, and potas- sium. To first approximation, then, we can think of the Earth as being heated from within and cooled at its surface. We seek an understanding of how the resulting heat flux generates volcanism and crustal motion at the surface. 2.2 Conductive vs. convective heat flow Measurements of temperature within the Earth’s crust show that heat “flows” upward out of the Earth. In general, there are two types of heat flux: conductive and convective. Conductive heat flux: only heat is transported, but not the material being heated. Convective heat flux: material is transported along with heat. Which one characterizes the geophysical heat flux? To investigate this problem, we consider a simpler problem in which a fluid confined between two parallel heat-conducting plates is heated from below. 14
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T=T 0 + δ T T=T 0 + δ T d g T=T 0 ( cold) fluid temperature pure conduction T 0 (hot) In the absence of convection—the transport of hot fluid up and cold fluid down —the temperature gradient is constant. Recall, however, that hot fluid rises in a thermally expansive fluid. There are thus two cases of interest: δT small: no convective motion, due to stabilizing effects of viscous friction. δT large: convective motion occurs. The convective case corresponds to the plate tectonic motions that interest us.
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