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| - Analysis of the cooling of a variable-viscosity fluid with applications to the Earth
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| - Summary.. Analysis shows that the convective cooling of a fluid with a temperature-dependent viscosity should exhibit simple behaviour which is consistent with geophysical data on the cooling of the oceanic lithosphere and asthenosphere. The cooling rate of convecting fluid is predicted to vary approximately linearly with (time)−1/2. This relationship has also been demonstrated for numerical solutions of the full governing equations of convection. It is found that a similarity solution can describe the evolution of temperature within the stagnant high-viscosity lid which forms over an actively convecting region. The rate of thickening of the lid (or lithosphere) is directly proportional to a single parameter, λ; and the overall cooling rate is also a function of λ. Expressions are derived which relate changes in the parameter (λ) to the initial average viscosity (or temperature of the fluid) and to the temperature and pressure dependence of viscosity. With assumptions about how the cooling of variable-viscosity fluids can be used to describe the cooling of the oceanic lithosphere and asthenosphere, values of sea-floor depth and the isostatic geoid height can be predicted as a function of time. Sea-floor depth is predicted to increase linearly with (time)1/2 and geoid height to vary nearly linearly with time in agreement with observations. The rate of change of the depth or geoid height is a strong function of the initial temperature of the convecting region. The mantle is taken to have physical properties appropriate for olivine. A change in the mantle temperature under the ridge of 150K causes only about a 20 per cent change in the rate of subsidence but causes nearly a 100 per cent change in the rate of change of the geoid height with time. The observed variations in these rates over different sections of oceanic ridges are of about this magnitude. Simple conductive cooling would require more than 1000 K variation in mantle temperature to account for the geoid height observations. This analysis can also be used to estimate the cooling rate of magma sills.
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