Graduate Thesis Or Dissertation

 

An approach to thermal convection problems in geophysics with application to the earth's mantle and ground water systems Public Deposited

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  • Two thermal convection problems of geophysical interest are examined, theoretically. First, convection in the earth's mantle is treated on the basis of a one-dimensional 'strip model'. This model results from further simplification of the well known 'Rayleigh model'. For homogeneous, Newtonian fluids, the strip model yields results similar to those obtained by the Rayleigh method. The strip model is used to determine the critical Rayleigh number for convection in an internally heated two-phase fluid. The critical number depends on the parameters of the phase transition, the physical properties of the fluid, and the depth of the fluid layer. Depending on these factors, a univariant phase transformation may either enhance or hinder convective instability. For the olivine-spinel and spinel-oxides transitions in (MgFe)₂SiO₄ which are thought to take place in the upper mantle, it is shown that the critical Rayleigh number is altered only slightly from the critical number for convection in a fluid with one phase. This result holds both for convection in the entire mantle or convection restricted to the upper mantle. Hence the phase changes are of minor importance regarding the existence of mantle convection in general. A method for estimating the order of magnitude of the displacement of the phase surface as a function of Rayleigh number is outlined for a fluid with only one phase transition. The strip model is also used to treat convection in non-Newtonian fluids obeying a power law rheological equation. If the mantle is governed by a flow law of this type, it appears that convection can take place. Lastly, the procedure for applying the strip model to fluids with variable viscosity and thermal conductivity is outlined. The second convection problem concerns some aspects of convection of fluids in thin vertical fractures in the crust. A steady state model is developed to estimate the magnitude of the mass flow as a function of fracture thickness. It is shown that fractures of the order of a millimeter thick or greater can carry a measurable convective flow. A time dependent model is used to estimate the rate of decay of the mass flow with time. The results indicate that in fractures of the order of a centimeter thick, a measurable decrease of the mass flow takes place after a period of the order of a day. This rapid decay rate suggests that the principal effect of sea water convection in extensive fracture systems which are expected on mid-ocean ridge crests is to cool a volume of crustal rock in the vicinity of the fractures. Circulation of sea water in vertical fractures in the upper crust may provide an explanation of 1) the relatively low conductive heat flow measured at some locations on ocean ridge axes and 2) the very 'noisy' data obtained in the axial zone.
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