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On the possibility of layered mantle convection numerical simulations in a spherical geometry

Oldham, David N. 2004. On the possibility of layered mantle convection numerical simulations in a spherical geometry. PhD Thesis, Cardiff University.

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We investigate the possibility of a deep, dense layer in Earth's mantle. For this purpose we have developed a tool to simulate stratified layered convection in three-dimensional spherical geometry. This was achieved by making alterations to a well-established parallel convection code. The chemical boundary is represented by markers distributed as a surface in the computational grid. These markers are advected by the velocity field, allowing the chemical boundary to deform, and the correct buoyancy forces to be calculated. This method was tested and verified. This method was used to simulate a number of layered cases with an Earth-like geometry. We investigated the effects of varying the depth of the boundary, the density contrast across the boundary, the heating mode used to power convection and the Rayleigh number (Ra) of the system. We found that the stability of the layer is strongly dependent on the buoyancy ratio B (B=Ap-i-paAT where Ap is the chemical density increase across the boundary, p is the density in the upper layer, a is the thermal expansivity and AT is the radial temperature difference across the whole system) with a dense layer becoming unstable when B becomes less than some critical value, Bc. Bc is weakly dependent on Ra, the depth of the interface, and the heating mode used. We find Bc 0.5, which is consistent with other work. As the Rayleigh number increases the system moves from viscous to thermal coupling. We present a relationship between the surface area of the interface and the buoyancy ratio, which is useful in defining the critical buoyancy ratio. We investigate the constraints provided by seismic reflection studies on layered convection. Seismic free oscillations suggest a density increase of less than 0.4% in the lower mantle. Assuming a thermal steady-state, we estimate the temperature increase across a thermo chemical boundary layer needed to produce Earth-like surface heat flux. We find that a deep layer with an intrinsic density contrast of 2% may be both dynamically stable and consistent with seismic observations. The presence of layering is expected from our work, to produce large lateral variations of temperature, density and seismic velocity at the depth of the interface between the layers. Current seismic tomography studies do not show such a feature in the lower mantle away from the core mantle boundary, suggesting that layering is unlikely.

Item Type: Thesis (PhD)
Status: Unpublished
Schools: Earth and Ocean Sciences
ISBN: 9781303200151
Date of First Compliant Deposit: 30 March 2016
Last Modified: 19 Mar 2016 23:33

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