Abstract Chemical heterogeneities of various origins have been observed in the Earth's mantle. Their assumed higher density acts on the style of mantle convection and therefore, as tectonic plates form the highly viscous upper boundary layer of mantle convection, the onset of surface motion is also affected by chemical heterogeneities. We perform 2D basally heated thermochemical mantle convection models which initially include layers of dense material at different mantle depths. In comparison to purely thermal convection models, the onset of first plate motion is delayed. This delay is even more pronounced, the deeper the location of dense material, the larger its volume and the higher its density. Additionally, we varied the starting temperature of our models. In an initially hot mantle, a strong temperature‐dependent viscosity contrast between the mantle and cold surface leads to a cold, highly viscous plate (stagnant lid). For an initially cold mantle, rising plumes first need to transport basal heat upwards to create a sufficient viscosity contrast. Consequently, the formation and subsequent breaking of the stagnant lid is delayed. Considering a hotter mantle after Earth's magma ocean phase, we find that plate motion can occur within approximately the first 0.5 Gyr of solid‐state convection if no chemical structures are present or for dense material situated at the surface. Deep chemical heterogeneities delay the onset by at least one order of magnitude. Furthermore, the early surface motion will have been more erratic than todays stable plate motion, probably with a few single subduction events.
We present a numerical study on convection in a rotating spherical shell that explores the influence of the two possible driving sources in planetary iron cores: temperature differences exceeding the adiabatic gradient and compositional differences that arise from the rejection of light elements at the inner core freezing front. Similarly, both effects play an important role in driving convection in Earth's outer core but their individual contribution remains uncertain. Dynamically, both components significantly differ in terms of their diffusion timescales since heat diffuses much faster than chemical elements. To investigate the influence of the driving mechanisms on the convective flow pattern, we consider different scenarios including the two extreme cases of purely thermally and purely compositionally driven convection and the more likely situation of a joint action of both sources. We solely focus on implications resulting from the given difference in the thermal and chemical diffusivity. For the present, we disregard the effects that might arise from the more realistic case of distinct thermal and chemical boundary conditions. We show that the driving mechanism strongly affects the resulting flow pattern, for example, differential rotation and global quantities such as mean energy and transport efficiencies. Additionally, we use a selected case for a specific comparison of two different codes based on a pseudospectral and a finite volume formulation, respectively.
Numerical models of mantle convection using the Boussinesq, extended Bousinessq and anelastic‐liquid approximation are compared. For steady state solutions there is good quantitative agreement between the results if they are scaled in a proper way. Time‐dependent extended Boussinesq and anelastic‐liquid flows show only qualitative agreement, the main difference being a distortion of timescale. Compressibility induces an asymmetry in the structure of upper and lower boundary layers that cannot be observed in Boussinesq fluids.
<p>The presence of a large variety of complex structures at the core-mantle boundary (CMB) has been reported. Besides the two prominent structures, the large low shear-wave velocity provinces (LLSVPs), also smaller structures, the ultra-low velocity zones (ULVZs), have been detected. The seismically observed locally sharp boundaries of LLSVPs and their stability in space and time suggests that these structures are possibly induced by chemically distinct material that forms from a layer above the CMB. Therefore models of mantle convection made some ad hoc assumptions in order to simulate the dynamics of this layer. In particular, density and mass of a compositionally enriched layer were prescribed. Both conditions are critical for the dynamics but hardly constrained. This dense CMB layer is considered to be either a remnant of the magma ocean or formed by segregated slabs or by core-mantle interaction processes. Various metal-silicate interaction mechanisms at the CMB have been considered such as diffusion-controlled enrichment of molten iron. Employing a thermochemical mantle convection model, we analyse the penetration of dense material by applying a diffusive chemical influx at the base of the model. In our simulations a dense basal layer develops self-consistently. We find that the chemical diffusion is strongly affected (and promoted) by the convective flow within the mantle. Convection-assisted diffusion yields a large compositional influx mainly in the areas where slabs spread over the bottom boundary and sweep dense material aside. Like in the cases with a prescribed dense layer (primordial layer scenario) this process leads to chemically distinct piles. We compare the spatial and temporal stability of the chemical structures resulting in the cases with a chemical influx to cases of the primordial layer scenario. Typically the chemical structures in the influx cases are much smaller and therefore more suited to explain ULVZs, but the structures are also more persistent due to the constant chemical influx. Combining the influx with the primordial layer scenario can possibly explain the simultaneous existence of LLSVPs and ULVZs along with the observation of a core-like isotopic composition in the mantle.</p>
Abstract Abstract We have studied heat and mass transport in two-dimensional, infinite Prandtl number, incompressible thermal convection for a range of Rayleigh numbers (Ra), between 106 and 108, and two different aspect-ratio boxes, between 1·8 and 10. This study has been motivated by recent developments in studying the transition from weak to strong turbulence in thermal convection. We have employed a two-dimensional finite element method in solving the time-dependent convection equations. Passive tracers, up to 900, have been put into the flow fields for monitoring the style and pattern of mass transport. At Ra around 106 convection does not take place in a strictly cellular mode. Thermals are ejected from the hot and cold boundary layers. These boundary-layer instabilities enhance the mass transport in the interior of individual cells. The fate of these instabilities is determined ultimately by the large-scale circulation. The persistent large-scale circulation gives rise to a significant decrease of the heat transport, compared to steady-state boundary-layer predictions. Cross-cell mass transport over large horizontal distances in large aspect ratio domains is inhibited by the primary rising and sinking currents, whose positions would vary over a time scale much longer those associated with boundary-layer instabilities. At high Ra, between 107 and 108, we find a total breakdown of globally connected thermal plumes for base-heated convection. In this hard turbulent regime the plumes become disconnected and efficiency in mass transport is enhanced. The efficiency of mixing is not only governed by the magnitude of the convective velocities but also by the style of convection. With internal heating the large-scale flow becomes smaller and mass transport between neighboring cells is increased by the temporal variabilities in the flow patterns induced by internal heating. Mixing in the Earth's mantle is thus influenced by many factors. Among them are the complexity and strength of time-dependent convection, the aspect-ratio of the global configuration and the amount of internal heating. Key words: Mantle convectionmixinghard turbulence
Numerical simulations of the process of convection and magnetic field generation in planetary cores still fail to reach geophysically realistic control parameter values. Future progress in this field depends crucially on efficient numerical algorithms which are able to take advantage of the newest generation of parallel computers. Desirable features of simulation algorithms include (1) spectral accuracy, (2) an operation count per time step that is small and roughly proportional to the number of grid points, (3) memory requirements that scale linear with resolution, (4) an implicit treatment of all linear terms including the Coriolis force, (5) the ability to treat all kinds of common boundary conditions, and (6) reasonable efficiency on massively parallel machines with tens of thousands of processors. So far, algorithms for fully self‐consistent dynamo simulations in spherical shells do not achieve all these criteria simultaneously, resulting in strong restrictions on the possible resolutions. In this paper, we demonstrate that local dynamo models in which the process of convection and magnetic field generation is only simulated for a small part of a planetary core in Cartesian geometry can achieve the above goal. We propose an algorithm that fulfills the first five of the above criteria and demonstrate that a model implementation of our method on an IBM Blue Gene/L system scales impressively well for up to O (10 4 ) processors. This allows for numerical simulations at rather extreme parameter values.
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