Three-dimensional Spherical Convection Research Articles

Seafloor spreading evolution in response to continental growth

The growth of the continental crust has shaped the evolution of the Earth from its interior to its fluid envelopes. Continents have played a major role in the evolution of global tectonics through their interaction with mantle convection. The feedback between continents and mantle convection has been studied for the past 25 years, but it is only recently that the dynamic influence of continents on seafloor spreading can be explored thanks to progress in convection modeling. In this work, we investigate how continental size impacts seafloor spreading activity with state-of-the-art three-dimensional spherical convection models. We show that increasing the continental area forces higher production rates of new seafloor with stronger fluctuations. As a consequence, the average age of the seafloor decreases with increasing continental area. This study suggests that mantle heat loss experienced significant fluctuations through continental growth and reinforces the estimate of

Convection in a spherical shell heated by an isothermal core and internal sources: Implications for the thermal state of planetary mantles

The parallelized three-dimensional spherical convection code, TERRA, is employed to study the mean temperatures and planforms of convecting planetary mantles in spherical shell geometries. We vary the factor f which controls the degree of curvature, defined as the ratio of the radii of the inner and outer bounding surfaces, the Bénard-Rayleigh number, R a B , and the dimensionless rate of internal heating, H. We develop parameterized expressions for predicting the mean temperature of convecting spherical shells which are heated partially from within and partially from below by a hot isothermal lower boundary. Our parameterization is fit to a data set of mean temperatures from 23 numerical model calculations for f = 0.547 (appropriate to Earth’s mantle). We then demonstrate that this parameterization of mean temperature in terms of f, R a B and H extends to other values of f as well. For all values of f, R a B and H considered in this study, our predicted mean temperatures agree with the model calculations to within 2.4%. The scaling analysis is extended to obtain an expression for surface heat flux in terms of R a B and H for f = 0.547 . In that case we obtain a predictive equation for surface heat flux that agrees to within 11% of the observed values. Our findings provide a useful tool for parameterizing the temperature and surface heat flux of planetary mantles of varying geometry and heating configurations.

An early lunar core dynamo driven by thermochemical mantle convection.

Although the Moon currently has no internally generated magnetic field, palaeomagnetic data, combined with radiometric ages of Apollo samples, provide evidence for such a magnetic field from approximately 3.9 to 3.6 billion years (Gyr) ago, possibly owing to an ancient lunar dynamo. But the presence of a lunar dynamo during this time period is difficult to explain, because thermal evolution models for the Moon yield insufficient core heat flux to power a dynamo after approximately 4.2 Gyr ago. Here we show that a transient increase in core heat flux after an overturn of an initially stratified lunar mantle might explain the existence and timing of an early lunar dynamo. Using a three-dimensional spherical convection model, we show that a dense layer, enriched in radioactive elements (a 'thermal blanket'), at the base of the lunar mantle can initially prevent core cooling, thereby inhibiting core convection and magnetic field generation. Subsequent radioactive heating progressively increases the buoyancy of the thermal blanket, ultimately causing it to rise back into the mantle. The removal of the thermal blanket, proposed to explain the eruption of thorium- and titanium-rich lunar mare basalts, plausibly results in a core heat flux sufficient to power a short-lived lunar dynamo.

Convection underneath a crust inhomogeneously enriched in heat sources: application to martian mantle dynamics

Two- and three-dimensional spherical convection models are presented which investigate the convection structure beneath a crust inhomogeneously enriched in radioactive elements. The resulting convection patterns show a focusing of upwellings under the enriched part of the crust and downwellings under the not enriched part that maintain large-scale horizontal motion from the warmer to the cooler region beneath the lithosphere and vice versa above the core–mantle boundary. This flow pattern is observed in all examined models independent of the mantle heating mode. It is, however, more pronounced for models with a considerable amount of internal heating than for models with almost total bottom heating. Thermal blanketing of the mantle beneath the enriched part of the crust plays only a minor role in the lateral heat flux distribution within the lithospheric mantle and is almost insignificant for the surface heat flux distribution, which is dominated by crustal heat generation. Implications of the results for Mars are discussed.

Effect of depth-dependent viscosity on the planform of mantle convection

LITHOSPHERIC plate motions at the Earth's surface result from thermal convection in the mantle1. Understanding mantle convection is made difficult by variations in the material properties of rocks as pressure and temperature increase from the surface to the core. The plates themselves result from high rock strength and brittle failure at low temperature near the surface. In the deeper mantle, elevated pressure may increase the effective viscosity by orders of magnitude2–5. The influence of depth-dependent viscosity on convection has been explored in two-dimensional numerical experiments6–8, but planforms must be studied in three dimensions. Although three-dimensional plan-forms can be elucidated by laboratory fluid dynamic experiments9,10, such experiments cannot simulate depth-dependent rheology. Here we use a three-dimensional spherical convection model11,12 to show that a modest increase in mantle viscosity with depth has a marked effect on the planform of convection, resulting in long, linear downwellings from the upper surface boundary layer and a surprisingly 'red' thermal heterogeneity spectrum, as observed for the Earth's mantle13. These effects of depth-dependent viscosity may be comparable to the effects of the plates themselves.

Modal growth and coupling in three-dimensional spherical convection

Abstract The growth of spherical harmonic modes with increasing Rayleigh number Ra (a nondimensional measure of convective vigor) in numerical simulations of three-dimensional, Boussinesq, infinite Prandtl number, basally heated, spherical-shell convection is analyzed. Two regular polyhedral convective patterns with tetrahedral and cubic symmetry are examined. Apart from the dominant spherical harmonic modes which define the polyhedral patterns, the most important modes (in terms of modifying the convection as Ra increases) are ones whose wavenumbers (i.e., spherical harmonic degree and order) are exactly triple those of the dominant modes. Modes with wavenumbers that are five times those of the dominant modes also maintain large growth rates with increasing Ra. These results indicate the possibility that the spherical harmonic modes which are primarily responsible for modifying convection (e.g., narrowing the boundary layers) with increasing Rayleigh number, occur at wavenumbers that are odd integer multiples of those of the dominant modes. This suggests that an extended mean field method—wherein solutions in which only these modes are kept—may reasonably represent steady convection with regular polyhedral patterns up to relatively high Ra; such a method would entail a significant simplification in the analysis of nonlinear convection.