The progress in our understanding of several aspects of turbulent Rayleigh-Benard convection is reviewed. The focus is on the question of how the Nusselt number and the Reynolds number depend on the Rayleigh number Ra and the Prandtl number Pr, and on how the thicknesses of the thermal and the kinetic boundary layers scale with Ra and Pr. Non-Oberbeck-Boussinesq effects and the dynamics of the large scale convection roll are addressed as well. The review ends with a list of challenges for future research on the turbulent Rayleigh-Benard system.

/pdf/heat-transfer-and-large-scale-dynamics-in-turbulent-rayleigh-39oz2czpiy.pdf

Heat transfer and large scale dynamics in turbulent Rayleigh-Bénard convection

Hf-W chronology of the accretion and early evolution of asteroids and terrestrial planets

Heterogeneous accretion, composition and core–mantle differentiation of the Earth

The inception of plate tectonics on Earth and its subsequent evolution are discussed on the basis of theoretical considerations and observational constraints. The likelihood of plate tectonics in the past depends on what mechanism is responsible for the relatively constant surface heat flux that is indicated by the likely thermal history of Earth. The continuous operation of plate tectonics throughout Earth's history is possible if, for example, the strength of convective stress in the mantle is affected by the gradual subduction of surface water. Various geological indicators for the emergence of plate tectonics are evaluated from a geodynamical perspective, and they invariably involve certain implicit assumptions about mantle dynamics, which are either demonstrably wrong or yet to be explored. The history of plate tectonics is suggested to be intrinsically connected to the secular evolution of the atmosphere, through sea-level changes caused by ocean-mantle interaction.

/pdf/initiation-and-evolution-of-plate-tectonics-on-earth-4kzgzs5xdk.pdf

Initiation and Evolution of Plate Tectonics on Earth: Theories and Observations

A review of continental growth models leaves open the possibilities that Earth during the Hadean Eon (∼4.5–4.0 Ga) was characterized by massive early crust or essentially none at all. Without support from the rock record, our understanding of pre-Archean continental crust must largely come from investigating Hadean detrital zircons. We know that these ancient zircons yield relatively low crystallization temperatures and some are enriched in heavy oxygen, contain inclusions similar to modern crustal processes, and show evidence of silicate differentiation at ∼4.5 Ga. These observations are interpreted to reflect an early terrestrial hydrosphere, early felsic crust in which granitoids were produced and later weathered under high water activity conditions, and even the possible existence of plate boundary interactions—in strong contrast to the traditional view of an uninhabitable, hellish world. Possible scenarios are explored with a view to reconciling this growing but fragmentary record with our knowledge of conditions then extant in the inner solar system.

/pdf/the-hadean-crust-evidence-from-4-ga-zircons-37w7n3pfey.pdf

The Hadean Crust: Evidence from >4 Ga Zircons

The effect of rheological parameters on plate behaviour in a self-consistent model of mantle convection

Using pattern recognition to automatically localize reflection hyperbolas in data from ground penetrating radar

High-resolution computer simulations of two-dimensional (2D) convection are often used to investigate turbulent flows. In this paper we compare numerical simulations in 2D with three-dimensional (3D) simulations. We investigate flows at a fixed Rayleigh number of Ra = 106. The velocity boundary conditions are rigid for the upper and lower boundary and stress-free for the side walls. For high values of the Prandtl number the flow structure and global quantities such as the Nusselt number (Nu) and the Reynolds number (Re) show similar behaviour in 3D and 2D simulations. For values of the Prandtl number smaller than unity, however, the 2D results diverge strongly form the 3D findings. This is true not only for global properties (Nu, Re) but also for local properties such as the structure of the boundary layer and the shapes of the up- and down-wellings. We relate this behaviour to the different large-scale structure of the flow and the toroidal component of the kinetic energy.

On the validity of two-dimensional numerical approaches to time-dependent thermal convection

[1] The Earth's mantle is chemically heterogeneous at all scales, as shown by elemental and isotopic analysis of oceanic basalts. This heterogeneity is continuously destroyed by convective stirring and slow diffusion. It has been argued that 3-D time-dependent convection is less efficient than 2-D convection, except in the presence of a toroidal component. In this study we question this conclusion with numerical simulations and show that mixing in 3-D time-dependent convection is as efficient as in 2-D, and only depends on convective vigor. We compute mixing times of thermal and chemical heterogeneities in the early Earth of 10 and 100 Myrs respectively.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2006GL027707

Mixing times in the mantle of the early Earth derived from 2-D and 3-D numerical simulations of convection

An understanding of the mechanism of mixing in highly viscous convecting fluids is of crucial importance in explaining the observed geochemically heterogeneous nature of Earth's mantle. Using constant viscosity numerical experiments, we describe the mixing mechanism of time-dependent Rayleigh-Benard convection with an infinite Prandtl number in a three-dimensional (3-D) rectangular container. Mixing is observed by following the positions of passive tracers advected by the flow. The major mixing mechanisms may be described in terms of the within-cell mixing and the cross-cell mixing. The flow structure in which tracers move on toroidal surfaces, that was previously observed in steady state 3-D convection systems is perturbed by boundary layer instabilities in the time-dependent experiments. This flow structure allows a very efficient exchange of mass between the boundary layers and the core of the convection cell even in the absence of time dependence. We compare this result with calculations carried out in two spatial dimensions. In similar two-dimensional (2-D) experiments, exchange of mass between boundary layers and core of the convection cell is entirely effected by the boundary layer instabilities. Mixing between neighboring cells appears much slower in three dimensions than in similar 2-D experiments, perhaps because the 3-D cell structure is more stable relative to the boundary layer instabilities. The inferred mixing rates are observed to be relatively insensitive to initial tracer location, but the timescale for mixing, tm, decreases with increasing Rayleigh number (tm goes approximately as Ra(−3/2)). The timescale of mixing is an important constraint on the large scale structure of Earth, because large-scale geochemical heterogeneities persist to the present day, implying that the mantle is not well mixed.

Jörg Schmalzl

Papers

The effect of rheological parameters on plate behaviour in a self-consistent model of mantle convection

Using pattern recognition to automatically localize reflection hyperbolas in data from ground penetrating radar

On the validity of two-dimensional numerical approaches to time-dependent thermal convection

Mixing times in the mantle of the early Earth derived from 2-D and 3-D numerical simulations of convection

Mixing in vigorous, time-dependent three-dimensional convection and application to Earth's mantle