The role of mobile belts for the longevity of deep cratonic lithosphere: The crumple zone model

Many Archean cratons are surrounded by Proterozoic mobile belts that have experienced episodes of tectonic re-activation over their lifetimes. This suggests that mobile belt lithosphere may be associated with long lived, inherited weakness. It is proposed that the proximity of this weakness can increase the longevity of deep Archean lithosphere by buffering Archean cratons from mantle derived stresses. The physical plausibility of this idea is explored through numerical simulations of mantle convection that include continents and allow for material rheologies that model the combined brittle and ductile behavior of the lithosphere. Within the simulations, the longevity of deep cratonic lithosphere does increase if it is buffered by mobile belts that can fail at relatively low stress levels.

The second law of thermodynamics and the global climate system : A review of the maximum entropy production principle

The long-term mean properties of the global climate system and those of turbulent fluid systems are reviewed from a thermodynamic viewpoint. Two general expressions are derived for a rate of entropy production due to thermal and viscous dissipation (turbulent dissipation) in a fluid system. It is shown with these expressions that maximum entropy production in the Earth s climate system suggested by Paltridge, as well as maximum transport properties of heat or momentum in a turbulent system suggested by Malkus and Busse, correspond to a state in which the rate of entropy production due to the turbulent dissipation is at a maximum. Entropy production due to absorption of solar radiation in the climate system is found to be irrelevant to the maximized properties associated with turbulence. The hypothesis of maximum entropy production also seems to be applicable to the planetary atmospheres of Mars and Titan and perhaps to mantle convection. Lorenz s conjecture on maximum generation of available potential energy is shown to be akin to this hypothesis with a few minor approximations. A possible mechanism by which turbulent fluid systems adjust themselves to the states of maximum entropy production is presented as a selffeedback mechanism for the generation of available potential energy. These results tend to support the hypothesis of maximum entropy production that underlies a wide variety of nonlinear fluid systems, including our planet as well as other planets and stars

Spectral nonlocality, absolute equilibria and Kraichnan-Leith-Batchelor phenomenology in two-dimensional turbulent energy cascades

We study the degree to which Kraichnan–Leith–Batchelor (KLB) phenomenology describes two-dimensional energy cascades in α turbulence, governed by ∂θ/∂t+J(ψ,θ)=ν∇2θ+f, where θ=(−Δ)α/2ψ is generalized vorticity, and ψ^(k)=k−αθ^(k) in Fourier space. These models differ in spectral non-locality, and include surface quasigeostrophic flow (α=1), regular two-dimensional flow (α=2) and rotating shallow flow (α=3), which is the isotropic limit of a mantle convection model. We re-examine arguments for dual inverse energy and direct enstrophy cascades, including Fjørtoft analysis, which we extend to general α, and point out their limitations. Using an α-dependent eddy-damped quasinormal Markovian (EDQNM) closure, we seek self-similar inertial range solutions and study their characteristics. Our present focus is not on coherent structures, which the EDQNM filters out, but on any self-similar and approximately Gaussian turbulent component that may exist in the flow and be described by KLB phenomenology. For this, the EDQNM is an appropriate tool. Non-local triads contribute increasingly to the energy flux as α increases. More importantly, the energy cascade is downscale in the self-similar inertial range for 2.5<α<10. At α=2.5 and α=10, the KLB spectra correspond, respectively, to enstrophy and energy equipartition, and the triad energy transfers and flux vanish identically. Eddy turnover time and strain rate arguments suggest the inverse energy cascade should obey KLB phenomenology and be self-similar for α<4. However, downscale energy flux in the EDQNM self-similar inertial range for α>2.5 leads us to predict that any inverse cascade for α≥2.5 will not exhibit KLB phenomenology, and specifically the KLB energy spectrum. Numerical simulations confirm this: the inverse cascade energy spectrum for α≥2.5 is significantly steeper than the KLB prediction, while for α<2.5 we obtain the KLB spectrum.

(Table S1) Age determination of Emperor Seamounts basement

The Hawaiian-Emperor hotspot track has a prominent bend, which has served as the basis for the theory that the Hawaiian hotspot, fixed in the deep mantle, traced a change in plate motion. However, paleomagnetic and radiometric age data from samples recovered by ocean drilling define an age-progressive paleolatitude history, indicating that the Emperor Seamount trend was principally formed by the rapid motion (over 40 millimeters per year) of the Hawaiian hotspot plume during Late Cretaceous to early-Tertiary times (81 to 47 million years ago). Evidence for motion of the Hawaiian plume affects models of mantle convection and plate tectonics, changing our understanding of terrestrial dynamics.

A laboratory-scale experiment and a numerical simulation of unusual spiral plumes in a High-Prandtl-number fluid, links supplementary material

We experimentally and numerically investigated the generation of plumes from a local heat source (LHS) and studied the interaction of these plumes with cellular convective motion (CCM) in a rectangular cavity filled with silicon oil at a Prandtl number (Pr) of approximately two thousand. The LHS is generated using a 0.2-W green laser beam. A roll-type CCM is generated by vertically heating one side of the cavity. The CCM may lead to the formation of an unusual spiral convective plume that resembles a vertical Archimedes spiral. A similar plume is obtained in a direct numerical simulation. We discuss the physical mechanism for the formation of a spiral plume and the application of the results to mantle convection problems. We also estimate the Reynolds (Re) and Rayleigh (Ra) numbers and apply self-similarity theory to convection in the Earth's mantle. Spiral plumes can be used to interpret mantle tomography results over the last decade.

Geochemistry of ODP Site 135-834 basalts

New major, trace element, and isotope data (Pb, Sr, and Nd) reveal an impressive compositional variation in the basalts recovered from Site 834. Major element compositions span almost the entire range observed in basalts from the modern axial systems of the Lau Basin, and variations are consistent with low-pressure fractionation of a mid-ocean-ridge-basalt (MORB)-like parent, in which plagioclase crystallization has been somewhat suppressed. Trace element compositions deviate from MORB in all but one unit (Unit 7) and show enrichments in large-ion-lithophile elements (LILEs) relative to high-field-strength elements (HFSEs) more typically associated with island-arc magmas. The Pb-isotope ratios define linear trends that extend from the field of Pacific MORB to highly radiogenic values similar to those observed in rocks from the northernmost islands of the Tofua Arc. The Sr-isotope compositions also show significant variation, and these too project from radiogenic values back into the field for Pacific MORB. The variations in key trace element and isotopic features are consistent with magma mixing between two relatively mafic melts: one represented by Pacific MORB, and the other by a magma similar to those erupted on 'Eua when it was part of the original Tongan arc, or perhaps members of the Lau Volcanic Group (LVG). Based on our model, the most radiogenic compositions (Units 2 and 8) represent approximately 50:50 mixtures of these MORB and arc end-members. Magma mixing requires that both components are simultaneously available, and implies that melts have not shown a compositional progression from arc-like to MORB-like with extension at this locality. Rather, it is apparent that essentially pristine MORB can erupt as one of the earliest products of backarc initiation. Indeed, repetition of isotopic and trace element signatures with depth suggests that eruptions have been triggered by periodic injections of fresh MORB melts into the source regions of these magmas. The slow and almost amagmatic extension of the original arc complex envisaged to explain the observed chemistry is also consistent with the horst-and-graben topography of the western side of the Lau Basin. Given the similarities between basalts erupted at the modern Lau Basin spreading centers and MORB from the Indian Ocean, the overwhelming evidence for involvement of mantle similar to Pacific MORB in the petrogenesis of basalts from Site 834 is a new and important observation. It indicates that the original arc was underlain by asthenospheric material derived from the Pacific mantle convection cell, and that this has somehow been replaced by Indian Ocean MORB during the last ~5.5 Ma.

Anisotropic viscous models of large-deformation Mohr-Coulomb failure

We have developed a way to represent Mohr-Coulomb failure within a mantle-convection fluid dynamics code. We use a viscous model of deformation with an orthotropic viscoplasticity (a different viscosity is used for pure shear to that used for simple shear) to define a prefered plane for slip to occur given the local stress field. The simple-shear viscosity and the deformation can then be iterated to ensure that the yield criterion is always satisfied. We again assume the Boussinesq approximation, neglecting any effect of dilatancy on the stress field. An additional criterion is required to ensure that deformation occurs along the plane aligned with maximum shear strain-rate rather than the perpendicular plane, which is formally equivalent in any symmetric formulation. We also allow for strain-weakening of the material. The material can remember both the accumulated failure history and the direction of failure. We have included this capacity in a Lagrangian-integration-point finite element code and show a number of examples of extension and compression of a crustal block with a Mohr-Coulomb failure criterion. The formulation itself is general and applies to 2- and 3-dimensional problems.

From point defects to plate tectonic faults

Understanding and explaining emergent constitutive laws in the multi-scale evolution from point defects, dislocations and two-dimensional defects to plate tectonic scales is an arduous challenge in condensed matter physics. The Earth appears to be the only planet known to have developed stable plate tectonics as a means to get rid of its heat. The emergence of plate tectonics out of mantle convection appears to rely intrinsically on the capacity to form extremely weak faults in the top 100 km of the planet. These faults have a memory of at least several hundred millions of years, yet they appear to rely on the effects of water on line defects. This important phenomenon was first discovered in laboratory and dubbed ``hydrolytic weakening''. At the large scale it explains cycles of co-located resurgence of plate generation and consumption (the Wilson cycle), but the exact physics underlying the process itself and the enormous spanning of scales still remains unclear. We present an attempt to use the multi-scale non-equilibrium thermodynamic energy evolution inside the deforming lithosphere to move phenomenological laws to laws derived from basic scaling quantities, develop self-consistent weakening laws at lithospheric scale and give a fully coupled deformation-weakening constitutive framework. At meso- to plate scale we encounter in a stepwise manner three basic domains governed by the diffusion/reaction time scales of grain growth, thermal diffusion and finally water mobility through point defects in the crystalline lattice. The latter process governs the planetary scale and controls the stability of its heat transfer mode.

CONSTRAINTS ON THE LITHOSPHERIC STRUCTURE OF MID OCEAN RIDGES FROM OCEANIC CORE COMPLEX MORPHOLOGY

The Mid-oceanic ridge system is a feature unique to Earth. It is one of the fundamental components of plate tectonics and reflects interior processes of mantle convection within the Earth. The thermal structure beneath the mid-ocean ridges has been the subject of several modeling studies. It is expected that the elastic thickness of the lithosphere is larger near the transform faults that bound mid-ocean ridge segments. Oceanic core complexes (OCCs), which are generally thought to result from long-lived fault slip and elastic flexure, have a shape that is sensitive to elastic thickness. By modeling the shape of OCCs emplaced along a ridge segment, it is possible to constraint elastic thickness and therefore the thermal structure of the plate and how it varies along-axis. This thesis builds upon previous studies that utilize thin plate flexure to reproduce the shape of OCCs. I compare OCC shape to a suite of models in which elastic thickness, fault dip, fault heave, crustal thickness, and axial infill are systematically varied. Using a grid search, I constrain the parameters that best reproduce the bathymetry and/or the slope of ten candidate OCCs identified along the 12°—15°N segment of the Mid-Atlantic Ridge. The lithospheric elastic thicknesses that explains these OCCs is thinner than previous investigators suggested and the fault planes dip more shallowly in the subsurface, although at an angle compatible with Anderson’s theory of faulting. No relationships between model parameters and an oceanic core complexes location within a segment are identified with the exception that the OCCs located less than 20km from a transform fault have slightly larger elastic thickness than OCCs in the middle of the ridge segment.

Continuous eclogite melting and variable refertilisation in upwelling heterogeneous mantle

Large-scale tectonic processes introduce a range of crustal lithologies into the Earth's mantle. These lithologies have been implicated as sources of compositional heterogeneity in mantle-derived magmas. The model being explored here assumes the presence of widely dispersed fragments of residual eclogite (derived from recycled oceanic crust), stretched and stirred by convection in the mantle. Here we show with an experimental study that these residual eclogites continuously melt during upwelling of such heterogeneous mantle and we characterize the melting reactions and compositional changes in the residue minerals. The chemical exchange between these partial melts and more refractory peridotite leads to a variably metasomatised mantle. Re-melting of these metasomatised peridotite lithologies at given pressures and temperatures results in diverse melt compositions, which may contribute to the observed heterogeneity of oceanic basalt suites. We also show that heterogeneous upwelling mantle is subject to diverse local freezing, hybridization and carbonate-carbon-silicate redox reactions along a mantle adiabat.

Forced convection to laminar flow of liquid egg yolk in circular and annular ducts

The steady-state heat transfer in laminar flow of liquid egg yolk - an important pseudoplastic fluid food - in circular and concentric annular ducts was experimentally investigated. The average convection heat transfer coefficients, determined by measuring temperatures before and after heating sections with constant temperatures at the tube wall, were used to obtain simple new empirical expressions to estimate the Nusselt numbers for fully established flows at the thermal entrance of the considered geometries. The comparisons with existing correlations for Newtonian and non-Newtonian fluids resulted in excellent agreement. The main contribution of this work is to supply practical and easily applicable correlations, which are, especially for the case of annulus, rather scarce and extensively required in the design of heat transfer operations dealing with similar shear-thinning products. In addition, the experimental results may support existing theoretical analyses.

The role of the observed tropical convection in the generation of frost events in the southern cone of South America

Based on previous results obtained from observations and linear wave theory analysis, the hypothesis that large-scale patterns can generate extreme cold events in southeast South America through the propagation of remotely excited Rossby waves was already suggested. This work will confirm these findings and extend their analysis through a series of numerical experiments using a primitive equation model where waves are excited by a thermal forcing situated in positions chosen according to observed convection anomalies over the equatorial region. The basic state used for these experiments is a composite of austral winters with maximum and minimum frequency of occurrence of generalized frosts that can affect a large area known as the Wet Pampas located in the central and eastern part of Argentina. The results suggest that stationary Rossby waves may be one important mechanism linking anomalous tropical convection with the extreme cold events in the Wet Pampas. The combination of tropical convection and a specific basic state can generate the right environment to guide the Rossby waves trigged by the tropical forcing towards South America. Depending on the phase of the waves entering the South American continent, they can favour the advection of anomalous wind at low levels from the south carrying cold and dry air over the whole southern extreme of the continent, producing a generalized frost in the Wet Pampa region. On the other hand, when a basic state based on the composites of minimum frosts is used, an anomalous anticyclone over the southern part of the continent generates a circulation with a south-southeast wind which brings maritime air and therefore humidity over the Wet Pampas region, creating negative temperature anomalies only over the northeastern part of the region. Under these conditions even if frosts occur they would not be generalized, as observed for the other basic state with maximum frequency of occurrence of generalized frosts.

Residence time distribution in holding tubes using generalized convection model and numerical convolution for non-ideal tracer detection

A procedure is proposed for the determination of the residence time distribution (RTD) of curved tubes taking into account the non-ideal detection of the tracer. The procedure was applied to two holding tubes used for milk pasteurization in laboratory scale. Experimental data was obtained using an ionic tracer. The signal distortion caused by the detection system was considerable because of the short residence time. Four RTD models, namely axial dispersion, extended tanks in series, generalized convection and PER + CSTR association, were adjusted after convolution with the E-curve of the detection system. The generalized convection model provided the best fit because it could better represent the tail on the tracer concentration curve that is Caused by the laminar velocity profile and the recirculation regions. Adjusted model parameters were well cot-related with the now rate. (C) 2010 Elsevier Ltd. All rights reserved.

Heat transfer and entropy generation optimization of forced convection in a porous-saturated duct of rectangular cross-section

We investigate analytically the first and the second law characteristics of fully developed forced convection inside a porous-saturated duct of rectangular cross-section. The Darcy-Brinkman flow model is employed. Three different types of thermal boundary conditions are examined. Expressions for the Nusselt number, the Bejan number, and the dimensionless entropy generation rate are presented in terms of the system parameters. The conclusions of this analytical study will make it possible to compare, evaluate, and optimize alternative rectangular duct design options in terms of heat transfer, pressure drop, and entropy generation. (c) 2006 Elsevier Ltd. All rights reserved.