Convective Instability of a Mushy Layer - I: Uniform Permeability

Mushy layers arise and are significant in a number of geophysical contexts, including freezing of sea ice, solidification of magma chambers and inner-core solidification. A mushy layer is a region of solid and liquid in phase equilibrium which commonly forms between the liquid and solid regions of a solidifying system composed of two or more constituents. We consider the convective instability of a plane mushy layer which advances steadily upwards as heat is withdrawn at a uniform rate from the bottom of a eutectic binary alloy. The solid which forms is assumed to be composed entirely of the denser constituent, making the residual liquid within the mush compositionally buoyant and thus prone to convective motion. In this article we focus on the large-scale mush mode of instability, arguing that the 'boundary-layer' mode is not amenable to the standard stability analysis, because convective motions occur on that scale for any non-zero value of the Rayleigh number. We quantify the minimum critical Rayleigh number and determine the structure of the convective modes of motion within the mush and the associated deflections of the mush-melt and mush-solid boundaries. This study of convective perturbations differs from previous analyses in two ways; the inhibition of motion and deformation of the mush-melt interface by the stable stratification of the overlying melt is properly quantified and deformation of the mush-solid interface is permitted and quantified. We find that the mush-melt interface is almost unaffected by convection while significant deformation of the mush-solid interface occurs. We show that each of these effects causes significant (unit-order) changes in the predicted critical Rayleigh number. The marginal modes depend on three dimensionless parameters: a scaled eutectic temperature, τ _e (which characterizes the eutectic temperature relative to the depression of the liquidus), a scaled superheat, τ_∞ (which measures the amount by which the temperature of the incoming melt exceeds the liquidus temperature) and the Stefan number, S (which measures the latent heat of crystallization). To survey parameter space, we focus on seven cases, a standard case having S = τ_∞ = τ _e = 1, and six others in which one of the parameters is either large or small compared with unity: a nearly pure case (τ _e = 100; having little of the light constituent), the large superheat limit (τ_∞→ ∞), a case of large latent heat (S = 100), the near eutectic limit (τ _e → 0), a case of small superheat (τ_∞ = 0.01) and the case of zero latent heat (S = 0). The critical Rayleigh number and the associated wavelength of the convection pattern are determined in each case. The eigenvector for each case is presented in terms of the streamlines and the isolines of the perturbation temperature and solid fraction.     

Deterministic chaos in frictional wedges revealed by convergence analysis

A triangular wedge, composed of a frictional material such as sand, and accreting additional material at its front, is the classical prototype for accretionary wedges and fold‐and‐thrust belts. A simplified method is proposed to capture the internal deformation of this structure resulting from a large number of faulting events during compression. The method combines the application of the kinematic approach of limit analysis to predict the optimum thrust‐fold and a set of geometrical rules to update the geometry accordingly, at each increment of shortening. It is shown that the structure topography remains approximately planar with a slope predicted by the critical Coulomb wedge theory. Failure by faulting occurs anywhere within the wedge at criticality, and its exact position is sensitive to topographic perturbations resulting from the deformation history. The convergence analysis in terms of the shortening increments and of the topography discretization reveals that the timing and the position of a single faulting event cannot be predicted. The convergence is achieved nevertheless in terms of the statistics of the distribution of the faulting events throughout the structure and during the entire deformation history. It is these two convergence properties that are presented to justify the claim that these compressed frictional wedges are imperfection sensitive, chaotic systems. Copyright © 2013 John Wiley & Sons, Ltd.     

WATERSHED SEDIMENT YIELD AND RANGELAND HEALTH

lINTRoDUCTIoNDifferencesintheprevailinglanduseandmanagementofaridandsemiaridareasaredeterminedinlargepartbyclimate.AridareasgenerallyreceivetoolittleprecipitationtosupportdrylandagricultureordomesticlivestockgrazingalthoughtheyaregrazedbywildIife,andattimes,bydomesticlivestock.Incontrast,insemiaridareasadequatemoistureisusuallyavaiIableatsometimeduringtheyeartoproduceforageforlivestockandwildlife,andtherearesomeyearswhendrylandcropproductionissuccessful.However,bothclimatesarecharacterize…     

Petrotectonic evolution of the high- to ultrahigh-pressure Maksyutov Complex, Karayanova area, south Ural Mountains: structural and oxygen isotope constraints

The Maksyutov Complex consists of three fault-bounded lithologic units: a quartzofeldspathic gneiss containing mafic eclogite boudins (Unit #1); a metasedimentary blueschist-facies (Yumaguzinskaya) unit; and a meta-ophiolitic mélange (Unit #2). The geologic history of the high- to ultrahigh-pressure (HP–UHP) assembly of the Maksyutov Complex is complicated by several stages of prolonged retrograde metamorphism and deformation. The Sakmara River exposes all three units near the former village of Karayanova. A structural/petrologic cross-section through the area yields new quantitative data for the complex and, regionally, for the south Urals. Analysis of the Karayanova area has identified the major structures. Regional folding within the complex is parallel to the dominant foliation trending northeast–southwest. Stereonet data show that, during exhumation, this large-scale folding was refolded about axes trending southeast. Unit #1 and the Yumaguzinskaya are tectonically and petrologically distinct units juxtaposed by west-vergent thrusting and recrystallization within the same subduction zone. A shear zone developed later between Unit #2 and the Unit #1+Yumaguzinskaya tectonic package accompanying exhumation. Field relations and petrofabric demonstrate that blueschist-facies recrystallization overprinted an earlier eclogite-facies metamorphism. Thermobarometric measurements yield P–T values of 594–637°C, 1.5–1.7 GPa for eclogite, but these conditions may reflect annealing during the early-stage exhumation at 375 Ma. Cuboid graphite aggregates testify to precursor conditions for Unit #1 within the diamond stability field, if such textures are correctly interpreted. Measured ¹⁸O/¹⁶O partitioning between pairs of coexisting phases yield three main recrystallization temperature ranges: (1) 678±83°C, attending Unit #1 eclogite-facies metamorphism; (2) 453±17°C, during transitional blueschist/greenschist-facies metamorphism for the amalgamated Unit #1+Yumaguzinskaya+Unit #2 assembly; and (3) 250±68°C, reflecting late-stage hydrothermal alteration and exhumation. Oxygen isotope data for Units #1 and #2 indicate that garnet, blue amphibole, and pyroxene crystallized in isotopic equilibrium, validating previous thermobarometric calculations for a Unit #1 retrograde metamorphic event. Variations in δ¹⁸O values for phengites suggest the possibility of late metamorphic fluid infiltration. Retrograde recrystallization at high pressure in the presence of fluids and a calculated slow exhumation rate for the Maksyutov Complex account for the fact that inferred UHP coesite and diamond were completely back-reacted during decompression.     

ATLANTA'S ROLE AS AN INFORMATION CENTER: INTERMETROPOLITAN SPATIAL LINKS

Atlanta has emerged in the 1980s as a major second-order command and control center within the US economy and demonstrates considerable dominance within the Southeast. Federal Express Corporation data permit examination of Atlanta's national and regional command and control functions. The concepts of information genesis, hierarchy of control, and spatial independence of information receipt clarify Atlanta's place within the specialized information network. Atlanta occupies an advantageous position within the intermetropolitan information network from which much of the Southeast's economic activity is organized.     

Snow-induced thermal variations around a single conifer tree

The influence of trees on the ground thermal regime is important to the overall winter energy exchange in a snow-covered, forested watershed. In this work, spatial zones around a single conifer tree were defined and examined for their controls on the snow cover, snow-ground interface temperatures and frozen ground extent. A large white spruce (Picea glauca), approximately 18 m tall with a crown diameter of 7.5 m and located in northern Vermont, was the subject of this study. The tree was instrumented with thermistors to measure the snow-ground interface temperature between the tree trunk and 6 m from the tree into undisturbed snow. Four distinct zones around the conifer are defined that affect the snow distribution characteristics: adjacent to the trunk; the tree well; the tree crown perimeter; and the unaffected area away from the tree. At the time of peak snow accumulation and during the ablation season, snow depth and density profiles were measured. The area beneath the canopy accumulated 34% of the snow accumulated in the undisturbed zone. By the end of the ablation season, the depth of snow under the canopy had decreased to 18% of the undisturbed snow depth. The tree and branch characteristics of spruce in this temperate climate resulted in a different snow depth profile compared with previous empirical relationships around a single conifer. A new relationship is presented for snow distribution around conifer trees that has the ability to better fit data from a variety of conifer types than previously published relationships. Less snow beneath the canopy led to colder snow-ground interface temperatures than measured in undisturbed snow. The depth of frozen ground in the different zones was modelled using a simple analytical solution that showed deeper frost penetration in the tree well than beneath the undisturbed snow.