Finite Prandtl number 2-D convection at high Rayleigh numbers

Finite Prandtl number thermal convection is important to the dynamics of planetary bodies in the solar system. For example, the complex geology on the surface of the Jovian moon Europa is caused by a convecting, brine-rich global ocean that deforms the overlying icy “lithosphere”. We have conducted a systematic study on the variations of the convection style, as Prandtl numbers are varied from 7 to 100 at Rayleigh numbers 106 and 108. Numerical simulations show that changes in the Prandtl number could exert significant effects on the shear flow, the number of convection cells, the degree of layering in the convection, and the number and size of the plumes in the convecting fluid. We found that for a given Rayleigh number, the convection style can change from single cell to layered convection, for increasing Prandtl number from 7 to 100. These results are important for determining the surface deformation on the Jovian moon Europa. They also have important implications for surface heat flow on Europa, and for the interior heat transfer of the early Earth during its magma ocean phase. Electronic Supplementary Material is available if you access this article at . On that page (frame on the left side), a link takes you directly to the supplementary material. Electronic Supplementary Material is available if you access this article at . On that page (frame on the left side), a link takes you directly to the supplementary material.     

Secondary upwelling instabilities developed in high Rayleigh number convection: Possible applications to hot spots

We have conducted numerical experiments for mantle convection in an axisymmetrical spherical-shell geometry from Rayleigh numbers ranging from three million to 10 billion for a purely basal heating configuration. We focus on the development of secondary instabilities developed from plumes and compare them with laboratory experiments by Skilbeck and Whitehead (1978) and Whitehead, (1982). For Rayleigh numbers between around thirty million to one billion, a string of these secondary instabilities can develop from a single plume. Analysis of the spectrum of wavelength associated with the fold instabilities shows that there is a window in the Rayleigh number between around ten million and one bilion where these secondary folding instabilities would develop. These results, when applied to the upper mantle, may explain the formation of hot-spots in a turbulently convecting upper-mantle with a Rayleigh number greater than ten million.     

Thermal convection in a heterogeneous mantle

Both seismology and geochemistry show that the Earth's mantle is chemically heterogeneous on a wide range of scales. Moreover, its rheology depends strongly on temperature, pressure and chemistry. To interpret the geological data, we need a physical understanding of the forms that convection might take in such a mantle. We have therefore carried out laboratory experiments to characterize the interaction of thermal convection with stratification in viscosity and in density. Depending on the buoyancy ratio B (ratio of the stabilizing chemical density anomaly to the destabilizing thermal density anomaly), two regimes were found: at high B, convection remains stratified and fixed, long-lived thermochemical plumes are generated at the interface, while at low B, hot domes oscillate vertically through the whole tank, while thin tubular plumes can rise from their upper surfaces. Convection acts to destroy the stratification through mechanical entrainment and instabilities. Therefore, both regimes are transient and a given experiment can start in the stratified regime, evolve towards the doming regime, and end in well-mixed classical one-layer convection. Applied to mantle convection, thermochemical convection can therefore explain a number of observations on Earth, such as hot spots, superswells or the survival of several geochemical reservoirs in the mantle. Scaling laws derived from laboratory experiments allow predictions of a number of characteristics of those features, such as their geometry, size, thermal structure, and temporal and chemical evolution. In particular, it is shown that (1) density heterogeneities are an efficient way to anchor plumes, and therefore to create relatively fixed hot spots, (2) pulses of activity with characteristic time-scale of 50–500 Myr can be produced by thermochemical convection in the mantle, (3) because of mixing, no ‘primitive’ reservoir can have survived untouched up to now, and (4) the mantle is evolving through time and its regime has probably changed through geological times. This evolution may reconcile the survival of geochemically distinct reservoirs with the small amplitude of present-day density heterogeneities inferred from seismology and mineral physics.     

An Approach to a Visual Language for Convective Fluid Flows: Visualization of Geophysical Simulations

It was known that deep within numbers and binary data from simulations of geophysical convective flows resided various patterns. Two models of convective fluid flows were being considered. One was a model of two-dimensional (768 × 256) air convection with finite Prandtl number of one and Rayleigh number of 10⁸−10¹⁰, and another was a model of three-dimensional (up to 120 × 120 × 90) mantle convection with infinite Prandtl number and Rayleigh number of 10⁶−10⁸. Clearly, phenomena existed which superceded each individual dimensionless computer model to provide a piece of information regarding actual fluid flows. The problem was how to find, prove, and communicate these patterns and phenomena for convection simulations with gigabytes of data. In a search for such an analytical and communicative tool, the alternative of visualization was considered. The need for visualization was recognized and discussed. Then, utilizing both two- and three-dimensional models of high Rayleigh number convection, basic techniques of style and content were developed. Applications of the visualization techniques were designed utilizing IBM’s Data Explorer in order to create communicative images and movies, and after the applications, the problems of data storage and transfer became apparent. Throughout the process though, it became clear how important the language of vision actually could be in the geophysics community. In a field in which words such as plumes and internal waves have in ways replaced mathematics as the basic language for science, there is a need for another resource, another language-the visualization of convective fluid flows.     

http://www.sciencedirect.com/science/article/pii/S1674987111000181

This study investigates the mechanism of formation of convection plumes of mushroom shape in sub-solidus mantle and their prediction.The seismic-tomographic images of columnar structures of several hundreds kilometers in diameter have been reported by several researchers,while the much cherished mushroom-shaped plume heads could only be found in computational geodynamics(CGD) models and simple small-scale laboratory analogue simulations.Our theory of transient instability shows that the formation of conv...     

Pulsations and breaks of tails of thermal mantle plumes

In the available numerical models, mantle plumes are represented by homogeneous ascending streams of thermal convection. Pulses are considered to be possible only in thermochemical plumes within the compositionally inhomogeneous mantle. We show that pulses can also occur under regular thermal convection in the homogeneous mantle. As the intensity grows, the flow in the tail of a thermal plume first begins pulsing and then the plume breaks up into a set of sequentially emerging thermals. For the present-day mantle, the pulsation periods for plumes in the lower mantle can range up to 10 Ma and about 1 Ma in the upper mantle.     

Laboratory testing and numerical simulation of properties and thermal-induced cracking of Eibenstock granite at elevated temperatures

The knowledge about thermo-mechanical properties of granite is still limited to some extent. Individual measurements are necessary to obtain reliable properties for specific granite types. A reliable numerical model of thermal cracking behaviours of granite exposed to extreme high temperatures (e.g. 800–1000 °C) is missing. In this study, the impact of temperature up to 1000 °C on physical, mechanical, and thermal properties as well as thermo-mechanical coupled behaviour of Eibenstock granite was investigated by laboratory testing and numerical simulations. The physical properties including mineral composition, density, P-wave velocity, and open porosity are measured to be temperature dependent. Uniaxial compression and Brazilian tests were carried out to measure uniaxial compressive strength (UCS), Young’s modulus, stress–strain relationship, and tensile strength of Eibenstock granite before and after thermal treatment, respectively. Thermal properties including specific heat, thermal conductivity, thermal diffusivity, and linear thermal expansion coefficient are also measured and found to be temperature dependent, especially the expansion coefficient which shows a steep increase around 573 °C as well as at 870 °C. The numerical simulation code FLAC^3D was used to develop a numerical scheme to simulate the thermal-induced damage of granite at high temperatures. Statistical methods combined with real mineral composition were used to characterize the heterogeneity of granite. The numerical model is featured with reliable temperature-dependent parameters obtained from laboratory tests. It can well reproduce the laboratory results in form of thermal-induced micro- and macrocracks, as well as the stress–strain behaviour and the final failure pattern of Eibenstock granite after elevated temperatures up to 1000 °C. The simulation results also reveal that the thermal-induced microcracks are randomly distributed across the whole sample. Although most thermal-induced damages are tensile failures, shear failure begins to develop quickly after 500 °C. The obvious UCS reduction in granite due to heating is mainly caused by the increase in shear failure. The simulation also shows that the dominant impact of α–β quartz transition is widening pre-existing cracks rather than the formation of new microcracks.

     

Atmospheric boundary layer studies at Jodhpur during MONTBLEX using sodar and tower

A monostatic sodar was set up at Jodhpur, near the western end of the monsoon trough, to investigate the atmospheric boundary layer dynamics. A 30 m instrumented tower was also located close to the sodar antenna. Data were collected from June to August during the monsoon period of 1990, as also from July 1992 to September 1993. Thermal plumes, surface-based stable layers (both flat or short spiky top and tall spiky top), elevated/multi-layers with or without undulations and dot echo structures were seen; however, erosion of the morning inversion layer in the form of a rising layer with growing thermal plumes under it was rarely seen, and that too only during the winter period. The observed structure of the stable layer with tall spikes and its depth have been found to be correlated with the intensity of the monsoon spell; the dot echoes have been found to be correlated with the approach of a monsoon depression near Jodhpur; and the elevated/multilayers have been attributed to the formation of a subsidence (shear instability).     

Geodynamic regimes of thermochemical mantle plumes

Laboratory and numerical experiments simulating the heat transfer and flow structure of thermochemical mantle plumes provide insights into the mechanisms of plume eruption onto the surface depending on the relative thermal power of plumes Ka = N/N₁, where N and N₁ are the heat transferred from the plume base to the plume conduit and the heat transferred from the plume conduit to the surrounding mantle, respectively, under steady thermal conduction. There are three main types of plumes according to the Ka criterion: (i) plumes with low thermal power (Ka < 1.15), which fail to reach the surface, (ii) plumes with intermediate thermal power (1.15 < Ka < 1.9), which occur beneath cratons and transport melts from depths below 150 km, where diamond is stable (diamondiferous plumes), and (iii) plumes with a mushroom-shaped head (1.9 < Ka < 10), which are responsible for large intrusive bodies, including batholiths. The volume of erupted melt and the depth from which the melt is transported to the surface are estimated for plumes of types (ii) and (iii). The relationship between the plume head area (along with the plume head diameter) and the relative thermal power is obtained. The relationship between the thickness of the block above the plume head and the relative thermal power is derived. On the basis of the results obtained, the geodynamic-regime diagram of thermochemical mantle plumes, including the plumes with Ka > 10, has been constructed.     

The helicity of the velocity field for cellular convection in a rotating layer

The helicity of a cellular convective flow in a horizontal layer of a compressible fluid (gas) heated from below and rotating about the vertical axis is studied using finite-difference numerical simulations. The medium is assumed to be polytropically stratified. A thermal perturbation that produces a system of Bénard-type hexagonal convection cells is introduced at the initial time. Next, the cells are deformed by the action of the Coriolis force; however, at some stage of the evolution, the flow is nearly steady (at later times, the cells break down). For given Rayleigh and Prandtl numbers, the velocity-field helicity for this stage averaged over the layer increases with decreasing polytrope index (i.e., with increasing the curvature of the static entropy profile) and has a maximum at a certain rotational velocity of the layer. Numerical simulations of such quasi-ordered convective flows should reduce the uncertainties in estimates of the helicity, a quantity important for the operation of MHD dynamos.     

Topographic analysis of Devana Chasma, Venus: implications for rift system segmentation and propagation

Devana Chasma is a rift system on Venus formed in association with the Beta Regio and Phoebe Regio volcanic highlands, which are interpreted as mantle plumes. We present a new analysis of a 2500-km-long segment of Devana. Based on the rift topography, the horizontal extension across the rift boundary faults is 3–9 km. This is a lower bound on the total rift extension because the altimetry does not resolve the topographic relief across the numerous faults that are visible in radar images of the rift floor. The total extension across Devana is approximately 20 km, similar in magnitude to continental rift systems on Earth. Rift flank elevations are up to 3.1 km in the regions nearest the mantle plumes and decay strongly with increasing distance from the plumes, indicating a strong thermal component to the rift flank topography, unlike the situation usually reported for terrestrial rifts. As on Earth, there is also a flexural uplift component to the flank topography. Rift depths are up to 2.5 km below the surrounding plains, with considerable along-strike variability. There is a 600 km lateral offset along Devana Chasma near the mid-point between the two mantle plumes. Devana most likely formed as two distinct rifts due to the horizontal stresses created by outflow from the upwelling plumes. The offset zone formed as a result of the interaction between the two rift tips, which requires that upwelling at the two mantle plumes overlapped in time.     

Global thermal and dynamical perturbations due to Cretaceous mantle avalanche

The numerical models of mantle convection agree to depict avalanches behaviour according to the level of endothermicity of the spinel → perovskite phase change. Their potential effects on the global thermal and dynamical states of the mantle have been computed thanks to a numerical code, which takes into account both the 400-km exothermic and the 660-km endothermic phase changes. The cycle followed by the avalanches is: local layering, destabilization of the 660-km thermal layer, travelling and spreading on the core, and reappearing of the local layering. Therefore, mantle convection is characterized by quiet periods of partial layering embedded in catastrophic events. During the avalanche, the amplitude of the surface velocity is multiplied by two, which would imply an enhanced plate tectonic and ridge activities. The global thermal effects of the avalanche are compatible with a high mantle temperature and an acceleration of Earth's rotation during the Cretaceous. They also offer a coherent explanation to locate the origin of mantle plumes both within the CMB and just below the transition zone.     

A numerical investigation of the thermal state of the earth's mantle

An idealized convecting mantle with internal heat generation and viscosity dependent on temperature and pressure is examined with numerical calculations. Temperature and viscosity are coupled and self-regulating in the quasi-steady solutions. The lack of any tendency for upwelling flow to constrict itself to narrow channels argues against the existence of plumes. Unsteadiness is an essential feature of mantle convection, not only for mixing at large Rayleigh numbers, but also to prevent the flow from being impeded by continuous rigid regions.     

Thermal diffusivity of silica glass at pressures up to 9 GPa

The thermal diffusivity of silica glass was measured at pressures up to 9 GPa and temperatures up to 1200 K. The measurements involve adopting the Ångström method to a cylindrical geometry in a uniaxial split-sphere apparatus. This method can be used to determine thermal diffusivity in samples with dominant conductive heat transfer. The thermal diffusivity of silica glass has a negative first pressure derivative but a positive second pressure derivative. Although the elastic moduli have minima near 3 GPa, the thermal diffusivity does not has minimum up to 9 GPa, which cannot be explained by the model of Kittel (1949). The negative pressure derivative of thermal diffusivity is a feature probably unique in silica glass, and its magnitude should decrease with the addition of Na₂O.     

Surface Water Metabolism Potential in a Tropical Estuary,Hilo Bay,Hawai’i,USA, During Storm and Non-storm Conditions

Surface water gross primary production potential (pGPP), respiration (RESP), metabolism potential (pMET), and CO₂ fluxes in Hilo Bay, Hawai’i, USA, were examined along two river plumes during storm (high-flow) and non-storm (low-flow) conditions. Significant differences in pGPP, RESP, and pMET were found between low- and high-flow conditions, with lowest rates of all processes occurring during high-flow conditions. CO₂ fluxes were influenced by metabolic processes at all but one site, with the bay’s surface waters being autotrophic and a sink for atmospheric CO₂ during low-flow conditions and less autotrophic and a source of atmospheric CO₂ during high-flow conditions. Significant differences in pMET were found between the two river plumes during low-flow conditions at spatial scales of 1.5 km; however, no differences between river plumes were found during high-flow conditions. Our study suggests that an increase in storms associated with global climate change could impact surface water metabolic dynamics of tropical estuaries.     

Recent Process in Near-Space Gravity Wave Analysis Based on Satellite Measurements

This article focused on the research progress in the gravity wave analysis based on satellite measurements including MODIS, AIRS, AMSU, MLS, DNB, COSMIC,HIRDLS and SOFIE. Besides, a few ground-based observation results and numerical models were briefly introduced and some cases of joint applications of satellite observations with ground-based observations and numerical models in the gravity waves were listed. In general, the satellite remote sensing data play an important role in the study of the characteristics in near-space environment, which can be applied to analyze the scales of gravity waves induced by different sources, correlations between the instabilities and waves as well as their patterns, the impacts in the climate process, wave-wave interactions and wave-flow interactions with other data.     

Biogeochemistry of landfill leachate plumes

The literature has been critically reviewed in order to assess the attenuation processes governing contaminants in leachate affected aquifers. Attenuation here refers to dilution, sorption, ion exchange, precipitation, redox reactions and degradation processes. With respect to contaminants, focus is on dissolved organic matter, xenobiotic organic compounds, inorganic macrocomponents as anions and cations, and heavy metals. Laboratory as well as field investigations are included. This review is an up-date of an earlier comprehensive review. The review shows that most leachate contamination plumes are relatively narrow and do not in terms of width exceed the width of the landfill. The concept of redox zones being present in the plume has been confirmed by the reported composition of the leachate contaminated groundwater at several landfills and constitutes an important framework for understanding the behavior of the contaminants in the plume as the leachate migrates away from the landfill. Diverse microbial communities have been identified in leachate plumes and are believed to be responsible for the redox processes. Dissolved organic C in the leachate, although it appears to be only slowly degradable when the volatile organic acids are gone, apparently acts as substrate for the microbial redox processes. Several xenobiotic organic compounds have been found to be degradable in leachate contaminated groundwater, but degradation rates under anaerobic redox conditions have only been determined in a few cases. Apparently, observations in actual plumes indicate more extensive degradation than has been documented in the laboratory. The behavior of cations in leachate plumes is strongly influenced by exchange with the sediment, although the sediment often is very coarse and sandy. Ammonium seems to be subject to anaerobic oxidation, but the mechanisms are not yet understood. Heavy metals do not seem to constitute a significant pollution problem at landfills, partly because the heavy metal concentrations in the leachate often are low, and partly because of strong attenuation by sorption and precipitation. Although complexation of heavy metals with dissolved organic matter is significant, the heavy metals are in most cases still strongly attenuated in leachate-polluted aquifers. The information available on attenuation processes has increased dramatically during the last 15 a, but the number of well-documented full scale leachate plumes are still few and primarily from sandy aquifers. Thus, the diversity of attenuation processes in leachate plumes is probably not yet fully understood. Apparently, the attenuation processes in leachate plumes may for many contaminants provide significant natural remediation, limiting the effects of the leachate on the groundwater to an area usually not exceeding 1000 m from the landfill.     

Conjectures on the thermal and tectonic evolution of the Earth

The tectonic modes operating at any given time in the Earth are intimately related to the thermal evolution, since tectonics is driven by heat removal from the Earth's interior. Conversely, the viability of a proposed tectonic mode depends on its ability to remove heat from the interior as well as on its inferred consistency with geological evidence. On this basis it seems that plate tectonics may have been dominant only in the later part of Earth history, and that proposed earlier modes involving only a subcrustal thermal boundary layer may never have been dominant unless the effects of the basalt-eclogite transition or of latent heat removal were able to enhance their heat transport efficiency. More generally, the tectonic mode driven by the cool thermal boundary layer at the top of the mantle may have depended very sensitively on the effects of composition and latent heat on density.

Calculations indicate that plumes could have operated through most of Earth history at about the present level of activity, unless heat conduction from the core into the mantle has been inhibited in later times, in which case they would have been hotter and more active in earlier times. Plumes could not have substituted for plate tectonics because plumes and plates are driven by different thermal boundary layers that operate largely independently.     

Voyage of the Indian subcontinent since Pangea breakup and driving force of supercontinent cycles: Insights on dynamics from numerical modeling

Recent advances in three-dimensional numerical simulations of mantle convection have aided in approximately reproducing continental movement since the Pangea breakup at 200 Ma. These have also led to a better understanding of the thermal and mechanical coupling between mantle convection and surface plate motion and predictions of the configuration of the next supercontinent. The simulations of mantle convection from 200 Ma to the present reveals that the development of large-scale cold mantle downwellings in the North Tethys Ocean at the earlier stage of the Pangea breakup triggered the northward movement of the Indian subcontinent. The model of high temperature anomaly region beneath Pangea resulting from the thermal insulation effect support the breakup of Pangea in the real Earth time scale, as also suggested in previous geological and geodynamic models. However, considering the low radioactive heat generation rate of the depleted upper mantle, the high temperature anomaly region might have been generated by upwelling plumes with contribution of deep subducted TTG(tonalite-trondhjemite-granite) materials enriched in radiogenic elements. Integrating the numerical results of mantle convection from 200 Ma to the present, and from the present to the future, it is considered that the mantle drag force acting on the base of continents may be comparable to the slab pull force, which implies that convection in the shallower part of the mantle is strongly coupled with surface plate motion.     

正削式隧道洞门结构简化计算方法的研究

切削式隧道洞门结构处于复杂的三维受力状态,需要采用三维数值计算才能得到相对正确的结果,为对计算模式进行简化,对Ⅴ级围岩条件下,1: 1.5坡度的正削式隧道洞门结构进行了尝试。首先对明挖法施工的洞门模型试验和三维数值计算所得到的拱顶围岩压力进行了验证,接着从研究围岩压力分布和结构受力特性着手,得到了结构横、纵向内力的控制截面,拱顶荷载q与 的关系,绘制了横向的压力分布图式,并给出了纵向荷载的计算方法,从而将三维地层结构数值计算模式简化成横向封闭环和纵向弹性地基的平面荷载-结构计算模式,分别计算横、纵向内力。