Understanding the turbulent structure of the atmospheric boundary layer: A diagnostic approach

In this paper, we have attempted a diagnostic study of the turbulence characteristics of the ABL by means of two one-dimensional models. The first model uses a first order non-local closure, based on the Transilient Turbulence Theory, for parameterizing turbulent fluxes. while the second model uses second order local closure for parameterizing these. The models have been applied to conduct case studies using the Kytoon data taken at Kharagpur, during 17th–21st June, 1990, as part of the MONTBLEX programme. Our findings bring out various interesting features regarding the non-local and local turbulent statistics such as kinematic fluxes, turbulence kinetic energy, vertical velocity variance, the contribution of the eddies of various sizes to the fluxes at different level and the mixing lengths. The one-dimensional anisotropy of the turbulent eddies has been revealed by the findings from the transilient model. The vertical variation of the turbulence kinetic energy, as computed directly by the second order model, is found to be strongly correlated with the vertical velocity variance. In particular, for stably stratified boundary layers, identification of two distinct zones of the turbulence kinetic energy and corresponding vertical velocity maxima is possible, which has been interpreted as positive evidence of patchy turbulence in the boundary layer.     

A generic approach to modelling flexible confined boundary conditions in SPH and its application

In this paper, a new approach to applying confining stress to flexible boundaries in the smoothed particle hydrodynamics (SPH) method is developed to facilitate its applications in geomechanics. Unlike the conventional SPH methods that impose confining boundary conditions by creating extra boundary particles, the proposed approach makes use of kernel truncation properties of SPH approximations that occur naturally at free-surface boundaries. Therefore, it does not require extra boundary particles and, as a consequence, can be utilised to apply confining stresses onto any boundary with arbitrary geometry without the need for tracking the curvature change during the computation. This enables more complicated problems that involve moving confining boundaries, such as confining triaxial tests, to be simulated in SPH without difficulties. To further enhance SPH applications in elasto-plastic computations of geomaterials, a robust numerical procedure to implement Mohr-Coulomb plasticity model in SPH is presented for the first time to avoid difficulties associated with corner singularities in Mohr-Coulomb model. The proposed approach was first validated against two-dimensional finite element (FE) solutions for confining biaxial compression tests to demonstrate its predictive capability at small deformation range when FE solutions are still valid. It is then further extended to three-dimensional conditions and utilised to simulate triaxial compression experiments. Simulation results predicted by SPH show good agreement with experiments, FE solutions, and other numerical results available in the literature. This suggests that the proposed approach of imposing confining stress boundaries is promising and can handle complex problems that involve moving confining boundary conditions.     

Zirconium and hafnium fractionation in differentiation of alkali carbonatite magmatic systems

Zirconium and hafnium are valuable strategic metals which are in high demand in industry. The Zr and Hf contents are elevated in the final products of magmatic differentiation of alkali carbonatite rocks in the Polar Siberia region (Guli Complex) and Ukraine (Chernigov Massif). Early pyroxene fractionation led to an increase in the Zr/Hf ratio in the evolution of the ultramafic–alkali magmatic system due to a higher distribution coefficient of Hf in pyroxene with respect to Zr. The Rayleigh equation was used to calculate a quantitative model of variation in the Zr/Hf ratio in the development of the Guli magmatic system. Alkali carbonatite rocks originated from rare element-rich mantle reservoirs, in particular, the metasomatized mantle. Carbonated mantle xenoliths are characterized by a high Zr/Hf ratio due to clinopyroxene development during metasomatic replacement of orthopyroxene by carbonate fluid melt.     

苏州氟铁云母岩--富氟A型花岗岩浆的残余分异物

位于苏州A型花岗岩主体相晚阶段衍生物(碱长花岗岩)上部,基本上由新矿物--氟铁云母组成的单矿物岩,具有独特的产状、结构、构造、岩石化学、矿物学、地球化学和成矿作用特征.种种典型的宏观、微观地质特征和合成氟铁云母的实验资料揭示,氟铁云母岩主要是从A型花岗岩浆演化至晚阶段熔离出来的富F,Fe和亲石性矿化元素及富碱性元素(且K>>Na)而相对贫水的高温硅酸盐熔体中直接结晶固化所成.氟铁云母岩应属一种新的岩浆岩,依产地命名为姑苏岩.姑苏岩拟归入岩浆云英岩范畴为宜.提出了包括姑苏岩、含黄玉的石英-氟铁云母云英岩(苏州岩)和氟铁云母碱长花岗岩等在内的苏州A型花岗岩的成岩、成矿模式.     

Dynamic soil-structure interaction: A three-dimensional numerical approach and its application to the Lotung case study

This paper presents a three-dimensional non-linear finite element (FE) approach to analyse the dynamic soil-structure interaction (SSI) phenomena observed at the Lotung Large-Scale Seismic Test (LSST) site. The numerical study is carried out in the time domain by a commercial FE code, taking into account the non-linear behaviour of soil and the multi-directional nature of real seismic events. The soil response is simulated by an isotropic hardening elasto-plastic hysteretic model (HSsmall) implemented in the material model library of the code. This model allows to describe the non-linear cyclic response ranging from small to large strain amplitudes and to account for the variation of the initial stiffness with depth.In the paper, the FE numerical approach is first validated through a series of parametric analyses simulating simplified cases (i.e. linear visco-elastic structures founded on a homogeneous linear visco-elastic soil deposit) for which analytical solutions exist. Then, it is adopted to back-analyse the behaviour of the 1/4-scale nuclear power plant containment structure constructed at the Lotung LSST site which was shook by several earthquakes of different intensities and frequency contents. The FE results are thus compared to the recorded in-situ free-field and structural motions, highlighting the satisfactory performance of the numerical model in replicating the observed response. The overall outcome of this research proves that nowadays complex dynamic SSI phenomena can be tackled by direct approach, overpassing the strong simplifications of the well-established substructure approaches.     

A possible boundary condition in bacterial sulfur isotope fractionation

The sulfur isotopic effect (δ³⁴S) shown by batch cultures of six species of sulfate-reducing bacteria was ?14.6%. (S.D.4.1).Fractionation appeared to be independent of electron donor, temperature (between 35 and 55°) and the extent of sulfate reduction.     

Titanite: A potential solidus barometer for granitic magma systems

Constraining crystallization pressure and thus intrusion depth of granites in various geodynamic settings remains challenging, yet important to further our understanding of magma system and crustal evolution. We propose that titanite, which is a common accessory in metaluminous and weakly peraluminous granites, can be used as a barometer if it crystallized in magmatic, near-solidus conditions and in equilibrium with amphibole, plagioclase, K-feldspar, quartz, biotite, and magnetite ± ilmenite. Titanite Al₂O₃ increases with pressure (P) according to: P (in MPa) = 101.66 × Al₂O₃ in titanite (in wt%) + 59.013 (R² = 0.83) with estimated uncertainties of ~±60 to ~±100 MPa for crystallization between ~150 and 400 MPa. We highlight that the current calibration dataset is limited, and that systematic experimental studies are needed to rigorously quantify the relation. The most important use of this empirical barometer will be for rocks in which amphibole is present but significantly altered, or in combination with amphibole barometry, as titanite can be easily dated by LA-ICP-MS.     

Chemical and isotopic fractionation of wet andesite in a temperature gradient: Experiments and models suggesting a new mechanism of magma differentiation

Piston-cylinder experiments were conducted to investigate the behavior of partially molten wet andesite held within an imposed temperature gradient at 0.5 GPa. In one experiment, homogenous andesite powder (USGS rock standard AGV-1) with 4 wt.% H₂O was sealed in a double capsule assembly for 66 days. The temperature at one end of this charge was held at 950 °C, and the temperature at the other end was kept at 350 °C. During the experiment, thermal migration (i.e., diffusion in a thermal gradient) took place, and the andesite underwent compositional and mineralogical differentiation. The run product can be broadly divided into three portions: (1) the top third, at the hot end, contained 100% melt; (2) the middle-third contained crystalline phases plus progressively less melt; and (3) the bottom third, at the cold end, consisted of a fine-grained, almost entirely crystalline solid of granitic composition. Bulk major- and trace-element compositions change down temperature gradient, reflecting the systematic change in modal mineralogy. These changes mimic differentiation trends produced by fractional crystallization. The change in composition throughout the run product indicates that a fully connected hydrous silicate melt existed throughout the charge, even in the crystalline, cold bottom region. Electron Backscatter Diffraction analysis of the run product indicates that no preferred crystallographic orientation of minerals developed in the run product. However, a significant anisotropy of magnetic susceptibility was observed, suggesting that new crystals of magnetite were elongated in the direction of the thermal gradient. Further, petrographic observation reveals alignment of hornblende parallel to the thermal gradient. Finally, the upper half of the run product shows large systematic variations in Fe-Mg isotopic composition reflecting thermal diffusion, with the hot end systematically enriched in light isotopes. The overall δ⁵⁶Fe_IRMM-14 and δ²⁶Mg_DSM-3 offsets are 2.8‰ and 9.9‰, respectively, much greater than the range of Fe-Mg isotope variation in high-temperature terrestrial samples.In contrast, no obvious chemical differentiation was observed in a similar experiment (of 33 days duration) where the temperature ranged from 550 to 350 °C, indicating the critical role of the melt in causing the differentiation observed in the 950-350 °C experiment. If temperature gradients can be sustained for the multi-million-year time scales implied by geochronology in some plutonic systems, thermal migration could play a heretofore unrecognized role in the development of differentiated plutons. Elemental distributions, dominated by phase equilibria, cannot be used to discriminate thermal migration from conventional magma differentiation processes such as fractional crystallization. However, the observation of Fe-Mg isotopic variations in partially molten portions of the experiment indicates that these isotopic systems could provide a unique fingerprint to this process. This result could also provide a possible explanation for the Fe-Mg isotope variations observed in high-temperature silicate rocks and minerals.     

A kinetic approach to describe trace-element distribution between particles and solution in natural aquatic systems

The partitioning of radioactive trace elements between seawater and particulate matter from surface sediments and sediment traps was investigated in laboratory experiments. For the elements Na, Zn, Se, Sr, Cd, Sn, Sb, Cs, Ba, Hg, Th and Pa (group I) constant distribution coefficients (K_d) were found after a few days of equilibration, whereas the elements Be, Mn, Co and Fe (group II) showed an increasing K_d over the whole time of observation of 108 days. The time dependence of K_d is described by an adsorption-desorption equilibrium (group I elements), followed by a lattice transport reaction step (group II elements). The reaction rate constants are compared to Mn oxidation rates and to adsorption rate constants derived from in situ measurements of the $\text{U}\text{Th}$ disequilibrium as available from literature.     

A model of reverse differentiation at Dikii Greben' Volcano,Kamchatka: progressive basic magma vesiculation in a silicic magma chamber

Dikii Greben' Volcano is the largest modern volcano with silicic rocks in the Kurile-Kamchatka island arc. It consists of many domes and lava flows of rhyodacite, dacite and andesite which were erupted in a reverse differentiation sequence. Non-equilibrium phenocryst assemblages (quartz + Mg-rich olivine, An-rich + An-poor plagioclase etc.), abundance of chilled mafic pillows in the dacites and andesites, and linear variations of rock compositions in binary plots are considered as mineralogical, textural and geochemical evidence for mixing. Mafic pillows in volcanics have a lower density (because of high porosity) and contain the same non-equilibrium phenocryst assemblages as the host rocks. Their groundmass contains skeletal microlites of plagioclase and amphibole proving that the groundmass as well as the pillows themselves formed from a water-rich basaltic magma at depth. They are considered as supercooled, vesiculated floating drops of a hot hybrid layer in the magma chamber which formed after refilling. The lower density of the inclusions allows them to float in the host magma and to concentrate at the top of the chamber prior to eruption. Magma mingling was effected by mechanical disintegration of the inclusions in the host magma during eruption. The rhyodacitic and basic end-members of the mixing series cannot be linked by low-P fractionation though high-P, amphibole-rich fractionation is not excluded.     

A mineral and cumulate perspective to magma differentiation at Nisyros volcano,Aegean arc

Lavas and pyroclastic products of Nisyros volcano (Aegean arc, Greece) host a wide variety of phenocryst and cumulate assemblages that offer a unique window into the earliest stages of magma differentiation. This study presents a detailed petrographic study of lavas, enclaves and cumulates spanning the entire volcanic history of Nisyros to elucidate at which levels in the crust magmas stall and differentiate. We present a new division for the volcanic products into two suites based on field occurrence and petrographic features: a low-porphyricity andesite and a high-porphyricity (rhyo)dacite (HPRD) suite. Cumulate fragments are exclusively found in the HPRD suite and are predominantly derived from upper crustal reservoirs where they crystallised under hydrous conditions from melts that underwent prior differentiation. Rarer cumulate fragments range from (amphibole-)wehrlites to plagioclase-hornblendites and these appear to be derived from the lower crust (0.5–0.8 GPa). The suppressed stability of plagioclase and early saturation of amphibole in these cumulates are indicative of high-pressure crystallisation from primitive hydrous melts (≥ 3 wt% H₂O). Clinopyroxene in these cumulates has Al₂O₃ contents up to 9 wt% due to the absence of crystallising plagioclase, and is subsequently consumed in a peritectic reaction to form primitive, Al-rich amphibole (Mg# > 73, 12–15 wt% Al₂O₃). The composition of these peritectic amphiboles is distinct from trace element-enriched interstitial amphibole in shallower cumulates. Phenocryst compositions and assemblages in both suites differ markedly from the cumulates. Phenocrysts, therefore, reflect shallow crystallisation and do not record magma differentiation in the deep arc crust.     

Wind profiles in the boundary layer over Kharagpur associated with synoptic scale systems

Doppler sodar wind data for the boundary layer over Kharagpur obtained during MONTBLEX-1990 at a height interval of 30 m from surface up to 1500 m have been analysed for the periods when intense synoptic scale disturbances from north Bay of Bengal moved along the eastern end of the monsoon trough. The variation in the vertical wind profile in the lower boundary layer over Kharagpur during the passage of synoptic scale disturbances has been discussed in the paper. The analysis indicates that the mean winds over Kharagpur veered with height in the lower boundary layer near the surface suggesting divergence over Kharagpur when the system lay south/southwest of the station. No such veering has been noticed when the centre of the system lay very close to the station.     

Basalt magma genesis and fractionation in collision- and extension-related provinces: A comparison between eastern, central and western Anatolia

Experimental studies of synthetic and natural basalt systems suggest that conditions of magma genesis and fractionation depend fundamentally on mantle temperatures and lithospheric stress fields. In general, compressional settings are more conducive to polybaric fractionation than extensional settings and in this regard, the Anatolian magmatic province offers a natural laboratory for comparing near-coeval basalt eruptions as a function of regional tectonics — compressional (collision-related) régimes dominating in eastern Anatolia and extensional tectonics characterizing a western province related to Aegean Sea opening. Projection of Plio-Quaternary basalt normative compositions from the Western Anatolia Extensional Province (WAEP), the Central Anatolian ‘Ova’ Province (CAOP), and Eastern Anatolia Compressional Province (EACP) are projected onto Ol–Ne–Cpx and Pl–Cpx–Ol planes in the simplified basalt system (Ne–Cpx–Ol–Qz), each showing distinctive liquid lines of descent. WAEP basalts are mostly constrained by low-pressure (< 0.5 GPa) cotectics while CAOP and EACP compositions conform to moderate and/or high-pressure (0.8–3.0 GPa) cotectics. Overall, a quasi-linear shift from moderate and/or high-pressure to low-pressure equilibria matches the westward transgression from compressional east Anatolia to the extensional west Anatolian–Aegean region. Comparison of their respective primary (mantle-equilibrated) magmas–simulated by normalizing their compositions to MgO = 15 wt.% (Mg-15)–with parameterized anhydrous and H₂O-undersaturated experimental melts suggests they segregated from spinel- to garnet-lherzolite mantle facies at pressures between c. 2 and 3 GPa (c. 70–100 km depth) under H₂O-undersaturated conditions. Interpolated potential temperatures (T_p) and lithospheric stretching factors (β) range as follows: (1) eastern Anatolian basalts associated with the Arabian foreland show T_p varying between 1250 and 1400 °C (except for the Karacalidag alkali basalts, south of the Bitlis–Zagros fracture zone, for which T_p ranges up to 1450 °C), for β values of 1.2–1.8. T_p values for central Anatolia (e.g. Sivas) range between 1300 and 1375 °C (except for Karapinar, Egrikuyu and Hasandag, which show < 1150 °C), and β values of 1.3–1.4. For western Anatolian basalts, T_p range mostly between 1250 and 1330 °C, except for a single value for Canakkale of 1400 °C and Kula sample showing T_p < 1200 °C, and β values of 1.3–2.0. Variation of these conditions is as great or greater than that between provinces, although there are clearly significant constraints on the inferred polybaric to low-pressure isobaric fractionation régimes. Covariation of total FeO, TiO₂, La/Yb, Ce/Sm, Zr/Y and Zr/Nb reflects small but significant differences in bulk composition and ambient melt fraction while the covariance of Ce/Sm and Sm/Yb is consistent with the segregation of primitive melts at the spinel- to garnet-lherzolite transition.     

The mechanism of magma ascent through the solid lithosphere and relation between mantle and crustal diapirism: numerical modeling and natural examples

Diapirism can be regarded as the main mechanism of transport through the lithosphere for both felsic and mafic/ultramafic magmas. However, the lack of field observations makes it difficult to identify the key mechanism responsible for the formation of dome-shaped structures. In this study, emplacement of natural diapirs is reconstructed by numerical experiments handling realistic rheological and petrological models for the crust and mantle lithosphere. Three different regimes of diapiric ascent were established depending on the chosen model rheology: (1) single-stage diapir ascent; (2) pulsating ascent of successive batches of mantle-derived magma to the base of the crust with a periodicity of 2-3 Myr; (3) emplacement of extensive magma bodies in the form of sills either beneath the base of the crust (underplating) or to deeper mantle levels. The timescale of 30 Myr for a heat source at the base of the lithosphere is sufficient to initiate the ascent of a diapir through the mantle and crust. The study provides the estimates of rheological properties of the lithosphere and partially molten material at which diapiric ascent through the mantle and crust can occur.     

Large static problem in numerical limit analysis: A decomposition approach

A general decomposition approach for the static method of limit analysis is proposed. It is based on piecewise linear stress fields, on a partition into finite element sub‐problems and on a specific coordination of the subproblem stress fields through auxiliary interface problems. The final convex optimization problems are solved using nonlinear interior point programming methods. As validated for the compressed bar with Tresca/von Mises materials in plane strain, this method appears rapidly convergent, so that very large problems with millions of constraints and variables can be solved. Then the method is applied to the classical problem of the stability of a Tresca vertical cut: the static bound to the stability factor is improved to 3.7752, a value to be compared with the recent best upper bound 3.7776. Copyright © 2010 John Wiley & Sons, Ltd.     

应用亮兰染色剂指示溶质迁移边界层的研究

应用边界层方法确定溶质迁移参数是一种简单可靠的方法,但如何确定边界层的位置是限制边界层方法应用的关键因素。而亮兰染色剂在土壤中迁移时,具有边界层清晰、容易确定的特点。基于此,以Cl-为例,研究了该染色剂指示非反应性溶质迁移边界层的可行性。研究结果表明:在同一土柱中,亮兰染色剂的边界层与Cl-的边界层的运动规律相似,亮兰染色剂和Cl-的边界层随时间的变化在弥散度很小的情况下都可以用线性关系式近似描述。根据这一规律,得出在风沙土和黄绵土中Cl-边界层与亮兰染色剂边界层之间的关系表达式。两者边界层之间转换关系的求得,为应用亮兰染色剂准确指示非反应性溶质迁移边界层成为可能提供了一条思路。     

A robust method to tackle pressure boundary conditions in porous media flow: application to biogrout

Biogrout is a soil improvement method in which microorganisms are used to produce the solid calcium carbonate, which strengthens the soil by connecting soil particles. Microorganisms in the soil are supplied with some nutrients, which they convert into calcium carbonate. These nutrients and the side product of the reaction are dissolved in water. Because of these chemicals, the fluid is denser than water. Moreover, the density changes as a result of the varying composition. This changing density has a significant impact on the flow. Since the composition and hence, the density is not known beforehand, a careful choice of the (pressure) boundary conditions, especially on the outflow boundary, is needed. In this article, several methods to approximate the pressure on the outflow boundary are compared. The method that we propose also works for an unstructured mesh, which gives a large freedom in the mesh generation.     

A numerical solution to seepage problems with complex drainage systems

Seepage problems with complex drainage systems are commonly encountered in civil engineering, with strong non-linearity. A numerical solution based on the Finite Element Method combining the substructure technique with a variational inequality formulation of Signorini’s type is proposed to solve these problems. The aims of this work are to accurately characterize the boundary conditions of the drainage systems, to reduce the difficulty in mesh generation resulting from the drainage holes with small radius and dense spacing, and to eliminate the singularity at the seepage points and the resultant mesh dependency. Numerical stability and robustness of the proposed method are guaranteed by an adaptive procedure for progressively relaxing the penalized Heaviside function associated with the formulation of the discrete variational inequality. Two challenging numerical examples are presented to validate the effectiveness and robustness of the proposed method.