A Unified Variational Principle of Fluid Mechanics and Application on Solitary Subdomain or Point

-According to basic equations of fluid mechanics, this paper presents a unified variational principle of fluid mechanics (UVPFM) by using the optimization method of weighted residuals (OMWR). The advantages are as follows, the establishment of the functional and the variational principle is easy, it can change various problems of fluid mechanics derived by basic equations into a unified optimization problem, and the solution is the optimum one in some sense. According to the OMWR for the solitary subdomain, this paper uses UVPFM onto any solitary subdomain and gives the solution of the hydrodynamics equation which is suitable only for that solitary subdomain. According to the OMWR for solitary point, this paper uses UVPFM to any solitary point and gives the solution of the hydrodynamics equation (point solution) which is suitable only for that solitary point. As the solution for the solitary subdomain or solitary point is developed independently, the compatibility with other subdomain or other points, do     

Model of a porous medium with an elastic fractured skeleton

The model of a saturated porous medium with a brittle deformable skeleton is formulated in an isothermal approximation. The general form of governing equations is found, which is necessary and sufficient to fulfill the principles of objectivity and thermodynamic consistency. It is shown that the kinetics of developing the ensemble of microcracks, determined by the derivative of the elastic potential of the skeleton with respect to the fracture parameter, results in a nonnegative dissipation of the scattered destruction with any type of loading. For small deviations from the initial state, a new elastic potential is proposed which has made it possible to describe the main irregularities of the behavior of the medium in question. The solution of the problem about the consolidation of a saturated porous half-space with a brittle skeleton under a normal load has been constructed.     

Retrieving earthquake signature in grace gravity solutions

The GRACE satellites have been orbiting the Earth since 2002, monitoring the time variable gravity field. Some of the observed fluctuations are due to geodynamic causes, but they are often hidden in the complex signal, composed of hydrology, ocean, atmosphere, and geodynamics, the signal of geodynamic origin being usually the smallest. In addition, dealiasing residuals and noise make the separation of the signal from the different causes more difficult. We proposed a method based on the Empirical Orthogonal Function decomposition to extract the signal of physical origin, under the hypothesis that the physical signal is spatially more consistent than the noise and aliasing incomplete correction. We used synthetic geoid variations associated with earthquakes located at nearly 2000 positions at the Earth surface, based on several examples of large actual subduction events. We show that, with the present day accuracy, we can retrieve the geoid variations associated with more than 98 per cent of the earthquakes of magnitude 9 or above, around 60 per cent for magnitude 8.8, 40 per cent for magnitude 8.6 and 33 per cent for magnitude 8.3. Some events, with the right properties and location, can be detected with magnitude as low as 8. We then applied the method to the GRACE solutions, and retrieved the Hokkaido event (2003) and the Sumatra event (2004), which is in agreement with the retrieval rates mentioned here above.     

Authigenic carbonates in methane seeps from the Norwegian sea: Mineralogy, geochemistry, and genesis

Authigenic carbonates in the caldera of an Arctic (72°N) submarine mud volcano with active CH₄bearing fluid discharge are formed at the bottom surface during anaerobic microbial methane oxidation. The microbial community consists of specific methane-producing bacteria, which act as methanetrophic ones in conditions of excess methane, and sulfate reducers developing on hydrogen, which is an intermediate product of microbial CH₄ oxidation. Isotopically light carbon (δ¹³C_av =−28.9%0) of carbon dioxide produced during CH₄ oxidation is the main carbonate carbon source. Heavy oxygen isotope ratio (δ¹⁸O_av = 5%0) in carbonates is inherited from seawater sulfate. A rapid sulfate reduction (up to 12 mg S dm⁻³ day⁻¹) results in total exhausting of sulfate ion in the upper sediment layer (10 cm). Because of this, carbonates can only be formed in surface sediments near the water-bottom interface. Authigenic carbonates occurring within sediments occur do notin situ. Salinity, as well as CO ₃ ²⁻ /Ca and Mg/Ca ratios, correspond to the field of nonmagnesian calcium carbonate precipitation. Calcite is the dominant carbonate mineral in the methane seep caldera, where it occurs in the paragenetic association with barite. The radiocarbon age of carbonates is about 10000 yr.     

Dangerous fogs on the territory of Georgia

The statistical structure of dangerous fogs with the visibility of less than 50 m is studied using the observation data of 50 meteorological stations in Georgia for the period of 1961–2006. The contribution of dangerous fogs to the total number of foggy days is estimated. The number of days with dangerous fogs and their duration in different regions of the country are determined and the empirical functions of their distribution, sizes of areas of their expansion, temperature regime, and peculiarities of annual variations are studied.     

Prime controls on Archaean–Palaeoproterozoic sedimentation: Change over time

Although the principle of uniformitarianism may be applied to the Precambrian sedimentary record as a whole, certain periods of the Archaean and Palaeoproterozoic witnessed a changing pattern of prime influences controlling the depositional systems. This paper examines the major controls on sedimentation systems and environments during the Archaean and Palaeoproterozoic within the broader perspective of Earth evolution. Earth's earliest sedimentary system (4.4?-3.7 Ga) was presumably comprised of deep oceanic realms and probably influenced primarily by bolide impacts, major tsunamis, localized traction and global contour current patterns, and bathymetry. As continental crust began to form, the impact-dominated, tsunami type sedimentation gave way to wider varieties of sedimentary environments, known from the oldest sedimentary records. During early continental crustal evolution (c. 3.7–2.7 Ga), sedimentation was essentially of greenstone-type. Volcanic and volcaniclastic rocks were the major components of the greenstone belts, associated with thin carbonates, stromatolitic evaporites, BIF, pelites and quartzites and lesser synorogenic turbidites, conglomerates and sandstones. Volcanism and active tectonism (reflecting dynamic depositional settings during island arc and proto-continental nucleus formation) were the predominant factors influencing sedimentation during this phase of Earth evolution. Transgressions and regressions under the combined influence of tectonics and eustasy are reflected in fining- and coarsening-upwards successions from the proto-cratonic settings; low freeboard enabled the transgression to affect large areas of the proto-cratons. As the earliest, relatively stable craton formed, through a combination of plate tectonic and mantle-thermal processes, continents and supercontinents with the potential for supercontinental cycles started to influence sedimentation strongly. Major controls on Neoarchaean–Palaeoproterozoic sedimentation systems (2.7–1.6 Ga) were provided by a combination of superplume events and plate tectonics. Two global-scale ‘superevents’ at c. 2.7 Ga and c. 2.2–1.8 Ga were accompanied by eustatic rise concomitant with peaks in crustal growth rates, and large epeiric seas developed. The operation of first-order controls leading to development of vast chemical sedimentary platforms in these epeiric seas and concomitant palaeo-atmospheric and palaeo-oceanic evolution combined to provide a second-order control on global sedimentary systems in the Neoarchaean–Palaeoproterozoic period. The supercontinental cycle had become well established by the end of the Palaeoproterozoic, with the existence of large cratons across broad spectrums of palaeolatitude enabling erg development. The entire spectrum of sedimentary systems and environments came into existence by c. 1.8 Ga, prime influences on sedimentation and depositional system possibly remaining essentially uniform thereafter.     

Application of Deuterium Excess for Identification of Freshwater Sources in the Bays of Novaya Zemlya Archipelago

Doklady Earth Sciences - An isotopic–geochemical study was carried out for waters of Tsivolkii and Sedov bays (southeastern coast of the Novaya Zemlya Archipelago). The waters of these bays...     

Unravelling the effects of melt depletion and secondary infiltration on mantle Re-Os isotopes beneath the French Massif Central

Spinel lherzolite xenoliths from Mont Briançon, French Massif Central, retain evidence for multiple episodes of melt depletion and melt/fluid infiltration (metasomatism). Evidence for primary melt depletion is still preserved in the co-variation of bulk-rock major elements (MgO 38.7-46.1 wt.%; CaO 0.9-3.6 wt.%), and many samples yield unradiogenic bulk-rock Os isotope ratios (¹⁸⁷Os/¹⁸⁸Os = 0.11541-0.12626). However, many individual xenoliths contain interstitial glasses and melt inclusions that are not in equilibrium with the major primary minerals. Incompatible trace element mass balance calculations demonstrate that metasomatic components comprise a significant proportion of the bulk-rock budget for these elements in some rocks, ranging to as much as 25% of Nd and 40% of Sr Critically, for Re-Os geochronology, melt/fluid infiltration is accompanied by the mobilisation of sulfide. Consequently, bulk-rock isotope measurements, whether using lithophile (e.g. Rb-Sr, Sm-Nd) or siderophile (Re-Os) based isotope systems, may only yield a perturbed and/or homogenised average of these multiple events.Osmium mass balance calculations demonstrate that bulk-rock Os in peridotite is dominated by contributions from two populations of sulfide grain: (i) interstitial, metasomatic sulfide with low [Os] and radiogenic ¹⁸⁷Os/¹⁸⁸Os, and (ii) primary sulfides with high [Os] and unradiogenic ¹⁸⁷Os/¹⁸⁸Os, which have been preserved within host silicate grains and shielded from interaction with transient melts and fluid. The latter can account for >97% of bulk-rock Os and preserve geochronological information of the melt from which they originally precipitated as an immiscible liquid. The Re-depletion model ages of individual primary sulfide grains preserve evidence for melt depletion beneath the Massif Central from at least 1.8 Gyr ago despite the more recent metasomatic event(s).