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SHARP simulation of discontinuities in highly convective steady flow

For steady multidimesional convection, the Quadratic Upstream Interpolation for Convective Kinematics (QUICK) scheme has several attractive properties. However, for highly convective simulation of step profiles, QUICK produces unphysical overshoots and a few oscillations, and this may cause serious problems in nonlinear flows. Fortunately, it is possible to modify the convective flux by writing the normalized convected control-volume face value as a function of the normalized adjacent upstream node value, developing criteria for monotonic resolution without sacrificing formal accuracy. This results in a nonlinear functional relationship between the normalized variables, whereas standard methods are all linear in this sense. The resulting Simple High Accuracy Resolution Program (SHARP) can be applied to steady multidimensional flows containing thin shear or mixing layers, shock waves, and other frontal phenomena. This represents a significant advance in modeling highly convective flows of engineering and geophysical importance. SHARP is based on an explicit, conservative, control-volume flux formation, equally applicable to one, two, or three dimensional elliptic, parabolic, hyperbolic, or mixed-flow regimes. Results are given for the bench-mark purely convective first-order results and the nonmonotonic predictions of second- and third-order upwinding.

Leonard, B. P.↗

Simple high-accuracy resolution program for convective modelling of discontinuities

For steady multidimensional convection, the Quadratic Upstream Interpolation for Convective Kinematics (QUICK) scheme has several attractive properties. However, for highly convective simulation of step profiles, QUICK produces unphysical overshoots and a few oscillations, and this may cause serious problems in nonlinear flows. Fortunately, it is possible to modify the convective flux by writing the normalized convected control-volume face value as a function of the normalized adjacent upstream node value, developing criteria for monotonic resolution without sacrificing formal accuracy. This results in a nonlinear functional relationship between the normalized variables, whereas standard methods are all linear in this sense. The resulting Simple High Accuracy Resolution Program (SHARP) can be applied to steady multidimensional flows containing thin shear or mixing layers, shock waves, and other frontal phenomena. This represents a significant advance in modeling highly convective flows of engineering and geophysical importance. SHARP is based on an explicit, conservative, control-volume flux formation, equally applicable to one, two, or three dimensional elliptic, parabolic, hyperbolic, or mixed-flow regimes. Results are given for the bench-mark purely convective first-order results and the nonmonotonic predictions of second- and third-order upwinding.

Leonard, B. P.↗

Finite element analysis in fluids; Proceedings of the Seventh International Conference on Finite Element Methods in Flow Problems, University of Alabama, Huntsville, Apr. 3-7, 1989

Recent advances in computational fluid dynamics are examined in reviews and reports, with an emphasis on finite-element methods. Sections are devoted to adaptive meshes, atmospheric dynamics, combustion, compressible flows, control-volume finite elements, crystal growth, domain decomposition, EM-field problems, FDM/FEM, and fluid-structure interactions. Consideration is given to free-boundary problems with heat transfer, free surface flow, geophysical flow problems, heat and mass transfer, high-speed flow, incompressible flow, inverse design methods, MHD problems, the mathematics of finite elements, and mesh generation. Also discussed are mixed finite elements, multigrid methods, non-Newtonian fluids, numerical dissipation, parallel vector processing, reservoir simulation, seepage, shallow-water problems, spectral methods, supercomputer architectures, three-dimensional problems, and turbulent flows.

Chung, T. J.↗

Ocean Turbulence I: One-Point Closure Model Momentum and Heat Vertical Diffusivities

Since the early forties, one-point turbulence closure models have been the canonical tools used to describe turbulent flows in many fields. In geophysics, Mellor and Yamada applied such models using the 1980 state-of-the art. Since then, no improvements were introduced to alleviate two major difficulties: 1) closure of the pressure correlations, which affects the correct determination of the critical Richardson number Ri(sub cr) above which turbulent mixing is no longer possible and 2) the need to express the non-local third-order moments (TOM) in terms of lower order moments rather than via the down-gradient approximation as done thus far, since the latter seriously underestimates the TOMs. Since 1) and 2) are still being dealt with adjustable parameters which weaken the credibility of the models, alternative models, not based on turbulence modeling, have been suggested. The aim of this paper is to show that new information, partly derived from the newest 2-point closure model discussed, can be used to solve these shortcomings. The new one-point closure model, which in its simplest form is algebraic and thus simple to implement, is first shown to reproduce a variety of data. Then, it is used in a Ocean-General Circulation Model (O-GCM) where it reproduces well a large variety of ocean data. While phenomenological models are specifically tuned to ocean turbulence, the present model is not. It is first tested against laboratory data on stably stratified flows and then used in an O-GCM. It is more general, more predictive and more resilient, e.g., it can incorporate phenomena like wave-breaking at the surface, salinity diffusivity, non-locality, etc. One important feature that naturally comes out of the new model is that the predicted Richardson critical value Ri(sub cr) is Ri (sub cr approx. = 1) in agreement with both Large Eddy Simulations (LES) and empirical evidence while all previous models predicted Ri (sub cr approx. = 0.2) which led to a considerable underestimate of the extent of turbulent mixing and thus to an incorrect mixed layer depth. The predicted temperature and salinity profiles (vs. depth) are presented and compared with those of the Kolmogorov-Petruvsky-Piskunuv (KPP) model and Levitus data.

Canuto, V. M.↗

The Origin of Carbon-bearing Volatiles in Surprise Valley Hot Springs in the Great Basin: Carbon Isotope aud Water Chemistry Characterizations

There are numerous hydrothermal fields within the Great Basin of North America, some of which have been exploited for geothermal resources. With methane and other carbon-bearing compounds being observed, in some cases with high concentrations, however, their origins and formation conditions remain unknown. Thus, studying hydrothermal springs in this area provides us an opportunity to expand our knowledge of subsurface (bio)chemical processes that generate organic compounds in hydrothermal systems, and aid in future development and exploration of potential energy resources as well. While isotope measurement has long been used for recognition of their origins, there are several secondary processes that may generate variations in isotopic compositions: oxidation, re-equilibration of methane and other alkanes with CO2, mixing with compounds of other sources, etc. Therefore, in addition to isotopic analysis, other evidence, including water chemistry and rock compositions, are necessary to identify volatile compounds of different sources. Surprise Valley Hot Springs (SVHS, 41º32'N, 120º5'W), located in a typical basin and range province valley in northeastern California, is a terrestrial hydrothermal spring system of the Great Basin. Previous geophysical studies indicated the presence of clay-rich volcanic and sedimentary rocks of Tertiary age beneath the lava flows in late Tertiary and Quaternary. Water and gas samples were collected for a variety of chemical and isotope composition analyses, including in-situ pH, alkalinity, conductivity, oxidation reduction potential (ORP), major and trace elements, and C and H isotope measurements. Fluids issuing from SVHS can be classified as Na-(Cl)-SO4 type, with the major cation and anion being Na+ and SO4 2-, respectively. Thermodynamic calculation using ORP and major element data indicated that sulfate is the most dominant sulfur species, which is consistent with anion analysis results. Aquifer temperatures at depth estimated by both dissolved SiO2 and Na-K-Ca geothermometers are in the range of 125.0 to 135.4 oC, and higher than the values measured at orifices (77.3 to 90.0 oC). CO2 and homologs of straight chain alkanes (C1-C5) were identified in gas samples. Carbon isotope values of alkanes increase with carbon numbers. The 13C fractionation between CO2 and dissolved inorganic carbon suggests they are out of carbon isotope equilibrium. The hypothesis regarding the formation of carbon-bearing compounds in SVHS may involve two processes: 1) Under high heat flow conditions which are caused by regional faulting and crustal extension, original high molecular weight organic compounds (kerogens) in clay-rich rocks decomposed to generate methane and other alkane homologs. 2) The SVHS area is associated with outflow structures, and distant from the heat source. Anaerobic oxidation of methane (AOM) with sulfate at shallow depth (< 90 oC) is suggested as being responsible for the generation of CO2 in SVHS.

Fu, Qi↗

The Origin of Carbon-bearing Volatiles in Surprise Valley Hot Springs in the Great Basin: Carbon Isotope and Water Chemistry Characterizations

There are numerous hydrothermal fields within the Great Basin of North America, some of which have been exploited for geothermal resources. With methane and other carbon-bearing compounds being observed, in some cases with high concentrations, however, their origins and formation conditions remain unknown. Thus, studying hydrothermal springs in this area provides us an opportunity to expand our knowledge of subsurface (bio)chemical processes that generate organic compounds in hydrothermal systems, and aid in future development and exploration of potential energy resources as well. While isotope measurement has long been used for recognition of their origins, there are several secondary processes that may generate variations in isotopic compositions: oxidation, re-equilibration of methane and other alkanes with CO2, mixing with compounds of other sources, etc. Therefore, in addition to isotopic analysis, other evidence, including water chemistry and rock compositions, are necessary to identify volatile compounds of different sources. Surprise Valley Hot Springs (SVHS, 41 deg 32'N, 120 deg 5'W), located in a typical basin and range province valley in northeastern California, is a terrestrial hydrothermal spring system of the Great Basin. Previous geophysical studies indicated the presence of clay-rich volcanic and sedimentary rocks of Tertiary age beneath the lava flows in late Tertiary and Quaternary. Water and gas samples were collected for a variety of chemical and isotope composition analyses, including in-situ pH, alkalinity, conductivity, oxidation reduction potential (ORP), major and trace elements, and C and H isotope measurements. Fluids issuing from SVHS can be classified as Na-(Cl)-SO4 type, with the major cation and anion being Na+ and SO4(2-), respectively. Thermodynamic calculation using ORP and major element data indicated that sulfate is the most dominant sulfur species, which is consistent with anion analysis results. Aquifer temperatures at depth estimated by both dissolved SiO2 and Na-K-Ca geothermometers are in the range of 125.0 to 135.4 C, and higher than the values measured at orifices (77.3 to 90.0 C). CO2 and homologs of straight chain alkanes (C1-C5) were identified in gas samples. Carbon isotope values of alkanes increase with carbon numbers. The C-13 fractionation between CO2 and dissolved inorganic carbon suggests they are out of carbon isotope equilibrium. The hypothesis regarding the formation of carbon-bearing compounds in SVHS may involve two processes: 1) Under high heat flow conditions which are caused by regional faulting and crustal extension, original high molecular weight organic compounds (kerogens) in clay-rich rocks decomposed to generate methane and other alkane homologs. 2) The SVHS area is associated with outflow structures, and distant from the heat source. Anaerobic oxidation of methane (AOM) with sulfate at shallow depth (< 90 C) is suggested as being responsible for the generation of CO2 in SVHS.

Fu, Qi↗

A new non-eddy viscosity subgrid-scale model and its application to channel flow

To date, most large-eddy simulations (LES) have been carried out with eddy viscosity subgrid scale (SGS) models, with only a few exceptions that used the mixed model. Even though the assumptions behind Smagorinsky's model are rather stringent, it has been applied successfully to a variety of turbulent flows. This success is attributed to the ability of eddy viscosity models to drain energy from large scales, thus simulating the dissipative nature of turbulence. Most SGS models are absolutely dissipative, i.e. they remove energy from the large scales at every instant. However, SGS stresses may transfer energy back to the large scales intermittently; this reverse transfer or backscatter is especially important in geophysical flows and in transition. In a fully developed channel flow, there is reverse flow of energy from small to large scales near the walls, but eddy viscosity models are unable to account for this important feature. The dynamic localization eddy viscosity model of Ghosal et al. (1995) allows backscatter by co-evolving an auxiliary equation for the SGS energy; however, the computational cost is considerably larger than for conventional SGS models (Cabot 1994). In this report, a new non-eddy viscosity model based on local approximation of total quantities in terms of filtered ones is introduced; the scale similarity model of Bardina (1983) is a special case of this model. This procedure does not require the assumption of homogeneity, permits backscatter of energy from small to large scales, and is readily implemented in finite difference codes. The results of applying the proposed model to second order finite volume simulation of plane channel flow at high Reynolds numbers (Re(sub b) = 38,000) is described in this report. Greater emphasis is placed on the high Reynolds number flow since it provides a more rigorous test of the SGS model and its potential application. The results are compared to ones produced by the conventional and dynamic Smagorinsky models and the spectral LES of Piomelli (1993).

Shah, K. B.↗

Geophysical and geochemical evolution of the lunar magma ocean

There is increasing evidence that at least the outer few hundred kilometers of the moon were melted immediately following accretion. This paper studies the evolution of this lunar magma ocean. The long time scale for solidification leads to the inference that the plagioclase-rich (ANT) lunar crust began forming, perhaps preceded by local accumulations termed 'rockbergs', at the very beginning of the magma ocean epoch. In this view the cooling and solidification of the magma ocean was primarily controlled by the rate at which heat could be conducted across the floating ANT crust. Thus the thickness of the crust was the factor controlling the lunar solidification time. Heat arising from enthalpy of crystallization was transported in the magma by convection. Mixing length theory is used to deduce the principal flow velocity (typically several cm/s) during convection. The magma ocean is deduced to have been turbulent down to a characteristic length scale of the order of 100 m, and to have overturned on a time scale of the order of 1 yr for most of the magma ocean epoch.

Herbert, F.↗

Grad E x B effects on heavy ions in the magnetosphere

Following a theory briefing on the currents in a plasma of mixed species caused by the motion of charged particles, the paper presents a report on the observations of regions of the magnetosphere in which significant values of grad E (E being the electric field) can be inferred from measurements of E made on board the IMP 6 satellite using two pairs of long (91.5 m and 45.7 m) unfurlable antenna sensors. Electric fields were measured by applying double floating probe techniques to the antenna sensors, and grad E values of up to 1.4/1000 emu were inferred from the fluctuations in E along the orbit. The critical values of grad E for various ions, in a range of magnetic fields are compared, and the difference in the behavior of Ba+ ions which cause Ba+ currents in the subcritical and supercritical regions is discussed. The results show that the electric currents flowing in the E x B direction may cause secondary polarization fields on the barium cloud. The possible significance of these effects to natural geophysical phenomena is also pointed out.

Cole, K. D.↗