A note on the performance of the multiply-upstream semi-Lagrangian advection schemes for one-dimensional nonlinear momentum conservation equation

Summary Two-time-level multiply-upstream semi-Lagrangian schemes were examined in the case of the self-advecting, one-dimensional nonlinear momentum conservation equation. The shock formation process was analyzed. It is pointed out that the shocks cannot be created in the truncated systems satisfying the Pudykiewicz, Benoit and Staniforth criterion.The numerical integrations were restricted to 12 h. It was shown that, at least in the sub-CFL range, increased complexity of the scheme can compensate reduced horizontal resolution. A considerable sensitivity of the schemes with respect to the time step was detected. In the super-CFL mode, several windows on various time scales were found within which the Pudykiewicz, Benoit and Staniforth criterion was satisfied. The time step of 1.44 times the maximum time step allowed by the CFL criterion was used in the semi-Lagrangian runs.The super-CFL, semi-Lagrangian solutions were diverging progressively from the sub-CFL ones as the forecasts advanced. This was also reflected in the energy spectra.Unacceptably large energy losses were encountered in the super-CFL, semi-Lagrangian runs. Most of these losses could be explained by the reduced mean wind speed, i.e., the amplitude of the zero wavenumber wave. At the same time, the energy content in the shorter waves increased. In a more complex model, such a situation would resemble a loss of zonal, and an increase of transient eddy kinetic energy.A trajectory error measure was defined as the maximum absolute value of the distance between the actual arriving point of the particle originating at the estimated departure point, and the grid point assumed to be the arrival point in the semi-Lagrangian procedure. In contrast to the sub-CFL regime, this measure could reach a considerable fraction of the grid distance in the computations with the super-CFL time steps.In the physical system considered, the trajectories are determined only by the velocities at the departure points. With the semi-Lagrangian schemes the distances traveled by the particles are estimated on the basis of the velocities at the points downstream with respect to the departure points. Thus, unless the solution is smooth (in space and time) on the scales of the extrapolation distances/times, the upstream extrapolation does not promise the convergence of the solution.With 16 Figures     

Pressure-temperature and evolution of fluid compositions of Al2SiO5-bearing rocks,Mica Creek,B.C., in light of fluid inclusion data and mineral equilibria

Metamorphosed pelitic rocks from Mica Creek, British Columbia contain sillimanite, kyanite with minor fibrolite and andalusite-bearing quartz pods. Mineral equilibria were used to infer peak P-T conditions and fluid compositions in equilibrium with the solid phases. Fluid inclusions in three schist samples appear to be good indicators of conditions affecting those rocks during and after peak metamorphic conditions. In samples from two localities, fluid inclusions from schist and quartz-rich segregations have densities appropriate to the peak metamorphic conditions. The observed compositions for these fluids (low salinity with 12 mole % dissolved CO₂) agree with calculated values of 0.84 to 0.85, based upon paragonite-quartz-albite-Al₂SiO₅ equilibria. The fluids unmixed as the schists were uplifted and cooled; fluid inclusions trapped during this stage outline a solvus in the CO₂-H₂O-NaCl system. A later influx of fluids containing CH₄ and N₂ accompanied formation of andalusite-bearing plagioclaserich segregations. The restricted association of andalusite-bearing pods and low density fluids suggest a localized but pervasive fluid influx during uplift. Preservation of high density fluid inclusions during uplift and erosion, coupled with evidence for unmixing of H₂O- and CO₂-rich fluids on the solvus, provide constraints on the P-T uplift path.     

The Gagarka gold deposit in the central Urals, Russia

The Gagarka gold deposit was formed in two stages. The gold-telluride ore of the main early stage was formed ～260 Ma ago synchronously with Permian collision, which was accompanied by retrograde metamorphism with mobilization of Au and Te from geochemically similar massive sulfide lodes in the rift zone. The Au-bearing argillic metasomatic rocks of the late stage presumably Mesozoic in age are distinguished by specific geochemistry and locally superposed on the ore related to the early stage. The upper part of the metasomatic column consists of quartz-kaolinite rock, which is confused in many cases with products of Mesozoic-Cenozoic weathering and because of this is not perceived as a guide for hidden Au-bearing argillic alteration, whose resource potential remains underestimated in the Urals.     

Copper, lead and cadmium concentrations in surface water, sediment and fish, C. Carpio, samples from Lake Naivasha: effect of recent anthropogenic activities

Following recent concerns of chemical pollution around Lake Naivasha, especially originating from recent agricultural activities in the catchment, samples of water, sediments, and fish Common carp (Cyprinus carpio) were collected from the Hippo Point, Kasarani, Mouth of Malewa River, Mouth of Karati River, Crescent Island, Sher Karuturi Discharge outlet and Oserian Bay for analysis of Cu, Cd and Pb by FAAS. The mean heavy metal levels ranged from 5.12?C58.11 (Pb), 1.06?C1.73 (Cd), and <0.03?C2.29 (Cu) mg/kg wet weight in C. carpio muscle, <100?C179.83 (Pb), <10.00?C10.06 (Cd) and <30.00?C32.33 (Cu) ??g/L in surface water, and 17.11?C53.07 (Pb), 1.18?C5.58 (Cd) and 3.00?C8.48 (Cu) mg/kg dry weight in sediment and showed a wide variation within and between samples with relatively high concentrations in sediments and fish muscle tissues. The results indicate that Lake Naivasha, in some parts, is polluted with these heavy metals of which relatively higher concentrations are found at the discharge outlets near Sher Karuturi and Oserian Bay. This indicates possible contribution from surrounding horticultural/floricultural activities and the Mouths of the Rivers Malewa and Karati which flow from it??s upper catchment.     

RECONSTRUCTING THE SOLAR CORONAL MAGNETIC FIELD AS A FORCE-FREE MAGNETIC FIELD

We present some preliminary results on different mathematical problems encountered in attempts to reconstruct the coronal magnetic field, assumed to be in a force-free state, from its values in the photosphere. We discuss the formulations associated with these problems, and some new numerical methods that can be used to get their approximate solutions. Both the linear constant- and the nonlinear cases are considered. We also discuss the possible use of dynamical 3D MHD codes to construct approximate solutions of the equilibrium force-free equations, which are needed for testing numerical extrapolation schemes.     

An Early Investigation Of The Striated Tail Of Comet Hale-Bopp (C/1995 O1)

The Sekanina-Farrell particle fragmentation model for the striated tails of dust comets is successfully applied to two images of comet Hale-Bopp to study the motions of 12 striae in a time span of March 12–15, 1997. There is evidence for recurring outbursts with a periodicity of 11^h21^m, consistent with results based on analysis of dust jets. The ejecta in all the striae appear to have been released from one source on the nucleus between the end of January and the second half of February 1997, some 60 to 40 days before perihelion. The parent particles were subjected to a radiation pressure acceleration of β_p ≃ 0.55 and their fragmentation lifetimes in 11 of the 12 striae were practically constant and equal to 13–15 days, when normalized to 1 AU from the Sun. Brief analysis of Watanabe et al.'s measurements of striae on their images from March 5–9, 1997 shows even shorter fragmentation lifetimes for the parent particles, mostly about 7–11 days at1 AU. This revised version was published online in July 2006 with corrections to the Cover Date.     

Variation of mineral composition,fabric and oxygen fugacity from massive to foliated eclogites during exhumation of subducted ocean crust in the North Qilian suture zone,NW China

Eclogites from the North Qilian suture zone are high‐pressure low‐temperature metamorphic rocks of ocean crust protolith, and occur in both massive and foliated varieties as individual blocks of tens to hundreds of metres in size. The massive type is weakly deformed and shows granoblastic texture characterized by a coarse‐grained peak mineral assemblage of Grt¹ + Omp¹ + Ph + Rt ± Lws (or retrograde Cz). In contrast, the foliated type is strongly deformed and shows a fine‐grained retrograde mineral assemblage of Grt² + Omp² + Cz + Gln + Ph. Both total FeO and aegirine contents in omphacite, as well as X_Fe[=Fe³⁺/(Fe³⁺ + Al^VI)] in clinozoisite/epidote, increase significantly from massive to foliated eclogites. Lattice preferred orientation (LPO) of omphacite, determined by electron back‐scatter diffraction analysis, is characterized by weak and strong SL‐type fabrics for massive and foliated eclogites, respectively. Clinozoisite/epidote also developed SL‐type fabric, but different from the LPOs of omphacite in <010> and <001> axes, owing to their opposite crystallographic long and short axis definitions. The transition of deformation mechanism from dislocation creep to diffusive mass transfer (DMT) creep in omphacite and the concomitant retrograde metamorphism both are efficiently facilitated when the original coarse‐grained Omp¹ + Grt¹ + Lws assemblage is dynamically recrystallized and retrogressed into the fine‐grained Fe³⁺‐rich assemblage of Omp² + Grt² + Cz + Gln. The DMT process with concomitant anisotropic growth assisted by fluids is considered to be an important deformation mechanism for most minerals in the foliated eclogite. P–T estimates yielded 2.3–2.6 GPa and 485?510 °C for the massive eclogite and 1.8–2.2 GPa and 450?480 °C for the foliated eclogite. The significant increase in total Fe and Fe³⁺ contents in omphacite and clinozoisite/epidote from massive to foliated eclogite suggests changes in mineral compositions accompanied by an increase in oxygen fugacity during ductile deformation associated with exhumation. The LPO transition of omphacite, clinozoisite and rutile from weak SL‐type in massive eclogites to strong SL‐type in foliated eclogites is interpreted to represent the increment of shear strain during exhumation along the ‘subduction channel’.     

High-resolution profiles of iron, manganese, cobalt, cadmium, copper and zinc in the pore water of estuarine sediment

The remobilization of iron, manganese, cobalt, cadmium, copper and zinc in the pore water of estuarine sediment cores at Yingkou was assessed using diffusive equilibrium in thin films and diffusive gradients in thin films techniques. A relatively anoxic system (+33.7 to ?224.1 mV) in the sediment cores might cause the reductive release of iron, manganese and cobalt into pore water from the estuarine sediment. High-average concentrations of iron (47.85 μg ml^?1) and manganese (3.81 μg ml^?1) were observed using diffusive equilibrium in thin films on the sediment core, but the concentration of cobalt (18.02 ng ml^?1) was relatively low. A strong correlation between iron and cobalt was observed based on the vertical profiles of the metals. Manganese and iron were more readily released from the solid phase to the solution. The peak cobalt, copper and zinc concentrations were observed in the upper layer (2–4 cm) measured using diffusive gradients in thin films. However, the peak iron, manganese and cobalt concentrations were located in the deeper layer (≥7 cm). In addition, the concentration profiles measured using diffusive gradients in thin films of cobalt, copper and zinc were independent of the iron, manganese and cobalt distribution with respect to depth.