Flow at high Reynolds numbers through anisotropic porous media

An approximate expression is developed for the relationship between the hydraulic gradient (J), the specific discharge (q) and fluid and porous matrix properties in the case of saturated, steady and uniform (macroscopic) flow of a Newtonian liquid at high Reynolds numbers through a homogeneous anisotropic porous medium:

$\text{g}\text{J}\text{=(v}\text{w}{}^{\mathrm{(2)}}\text{+}\text{B}{}^{\mathrm{(4)}}\text{:}\text{qq}\text{/q+}\text{C}{}^{\mathrm{(3)}}\text{·}\text{q}\text{)·}\text{q}$

In this expression, the tensors w⁽²⁾, B⁽⁴⁾ and C⁽³⁾ denote properties of the solid matrix only. The tensors W⁽²⁾, and C⁽³⁾ are symmetrical; the tensor B⁽⁴⁾ is symmetrical only in the first and last pairs of indices. It seems that no mathematical expression with a finite number of parameters exists, which can serve as a universal exact expression for the sought relationship between J and q.     

A new look at the Rockall region, offshore Ireland

A 700 km wide-angle reflection/refraction profile carried out in the central North Atlantic west of Ireland crossed the Erris Trough, Rockall Trough and Rockall Bank, and terminated in the western Hatton-Rockall Basin. The results reveal the presence of a number of sedimentary basins separated by basement highs. The Rockall Trough, with a sedimentary pile up to 5 km thick, is underlain by thinned continental crust 8–10 km thick. Some major fault block structures are identified, especially on the eastern margin of the Rockall Trough and in the adjacent Erris Trough. The Hatton-Rockall Basin is underlain by westward-thinning continental crust 22–10 km thick. Sedimentary strata are up to 5 km thick. The strata in the Rockall Trough and Hatton-Rockall Basin probably range in age from Late Palaeozoic to Cenozoic. However, the basins have different sedimentation histories and differ in structural style. The geometry of the crust and sediments suggests that the Rockall Trough originated by pure shear crustal stretching, associated with rift deposits and Cenozoic thermal sag strata. In contrast, the development of the Erris Trough, located on unthinned continental crust, was facilitated by shallow, brittle extension with little deep crustal attenuation. A two-layered crust occurs throughout the region. The lower crustal velocity in the Hatton-Rockall Basin is higher than that in the Rockall Trough. The velocity structure shows no indication of crustal underplating by upper mantle material in the region.     

Shoaling of sixth-order Stokes waves on a current

Jonsson and Arneborg (Jonsson, I.G., Arneborg, L., 1995. Energy properties and shoaling of higher-order Stokes waves on a current. Ocean Engng 22, 819-857.) combined energy flux and set-down to make shoaling predictions for fourth-order Stokes waves with and without a net volume flux. With basis in their expressions, sixth-order expressions are derived and combined to make shoaling predictions correct to sixth order with an arbitrary net volume flux. The new sixth-order results are compared with the fourth-order results and the practically exact results obtained by Sobey and Bando (Sobey R.J., Bando K., 1991. Variations on higher-order shoaling. J. Waterway, Port, Coastal Ocean Engng ASCE 117, 348-368) with a Fourier 18 model. The effects of introducing sixth-order theory rather than the fourth-order theory in shoaling calculations are in general found to be small. As expected the deviations increase with increasing wave-steepness, decreasing depth and opposing currents. Also as expected, the results obtained with the sixth-order expressions improve the results obtained with the fourth-order expressions when compared to the results of Sobey and Bando. As novelties, some considerations regarding the consistency of odd- and even-order shoaling calculations, and the magnitude of the bottom slope, are presented. Furthermore a comparison between the wave-induced current and the total current is given.     

Rb-Sr geochronology in favour of polymetamorphism in the Pan African Damara belt of Namibia (South West Africa)

New Rb-Sr whole rock age data are reported from two metasedimentary sequences of the Damara Supergroup in the central Pan African Damara belt of Namibia (South West Africa).Calc-granofels rocks of the Karibib Formation (Swakop Group) near Usakos are dated at 665±34 Ma (⁸⁷Rb=1.39×10^–11 a^–1) which is interpreted as reflecting a high-grade metamorphic event predating widespread granite intrusion.Pyroxene-bearing feldspathic gneisses of the Khan Formation (Nosib Group) from the Khan-Swakop River area east of Swakopmund show incomplete homogenization at 474±16 Ma. In view of similar ages obtained on the nearby Rössing alaskite granite and on biotites from a variety of rock assemblages this age is interpreted as reflecting a second Damaran metamorphic event rather than a specific stage in a long cooling history as previously thought.It is probable that the new ages characterize two distinct Pan-African tectono-metamorphic events previously named Katangan and Damaran episodes respectively (Clifford, 1967). The younger of these has affected large areas of south western Africa both within orogenic zones and on the neighbouring Kalahari Craton and may reflect crustal processes of sub-continental proportion during the closing stages of the Pan-African tectogenesis.

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Zusammenfassung Neue Rb-Sr-Gesamtgesteins-Isochronenalter von zwei sedimentären Abfolgen der spätpräkambrischen Damara-Supergruppe in der Zentralzone des Pan-Afrikanischen Damara-Orogens von Namibia (Südwest-Afrika) deuten auf eine mehrphasige metamorphe Geschichte hin.Kalk-Granofels-Gesteine der Karibib-Formation (Swakop-Gruppe) südöstlich von Usakos ergaben ein Alter von 665±34 M. J. (⁸⁷Rb=1,39×10^–11 a^–1) und wir interpretieren dieses Alter als das Resultat isotoper Homogenisierung während einer intensiven Regionalmetamorphose, die vor dem Eindringen weitverbreiteter Granite stattfand.Pyroxenführende und feldspathaltige Gneise der Khan-Formation (Nosib-Gruppe) aus dem Gebiet der Khan- und Swakop-Flüsse östlich von Swakopmund zeigen unvollständige Homogenisierung ihrer Sr-Isotope um 474±16 M. J. In Anbetracht ähnlicher Alter für den benachbarten Rössing-Alaskitgranit und für Biotite verschiedener Gesteinstypen aus dem gesamten Zentralbereich des Orogens interpretieren wir obiges Alter eher als den Höhepunkt einer zweiten Regionalmetamorphose als ein bestimmtes Stadium in der post-orogenen Abkühlungsgeschichte.Es ist wahrscheinlich, daß unsere Altersbestimmungen zwei deutlich voneinander getrennte pan-afrikanische tektono-metamorphe Phasen charakterisieren, vor allem wenn man sie in Zusammenhang mit publizierten Daten betrachtet, und wir nehmen an, daß diese den vonClifford (1967) postulierten Katanga- und Damara-Episoden entsprechen. Die jüngere dieser Episoden hat nicht nur die pan-afrikanischen orogenen Bereiche im südwestlichen Afrika, sondern auch weite Teile des Kalahari-Kratons erfaßt und mag auf tektogenetische Prozesse von nahezu kontinentalen Ausmaßen in und unter der Kruste im frühen Paläozoikum zurückzuführen sein.

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Résumé Deux séquences métasédimentaires du supergroupe du Damara ont été datées par la méthode Rb/Sr.Des gneiss calciques («granofels») de la formation de Karibib (groupe de Swakop), récoltés près d'Usakos ont été datés à 665±34 Ma (avec⁸⁷Rb=1.39× 10^–11 a^–1). Cet âge est interprété comme le résultat d'un événement métamorphique de degré é levé antérieur à la mise en place des grandes masses de granite.Des gneiss feldspathiques à pryoxène de la Formation de Khan (Groupe de Nosib), échantillonnés dans la région de la Khan River — Swakop à l'Est de Swakopmund, montrent une homogénéisation isotopique incomplète à 474±16 Ma. Des âges voisins ayant été obtenus pour l'Alaskite de Rössing qui affleure dans la même zone et pour les biotites de différentes roches, cet âge est interprété comme le résultat d'un second métamorphisme damarien plutôt que comme un stade de la longue histoire de refroidissement comme cela avait été imaginé auparavant.Ces nouveaux âges caractériseraient les deux épisodes tectonométamorphiques distincts de l'orogénie Pan-Africaine, qui avaient été appelés respectivement épisode katangien et épisode demarien parClifford (1967). Le plus récent de ces événements a affecté une grande partie de l'Afrique du S.W. aussi bien dans les zones orogéniques que dans le craton voisin du Kalahari; il peut refléter une évolution crustale d'échelle subcontinentale se produisant pendant les derniers stades du tectogène Pan-Africain.

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Rb/Sr - , - ; , .- , , 665±34 (⁸⁷Rb=1,39 10^–1a^–1); , . , , , , 474 ± 16 . - ; , , . , - - , , . , 1967 , . - - , ; , , .

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Contribution No. 27 of the South African Geodynamics Project, presented at the 9th Colloquium on African Geology, Göttingen, April 1977.     

On wave motions in a tropical spectral experiment

An attempt is made to use the barotropic vorticity equation in spectral form in order to study barotropic instability when the basic current has east-west quasi-stationary asymmetries on the scale of long waves. This is done by expressing the spectral equations in three different ways. In the first experiment a 9-component system is integrated and the long waves are allowed to propagate freely. In the second experiment the long waves are constrained to propagate slowly and in the third experiment, they are removed altogether.The motivation behind the present investigation is due to observations made in the motion fields of the tropics. These are characterized by quasi-stationary long waves and very energetically active and propagating short waves.The presence of quasi-stationary long waves seems to enhance the energy exchanges between the short waves and the mean zonal current and also allow for larger energy values for the short waves. Long term integration (90 days) shows a 6-day mode in thev time spectra at latitude 10°N and a 15-day mode in theu time spectra at individual grid points in the equatorial latitudes. Any possible connection between this peak and the observed peak of 15 days in the completely different physics of Kelvin waves is left as a conjecture.     

The coprecipitation of strontium,magnesium, sodium,potassium and chloride ions with gypsum. An experimental study

The coprecipitation of Sr²⁺, Mg²⁺, Na⁺, K⁺ and Cl^? into gypsum was studied as a function of temperature, brine concentration and growth rate. The concentrations of the studied cations in the gypsum increase with growth rate (kinetic effect), with a tendency to reach a limiting value at high growth rates. The partition coefficients of Sr tend to increase with brine concentration and decrease with temperature. The partition coefficients of the other cations also decrease with temperature but depend only very slightly on brine concentration. The concentrations of coprecipitated chloride are negligibly small.The coprecipitation behavior is explained in terms of the relation between the rate of desorption of the coprecipitating ions from the surface of the growing crystal, and the rate of growth. The studied cations may substitute for Ca²⁺ in its normal lattice sites and/or reside in interstitial positions among the structural water molecules. The relative amount of foreign cations occupying interstitial positions increases with increasing growth rate.The elucidation of the behavior of coprecipitated ions in gypsum given here forms a basis for the utilization of these ions as geochemical indicators for the environment of deposition of gypsum. These indicators may help in reconstructing important parameters such as temperature, brine concentration and growth rate.     

Calcmylonites and solution transfer in a Devonian reef at Warstein,Germany

Massive limestone complexes of Late Palaeozoic age are scattered across the allochthonous foreland of the Hercynides in Germany. One of these complexes is situated at Warstein. Stratigraphic facies studies have represented the Warstein complex as a reef in a coastal shelf. Our study emphasizes that at least part of the reef consists of a pile of calcmylonites.The calcmylonites have a strong foliation (S_m) and lineation (L_m) and a structural asymmetry indicating non-coaxial deformation. X-ray textures and calcite microstructures show that the mylonitization involved intracrystalline deformation and dynamic recrystallization. These processes competed with solution transfer, as the mylonites are corroded at S_m-parallel stylolites and contain carbonate veins. Cathodoluminescopy shows that some veins are parallel to S_m and have been recrystallized, whereas others are normal to S_m and retain a fibrous crackseal microstructure. The latter type created limestones showing a pair of preferred grain boundary orientations; one normal to S_m, one in S_m. This orthogonal boundary fabric is distinct from crystalplastic fabrics: the latter show only one preferred grain boundary orientation (in S_m).

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Zusammenfassung Massenkalkkomplexe spätpaläozoischen Alters liegen verstreut über das allochthone Vorland des Variszischen Gebirges in Deutschland. Einer dieser Komplexe liegt bei Warstein. Stratigraphische Faziesstudien haben den Warsteiner Komplex als ein Riff in einem küstennahen Schelf dargestellt. Die vorliegende Arbeit betont, daß wenigstens ein Teil des Riffes aus einer Stapelung von Kalkmyloniten besteht.Die Kalkmylonite haben eine starke Foliation (S_m) und Lineation (L_m), und eine strukturelle Asymmetrie die auf nicht-koaxiale Verformung hinweist. Röntgentexturen und Calcitmikrostrukturen zeigen, daß die Mylonitisierung intrakristalline Verformung und dynamische Rekristallisation beinhaltet. Diese Prozesse müssen mit Lösungstransport konkurriert haben, da die Mylonite an S_m-parallelen Styloliten korrodiert sind und Karbonatgänge erhalten. Kathodolumineskopie zeigt, daß einige Gänge (parallel zu S_m) rekristallisiert sind, während andere (senkrecht zu S_m) eine faserige crack-seal Mikro-Struktur enthalten. Der letzte Typ ist verbunden mit Konformgefügen. Diese unterscheiden sich von kristallplastischen Kornformgefügen, da sie eine zweite bevorzugte Korngrenzorientierung aufweisen, die senkrecht zur ersten (in S_m) einfällt.

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Résumé Les complexes de calcaires massifs de l'Âge paléozoîque supérieure sont repandus sur l'avantpays allochthone des Hercynides en Allemagne. Un de ces complexes est situé à Warstein. Les Études de faciès stratigraphiques ont répresenté le complexe à Warstein comme un Récif littoral. Notre étude montre que au moins partie de ce «Récif» consiste en un empilement des calcmylonites.Les calcmylonites ont une foliation (S_m) et linéation (L_m) fort, et une asymmetrie structurale indiquant de la déformation non-coaxiale. Les textures röntgenographiques et les microstructures calcitiques montrent que la mylonitization était incluse de déformation intracristalline et récristallisation dynamique. Ces processus auront été en compétition avec dissolution-cristallization («solution transfer»), car les mylonites sont corrodées aux stylolites parallel à S_m et contient des veines carbonatiques. La cathodoluminescopie montre que quelques veines (parallel à S_m) sont récristallisées, pendant que les autres (perpendiculaire à S_m) ont retenu une microstructure fibreuse («crack-seal»). Le dernier type est lié avec des fabriques de forme des grains. Ils se sont distingués des fabriques de plasticité cristalline par la présence d'une deuxième orientation préférentielle des bordures des grains, perpendiculaire à la première (dans S_m).

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. Warstein'a. , . , , , »« . (S_m) (L_m), , . , - , . , .. , S_m, . , , S_m, , , S_m, = »crack-seal«. : , S_m.

     

A Spatial Filtering Specification for an Auto-negative Binomial Model of Anopheles arabiensis Aquatic Habitats

This research accounts for spatial autocorrelation by including latent map pattern components as predictor variables in a malaria mosquito aquatic habitat model specification. The data used to derive the model was from a digitized grid-based algorithm, generated in an ArcInfo database, using QuickBird visible and near-infrared (NIR) data. The Feature Extraction (FX) Module in ENVI 4.4^® was used to categorize individual pixels of field sampled aquatic habitats into separate spectral classes, convert remotely sensed raster layers to vector coverages, and classify output layers to vector format as ESRI shapefiles. These data were used to construct a geographic weights matrix for evaluation of field and remote sampled covariates of Anopheles arabiensis aquatic habitats, a major vector of malaria in East Africa. The principal finding is that synthetic map pattern variables, which are eigenvectors computed for a geographic weights matrix, furnish an alternative way of capturing spatial dependency effects in the mean response term of a regression model. The spatial autocorrelation components suggest the presence of roughly 11 to 28% redundant information in the aquatic habitat larval count samples. The presence of redundant information in the models suggest that the sampling configuration of the An. arabiensis aquatic habitats, in the study sites, may cause field and remote observations of aquatic habitats to be dependent, rather than independent, moving data analysis away from the classical statistical independence model. A Poisson regression model, with a non-constant, gamma-distributed mean, can decompose field and remote sampled An. arabiensis data into positive and negative spatial autocorrelation eigenvectors, which can assess the precision of a malaria mosquito aquatic habitat map and the significance of all factors associated with larval abundance and distribution in a riceland agroecosystem.     

Multisite campaign on the open cluster M67 – II. Evidence for solar-like oscillations in red giant stars

Measuring solar-like oscillations in an ensemble of stars in a cluster, holds promise for testing stellar structure and evolution more stringently than just fitting parameters to single field stars. The most-ambitious attempt to pursue these prospects was by Gilliland et al. who targeted 11 turn-off stars in the open cluster M67 (NGC 2682), but the oscillation amplitudes were too small (<20 μmag) to obtain unambiguous detections. Like Gilliland et al. we also aim at detecting solar-like oscillations in M67, but we target red giant stars with expected amplitudes in the range 50–  500 μmag  and periods of 1 to 8 h. We analyse our recently published photometry measurements, obtained during a six-week multisite campaign using nine telescopes around the world. The observations are compared with simulations and with estimated properties of the stellar oscillations. Noise levels in the Fourier spectra as low as  27 μmag  are obtained for single sites, while the combined data reach  19 μmag  , making this the best photometric time series of an ensemble of red giant stars. These data enable us to make the first test of the scaling relations (used to estimate frequency and amplitude) with an homogeneous ensemble of stars. The detected excess power is consistent with the expected signal from stellar oscillations, both in terms of its frequency range and amplitude. However, our results are limited by apparent high levels of non-white noise, which cannot be clearly separated from the stellar signal.