On the REYNOLDS Stresses in Mean‒Field Hydrodynamics I. Incompressible Homogeneous Isotropic Turbulence

We consider an incompressible fluid undergoing turbulent motions. Using the methods of mean-field electrodynamics the relations between the REYNOLDS stresses and the mean velocity field are deduced in linear approximation. The homogeneous isotropic case is treated in more detail and we show that the effects can be described by a turbulent viscosity which proved to be positive in any case.     

Remark on the Mean Energy of the Fluctuating Magnetic Field in Mean-field Magnetohydrodynamics

A relation between the mean square of the fluctuating magnetic field, B′ , and the square of the mean magnetic field, B̄ , is derived for the case of homogeneous isotropic turbulence. The second order correlations approximation is used under the assumption that the space and time scales L̄ and T̄ of the mean field are large compared with the scales L and T of the fluctuations. BOCHNER 's theorem manifests itself as a guarantee for the ratio B̄′²|B̄² to be non-negative.     

Simple nonlinear recursions and the mean-field concept

Some questions concerning the formation of mean-field theories are analyzed by a consideration of simple nonlinear recursions. The results suggest that a general closure scheme does not exist, rather there is a great variety of closures, each of the valid in only a certain interval of the characteristic parameter. Furthermore, questions connected with the appearance of random behaviour in these deterministic systems and the modelling of random reversals are discussed.     

An improved methodology to measure flag performance for the shipping industry

The subject of measuring the performance of registries has been a topic of policy discussions in recent years at the regional level due to the recasting of the European Union (EU) port state control (PSC) directive which introduces incentives for flags which perform better. Since the current method used in the EU region entails some shortcomings, it has therefore been the subject of substantial scrutiny. Furthermore, the International Maritime Organization (IMO) developed a set of performance indicators which however lacks the ability to measure compliance as set out in one of its strategic directions towards fostering global compliance. This article develops a methodology to measure flag state performance which can be applied on the regional or global level and to other areas of legislative interest (e.g. recognized organizations, Document of Compliance Companies). The proposed methodology overcomes some of the shortcomings of the present method and presents a more refined, less biased approach of measuring performance. To demonstrate its usefulness, it is applied to a sample of 207,821 observations for a 3-year time frame and compared to the current method.     

Isotopic age determinations of crystalline rocks of the Upper Harz Mountains,Germany

Dating of crystalline rocks occurring in the Upper Harz Mountains was carried out by means of U-Pb isotope investigations on zircons and sphene as well as by Rb-Sr isotope measurements on whole-rock samples and biotites.U-Pb data of euhedral and rounded, detrital zircons of the allochthonous block of the Ecker gneiss point to an age (upper intercept) of the source area of the predominantly metasedimentary rocks of about 1.6 Ga or older. The lower intercept indicates a possible metamorphic event at ca. 560 Ma in the Ecker gneiss or in the source rock of the zircons of this complex. The concordant data point of a sphene fraction from a metavolcanic sample documents contact metamorphic influence on the Ecker gneiss by the Variscan intrusions of the Upper Harz Mountains.Emplacement of the intrusions of the Harzburg gabbronorite and the Brocken and Oker granites occurred contemporaneously 293–297 Ma ago within the analytical error limits. This points to a common geotectonic cause of the ascent of the magmas. Uplift of the Ecker gneiss block, now squeezed in between Harzburg gabbronorite and Brocken granite, was connected to these processes.The mineral ages of the plutonites are close to the intrusion ages indicating fast cooling processes in shallow crustal levels.

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Zusammenfassung Eine altersmäßige Einstufung der im Oberharz vorkommenden kristallinen Gesteine wurde durch U-Pb-Isotopenuntersuchungen an Zirkonen und Titanit sowie Rb-Sr-Isotopenmessungen an Gesamtgesteinsproben und Biotiten durchgeführt.U-Pb-Daten von idiomorphen und runden, detritischen Zirkonen der allochthonen Eckergneis-Scholle deuten auf ein Alter des Ursprungsgebietes der weitgehend metasedimentären Gesteine von etwa 1. 6 Ga oder älter hin und sie weisen ferner auf ein mögliches Metamorphose-Ereignis vor rund 560 Ma im Eckergneis oder im Liefergestein der Zirkone des Eckergneises hin. Der konkordante Datenpunkt bei ca. 295 Ma einer Titanit-Fraktion aus einer Metavulkanit-Probe dokumentiert die kontaktmetamorphe Beeinflussung des Eckergneises durch die variskischen Intrusionen des Oberharzes.Die Platznahme der Intrusionen der Gesteine des Harzburger Gabbronorit-Massivs sowie des Brokken- und Oker-Granits erfolgten innerhalb der analytischen Fehlergrenzen zeitgleich vor 293–295 Ma. Dies deutet auf eine gemeinsame geotektonische Ursache des Aufdringens der Magmen. Damit verbunden war der Aufstieg der Eckergneis-Scholle, die jetzt zwischen Harzburger Gabbronorit und Brockengranit »eingeklemmt« ist.Mineralalter der Plutonite liegen nahe bei den Intrusionsaltern und weisen auf rasche Abkühlungsvorgänge in seichtem Krustenniveau hin.

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Résumé Des mesures d'âge ont été effectuées sur des roches cristallines de l'Oberharz par les méthodes de l'U-Pb sur zircon et sphène et du Rb-Sr sur roches totales et sur biotites. La méthode U-Pb, appliquée aux zircons idiomorphes et détritiques arrondis de l'écaille allochtone des gneiss d'Ecker, fournit un âge (intersection supérieure) d'environ 1,6 Ga au moins pour la source des matériaux surtout métasédimentaires. L'intersection inférieure indique la possibilité d'un événement métamorphique à ± 560 Ma soit dans les gneiss d'Ecker, soit dans les roches-sources de leurs zircons. Un résultat concordant à ± 295 Ma fourni par le sphène d'une métavolcanite enregistre l'action du métamorphisme de contact engendré dans les gneiss d'Ecker par les intrusions varisques.La mise en place des intrusions du massif gabbronoritique du Harzburg et celle des granite de Brocken et d'Ocker ont été contemporaines: âges de 293 à 297 Ma, compris dans l'intervalle d'approximation des mesures. Ce résultat est en faveur d'une même cause géotectonique pour l'ascension de ces magmas. C'est en relation avec ce processus que s'est produit le soulèvement de l'écaillé des gneiss d'Ecker, actuellement coincée entre le gabbro du Harzburg et le granite de Brocken.Les âges minéraux des plutons sont voisins des âges d'intrusion, ce qui indique un refroidissement rapide dans un niveau crustal peu profond.

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The role of ternary projections in colour displays for geochemical maps and in economic mineralogy and petrology

Ternary (triangular) diagrams show the compositional variation of three end-members, recalculated to 100%, and represent the projection into two dimensions of three or more components (since an end-member may represent the sum of more than one original component), and hence multiple space. During the present century they have been of particular importance in chemistry, the earth sciences, colour-mixing and the studies of colour that underlie the development of geochemical colour maps. Such concepts can be traced back to Newton's Opticks although he did not use an explicit ternary theory of colour mixing. Development of the trichromatic theory of colour deficiency began with Mariotte in the 17th century and was definitively established by Maxwell in the 1850s. These colour theorems underlie the development in recent years of the colour maps now in widespread use in geochemistry. The progress of regional geochemical mapping in the British Isles has gone hand-in-hand with the development of computer software and hardware. The use of multi-element colour-combined geochemical maps can be traced from early work at Imperial College by Webb and his co-workers (1964–79) to its later application in the British Geological Survey's Geochemical Atlas series (from 1983 onwards). Between 1955 and 1975 the use of ternary diagrams came to be commonly used in studies of mineralogical composition, including economic minerals, petrology, classification, and phase relationships. In igneous petrology, the quartz–alkali-feldspar–plagioclase-feldspathoid double-triangle has achieved increasing international acceptance. We illustrate these applications with examples pertinent to the Northern Highland Caledonides, with particular emphasis on the lamprophyres and associated rocks. Two distinct multivariate trends of variation are shown to be present which may warrant further investigation to elucidate their bearing on Caledonian mineralisation.     

The role of ternary projections in colour displays for geochemical maps and in economic mineralogy and petrology

Ternary (triangular) diagrams show the compositional variation of three end-members, recalculated to 100%, and represent the projection into two dimensions of three or more components (since an end-member may represent the sum of more than one original component), and hence multiple space. During the present century they have been of particular importance in chemistry, the earth sciences, colour-mixing and the studies of colour that underlie the development of geochemical colour maps. Such concepts can be traced back to Newton's Opticks although he did not use an explicit ternary theory of colour mixing. Development of the trichromatic theory of colour deficiency began with Mariotte in the 17th century and was definitively established by Maxwell in the 1850s. These colour theorems underlie the development in recent years of the colour maps now in widespread use in geochemistry. The progress of regional geochemical mapping in the British Isles has gone hand-in-hand with the development of computer software and hardware. The use of multi-element colour-combined geochemical maps can be traced from early work at Imperial College by Webb and his co-workers (1964–79) to its later application in the British Geological Survey's Geochemical Atlas series (from 1983 onwards). Between 1955 and 1975 the use of ternary diagrams came to be commonly used in studies of mineralogical composition, including economic minerals, petrology, classification, and phase relationships. In igneous petrology, the quartz–alkali-feldspar–plagioclase-feldspathoid double-triangle has achieved increasing international acceptance. We illustrate these applications with examples pertinent to the Northern Highland Caledonides, with particular emphasis on the lamprophyres and associated rocks. Two distinct multivariate trends of variation are shown to be present which may warrant further investigation to elucidate their bearing on Caledonian mineralisation.     

On the turbulent decay of strong magnetic fields and the development of sunspot areas

This paper deals with the conception that two-dimensional turbulence is present in a sunspot where the magnetic field is strong. This conception is based upon the incapacity of even a strong magnetic field to influence an arbitrary two-dimensional turbulence, if the magnetic field is parallel to a constant direction and the motion occurs in planes orthogonal to it. It is, moreover, shown that such a two-dimensional turbulence provides for a turbulent decay of the magnetic field. The decay rate possesses nearly the same dependence on the scales as for three-dimensional turbulence. Finally, the turbulent decay is studied by investigating a simple model and comparing the results with those deduced by Bumba from the observed decay of sunspot groups areas. By means of our conception even a good quantitative agreement is stated.     

Oxygen Utilization and Organic Carbon Remineralization in the Upper Water Column of the Pacific Ocean

As a part of the JGOFS synthesis and modeling project, researchers have been working to synthesize the WOCE/JGOFS/DOE/NOAA global CO₂ survey data to better understand carbon cycling processes in the oceans. Working with international investigators we have compiled a Pacific Ocean data set with over 35,000 unique samples analyzed for at least two carbon species, oxygen, nutrients, chlorofluorocarbon (CFC) tracers, and hydrographic parameters. We use these data here to estimate in-situ oxygen utilization rates (OUR) and organic carbon remineralization rates within the upper water column of the Pacific Ocean. OURs are derived from the observed apparent oxygen utilization (AOU) and the water age estimates based on CFCs in the upper water and natural radiocarbon in deep waters. The rates are generally highest just below the euphotic zone and decrease with depth to values that are much lower and nearly constant in water deeper than 1200 m. OURs ranged from about 0.02–10 μmol kg⁻¹yr⁻¹ in the upper water masses from about 100–1000 m, and averaged = 0.10 μmol kg⁻¹yr⁻¹ in deep waters below 1200 m. The OUR data can be used to directly estimate organic carbon remineralization rates using the C:O Redfield ratio given in Anderson and Sarmiento (1994). When these rates are integrated we obtain an estimate of 5.3 ± 1 Pg C yr⁻¹ for the remineralization of organic carbon in the upper water column of the Pacific Ocean. This revised version was published online in July 2006 with corrections to the Cover Date.