Convergent solutions of the inviscid solar wind equations

Formal solutions of the inviscid solar wind equations as power series in the inverse one seventh power and in the inverse one fifth power of the distance from the sun are shown to be convergent.     

Free convection effects on the oscillatory flow in the Stokes's problem past an infinite porous vertical limiting surface with constant suction — I

An analysis of Rayleigh's problem (also Stokes's problem) for the flow of a viscous fluid (e.g. of a stellar atmosphere) past an impulsively started infinite, vertical porous limiting surface (e.g. of a star) with constant suction, when the free stream velocity oscillates in time about a constant mean, has been carried out. On solving the coupled non-linear equations in approximate way, expressions for the mean velocity, the mean temperature, the mean skin-friction and the mean rate of heat transfer, expressed in terms of Nusselt number, are obtained. The effects of Grashof numberG, Eckert numberE and Prandtl numberP, on these quantities, is discussed for the cases of an externally heating and cooling of the limiting surface, by the free convection currents, and the variations of them are shown graphically.     

Evaluation of Interactions Between Oilfield Chemicals and Reservoir Rocks

Natural Resources Research - Sand failure and production occurs when the formation stress exceeds the strength of the formation, which is derived majorly from the natural material that cements the...     

Wollastonite at Nuliyam,Kerala, southern India: a reassessment of CO2-infiltration and charnockite formation at a classic locality

The occurrence of a charnockitised felsic gneiss adjacent to a marble/calc-silicate horizon at Nuliyam, southern India, has been cited in recent literature as a classic example of the dehydration of crustal rocks resulting from the advective infiltration of CO₂-rich fluids generated from a local carbonate source. Petrographic study of the Nuliyam calc-silicate, however, reveals it to consist of abundant wollastonite and scapolite and contain locally discordant veins rich in wollastonite. At the pressure—temperature conditions proposed for charnockite formation in recent studies, 5 kbar and 725°C, this wollastonite-bearing mineral assemblage was stable in the presence of a fluid phase only if X _CO2 was near 0.25 and could not have coexisted with the fluid causing biotite breakdown and charnockite development in adjacent rocks (X _CO2>0.85). The stable coexistence of wollastonite and scapolite prohibits the calc-silicate from being a source for fluid driving charnockitisation at the required P-T conditions. Textural observations such as the limited replacement of wollastonite by calcite+quartz symplectites and mosaics, are consistent with late fluid infiltration into the calc-silicate. The extensive isotopic, chemical and mineral abundance data of Jackson and Santosh (1992) are re-interpreted and integrated with these observations to develop a model involving the infiltration of an externally derived CO₂-rich fluid during high-temperature decompression. Increased charnockite development next to the calc-silicate has arisen because the calc-silicate acted as a relatively unreactive and impermeable barrier to fluid transport and caused fluid ponding beneath antiformal closures. The Nuliyam charnockite/calc-silicate locality is an example of a structural trap in a metamorphic setting rather than a site where charnockite formation can be attributed to local fluid sources.     

La forme rotationnelle des équations de la dynamique atmosphérique et les invariants du mouvement de l'air

Résumé Après avoir rappelé quelques notions de calcul tensoriel et les équations de la dynamique atmosphérique en coordonnées généralisées, l'auteur établit l'équation fondamentale de la rotationnelle absolue de l'air. Diverses formes de cette équation sont mentionnées. La première de ces formes est celle d'un bilan qui permet de définir le transport et le taux de production de la rotationnelle absolue de l'air. De la forme particulière de ce transport, il résulte que ce bilan se réduit à un bilan dans un espace à deux dimensions. Deux exemples illustrent les formules générales, le premier, en coordonnées sphériques (, ,r), le second, en coordonnées (, , ) où est un scalaire quelconque (pression atmosphérique, température potentielle, ...). Une autre forme de l'équation fondamentale est celle qui donne le taux d'accroissement individuel d'une composante de la rotationnelle absolue. Cette forme conduit à l'équation d'Ertel. En terminant, l'auteur généralise l'invariant d'Ertel-Rossby.

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Summary Having recalled some results of the tensor analysis and the equations of atmospheric motion in general coordinates, the writer establishes the fundamental equation of the absolute vorticity. Different forms of this equation are mentioned. One of these is the equation of balance from which it is possible to deduce the definition of transport and production of vorticity. It is shown that the equation of balance of the absolute vorticity may be reduced to an equation of balance in two-dimensional space. Two examples illustrate the general equations and formulas: the first example, in spherical coordinates (, ,r), the second one in the coordinates (, , ) where is an arbitrary single-valued scalar quantity (pressure, potentiel temperature, ...). Another form of the absolute vorticity equation expresses the individual change of an arbitrary component of the absolute vorticity. This form leads toErtel's equation. Finally, the writer generalizes theErtel-Rossby invariant.

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Zusammenfassung Nach einer Rekapitulation einiger Resultate der Tensorrechnung und der atmosphärischen Bewegungsgleichungen in generalisierten Koordinaten wird die absolute Wirbelgleichung aufgestellt und es werden verschiedene Formen dieser Gleichung erwähnt. Eine derselben ist die Bilanzformel, aus der die Definition des Wirbeltransports und der Anteil der Wirbelbildung abgeleitet werden können. Es wird gezeigt, daß die Bilanzgleichung des absoluten Wirbels auf eine Bilanzgleichung im zweidimensionalen Raum reduziert werden kann. Die allgemeinen Formeln werden durch zwei Beispiele erläutert: das erste in Kugelkoordinaten (, ,r), das zweite in den Koordinaten (, , ), wo eine beliebige skalare Größe (luftdruck, potentielle Temperatur usw.) darstellt. Eine andere Form der absoluten Wirbelgleichung gibt die individuelle Zunahme einer beliebigen Komponente der absoluten Wirbelstärke wieder; diese Form führt zurErtelschen Gleichung. Zum Schlusse wird dieErtel-Rossbysche Invariante verallgemeinert.