Les bilans énergétiques en météorologie dynamique

Résumé L'objet de cet article est d'établir les bilans énergétiques dans un référentiel quelconque, animé d'un mouvement variable d'un point à un autre et d'un instant à un autre. Le bilan de l'énergie mécanique se déduit, grâce au théorème des forces vives, des équations du mouvement de l'air par rapport au référentiel mobile. Le bilan qui exprime la conservation de l'énergie totale s'obtient en transposant, dans le référentiel mobile, l'expression du premier principe de la thermodynamique, énoncé dans le référentiel galiléen.

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Summary In this paper, energy equations of balance are established in any type of frame moving with an arbitrary, variable velocity with respect to space aud time. The equation of balance of mechanical energy can be deduced from the eqnations of motion of the air with respect to the moving frame. The equation of balance showing the conservation of total energy will be obtained by transposing in the moving frame, the expression of the first principle of thermodynamics given for the absolute frame.

     

Fluid-assisted granulite metamorphism: A continental journey

Lower crustal granulites, which constitute the base of all continents, belong to two series: high-pressure granulites generated by crustal thickening (subduction) and (ultra)high-temperature granulites associated with crustal extension. Fluid inclusions and metasomatic features indicate that the latter were metamorphosed in the presence of low-water activity fluids (high-density CO₂ and brines), which have invaded the lower crust at peak metamorphic conditions (fluid-assisted granulite metamorphism). High-pressure and (ultra)high-temperature granulites commonly occur along elongated paired belts. They were formed, from the early Proterozoic onwards, during a small number of active periods lasting a few hundreds of m.y. These periods were separated from each other by longer periods of stability. Each period ended with the formation of a supercontinent whose amalgamation coincided with low- to medium pressure (ultra)high-temperature granulite metamorphism, immediately before continental break-up. It is proposed that large quantities of mantle-derived CO₂ stored in the lower crust at the final stage of supercontinent amalgamation, are released into the hydro- and atmosphere during breakup of the supercontinent. Fluid-assisted granulite metamorphism, therefore, appears to be an important mechanism for transferring deep mantle fluids towards the Earth's surface. Possible consequences were, for example, the sudden end of Proterozoic glaciations, as well as the post-Cambrian explosion of life.     

Le facies granulite en norvege meridionale: I. Les associations minéralogiques

The basement of Southern Norway is a genetically homogeneous migmatite complex in which old supracrustals produced granitic and granodioritic ‘neosome’ during a late Precambrian (10⁹ years ago) regional metamorphism. Observed isograds of critical minerals: muscovite, cordierite, orthopyroxene indicate that the Telemark amphibolite facies in the North passes into the coastal Bamble granulite facies in the South. The data of expeimental petrology suggest that the transition, which took place at temperatures of 700–800°C, is essentially due to a decrease of the partial water pressure. P_H2O was equal to total pressure P_s in the amphibolite facies and lower than 2 kb in the granulite facies.     

Long-term evolution of the spin of Mercury: I. Effect of the obliquity and core-mantle friction

The present obliquity of Mercury is very low (less than 0.1°), which led previous studies to always adopt a nearly zero obliquity during the planet’s past evolution. However, the initial orientation of Mercury’s rotation axis is unknown and probably much different than today. As a consequence, we believe that the obliquity could have been significant when the rotation rate of the planet first encountered spin-orbit resonances. In order to compute the capture probabilities in resonance for any evolutionary scenario, we present in full detail the dynamical equations governing the long-term evolution of the spin, including the obliquity contribution.The secular spin evolution of Mercury results from tidal interactions with the Sun, but also from viscous friction at the core-mantle boundary. Here, this effect is also regarded with particular attention. Previous studies show that a liquid core enhances drastically the chances of capture in spin-orbit resonances. We confirm these results for null obliquity, but we find that the capture probability generally decreases as the obliquity increases. We finally show that, when core-mantle friction is combined with obliquity evolution, the spin can evolve into some unexpected configurations as the synchronous or the 1/2 spin-orbit resonance.     

Meta-analysis from different tracers of the small Local Arm around the Sun—extent,shape, pitch,origin

The Sun in not located in a major spiral arm, and sits in a small ‘Local Arm’ (variously called arm, armlet, blob, branch, bridge, feather, finger, segment, spur, sub-arm, swath, etc.). The diversity of names for the ‘Local Arm’ near the Sun indicates an uncertainty about its shape or pitch or its extent from the Sun in each galactic quadrant, as well as an uncertainty about its origin.Here we extract data about the small ‘Local Arm’ near the Sun, from the recent observational literature, over many arm tracers, and we use statistics in order to find the local arm’s mean extent from the Sun, its possible shape and pitch angle from the direction of galactic longitude \(90^{\circ}\). Employing all tracers, the Local Arm is about 4 kpc long by 2 kpc large. The Sun is within 1 kpc of the center of the local arm. Proposed ‘bridges’ and ‘fingers’ are assessed. These bridges to nearby spiral arms and fingers across spiral arms may not reach the nearest spiral arms, owing to kinematic and photometric distance effects.We then compare these statistical results with some predictions from recent models proposed to explain the local arm (perturbations, resonances, density wave, halo supercloud, debris trail from a dwarf galaxy).The least controversial models involve importing materials from elsewhere (halo supercloud, debris trail) as a first step, and to be later deformed in a second step (by the Galaxy’s differential rotation into become roughly parallel to spiral arms) and then subjected to ongoing forces (global density waves, local perturbations).     

Observations of the Oh Radio Lines of Comets at Nançay – Recent Developments

The 18 cm lines of OH have been observed in more than 70 comets withthe Nançay radio telescope since 1974. The observations made from1982 to 1999 are now organized in a data base. The Nançay radiotelescope has been recently upgraded, and observations since 2000 aremade with a sensitivity increased by about a factor of two. Twelvecomets were observed from July 2000 to May 2002.     

Spin axis evolution of two interacting bodies

We consider the solid-solid interactions in the two body problem. The relative equilibria have been previously studied analytically and general motions were numerically analyzed using some expansion of the gravitational potential up to the second order, but only when there are no direct interactions between the orientation of the bodies. Here we expand the potential up to the fourth order and we show that the secular problem obtained after averaging over fast angles, as for the precession model of Boué and Laskar [Boué, G., Laskar, J., 2006. Icarus 185, 312-330], is integrable, but not trivially. We describe the general features of the motions and we provide explicit analytical approximations for the solutions. We demonstrate that the general solution of the secular system can be decomposed as a uniform precession around the total angular momentum and a periodic symmetric orbit in the precessing frame. More generally, we show that for a general n-body system of rigid bodies in gravitational interaction, the regular quasiperiodic solutions can be decomposed into a uniform precession around the total angular momentum, and a quasiperiodic motion with one frequency less in the precessing frame.     

On Poincaré's second species solutions

A proof of the existence of Poincaré's second species solution in the restricted three body problem is given. It is not based, as Perko's and Guillaume's work, on singular perturbation and asymptotic approximation but rather on topological equivalence between differential systems in the neighborhood of an equilibrium.Proceedings of the Sixth Conference on Mathematical Methods in Celestial Mechanics held at Oberwolfach (West Germany) from 14 to 19 August, 1978.