Microstructural criteria for reliable thermometry in low-temperature eclogites

Two Alpine eclogite bodies, sampled in metaophiolitic complexes of the Piemonte Zone, have been studied for geothermometry. It is demonstrated that temperature estimates, by both exchange thermometry and sizes of antiphase domains in omphacites, give rise to erratic results when the defect structures of the minerals are not taken into account. Microstructural criteria, by means of both optical and TEM microscopy, for reliable thermometry in low-temperature eclogites are disscussed. The dynamically recrystallized grains are the more suitable sites for the application of exchange thermometry, while only low-strained omphacites can be used for thermometry based on APD's.     

Flood Events of Selected European Rivers in the Sixteenth Century

The severity and frequency of sixteenth-century floods of the Rhine, the Main, the middle and upper Elbe with its tributaries, rivers of northern and central Italy, the Garonne and rivers in Catalonia and Andalusia are analyzed using documentary evidence. The basic topographical and hydrological characteristics of the rivers investigated as well as the synoptic causes of their flooding during the instrumental period are presented. Different examples of modifications of the run-off process due to anthropogenic activity are discussed. Prevalence in flood occurrence during the second half of the sixteenth century in comparison to the first half is typical for central European and Andalusian rivers (mainly in the 1560s and 1590s) and agrees with the evolution of precipitation patterns. On the other hand, Italian and Catalonian rivers, in part, had a higher occurrence of floods during the first half of the century. Changes in the flooding seasons in both halves of the century are not unambiguous. Results of an analysis on a broader European scale show floods to be a random natural phenomena with limited areal extent defined by the spatial influence of forcing meteorological factors (continuous heavy rains, sudden melting of thick snow cover, etc.). Despite some limitations of documentary evidence, series of reconstructed historical floods are valuable sources of proxy data which can be utilized for the study of the flooding fluctuations in the pre-instrumental period.     

Cation exchanged Fe(II) and Sr compared to other divalent cations (Ca, Mg) in the bure Callovian–Oxfordian formation: Implications for porewater composition modelling

Iron and Sr bearing phases were thoroughly investigated by means of spectrometric and microscopic techniques in Callovian–Oxfordian (COX) samples originating from the ANDRA Underground Research Laboratory (URL) in Bure (France). Strontium was found to be essentially associated with celestite, whereas Fe was found to be distributed over a wide range of mineral phases. Iron was mainly present as Fe(II) in the studied samples (∼93% from Mössbauer results). Most of the Fe(II) was found to be in pyrite, sideroplesite/ankerite and clay minerals. Iron(III), if present, was associated with clay minerals (probably illite, illite-smectite mixed layer minerals and chlorite). No Fe(III) oxy(hydro)xide could be detected in the samples. Strontianite was not observed either. Based on these observations, it is likely that the COX porewater is in equilibrium with the following carbonate minerals, calcite, dolomite and ankerite/sideroplesite, but not with strontianite. It is shown that this equilibrium information can be combined with clay cation exchange composition information in order to give direct estimates or constraints on the solubility products of the carbonate minerals dolomite, siderite and strontianite. As a consequence, an experimental method was developed to retrieve the cation exchanged Fe(II) in very well preserved COX samples.     

Symplectic Integrators: Rotations and Roundoff Errors

We investigate the numerical implementation of a symplectic integrator combined with a rotation (as in the case of an elongated rotating primary). We show that a straightforward implementation of the rotation as a matrix multiplication destroys the conservative property of the global integrator, due to roundoff errors. According to Blank et al. (1997), there exists a KAM-like theorem for twist maps, where the angle of rotation is a function of the radius. This theorem proves the existence of invariant tori which confine the orbit and prevent shifts in radius. We replace the rotation by a twist map or a combination of shears that display the same kind of behaviour and show that we are able not only to recover the conservative properties of the rotation, but also make it more efficient in term of computing time. Next we test the shear combination together with symplectic integrator of order 2, 4, and 6 on a Keplerian orbit. The resulting integrator is conservative down to the roundoff errors. No linear drift of the energy remains, only a divergence as the square root of the number of iterations is to be seen, as in a random walk. We finally test the three symplectic integrators on a real case problem of the orbit of a satellite around an elongated irregular fast rotating primary. We compare these integrators to the well-known general purpose, self-adaptative Bulirsch–Stoer integrator. The sixth order symplectic integrator is more accurate and faster than the Bulirsch–Stoer integrator. The second- and fourth- order integrators are faster, but of interest only when extreme speed is mandatory. This revised version was published online in August 2006 with corrections to the Cover Date.     

Accretion disc outbursts: a new version of an old model

We have developed 1D time-dependent numerical models of accretion discs, using an adaptive grid technique and an implicit numerical scheme, in which the disc size is allowed to vary with time. The code fully resolves the cooling and heating fronts propagating in the disc. We show that models in which the radius of the outer edge of the disc is fixed produce incorrect results, from which probably incorrect conclusions about the viscosity law have been inferred. In particular we show that outside-in outbursts are possible when a standard bimodal behaviour of the Shakura–Sunyaev viscosity parameter α is used. We also discuss to what extent insufficient grid resolution has limited the predictive power of previous models. We find that the global properties (magnitudes, etc.) of transient discs can be addressed by codes using a high, but reasonable, number of fixed grid points. However, the study of the detailed physical properties of the transition fronts generally requires resolutions which are out of reach of fixed grid codes. It appears that most time-dependent models of accretion discs published in the literature have been limited by resolution effects, improper outer boundary conditions, or both.     

The mesoscale variability in the Caribbean Sea. Part II: Energy sources

The processes which drive the production and the growth of the strong mesoscale eddy field in the Caribbean Sea are examined using a general circulation model. Diagnostics of the simulations suggest that:(1) The mean currents in the Caribbean Sea are intrinsically unstable. The nature of the instability and its strength vary spatially due to strong differences of current structure among basins.(2) The greatest and most energetic eddies of the Caribbean Sea originate in the Venezuela Basin by mixed barotropic-baroclinic instability of an intense jet, formed with waters mostly from the surface return flow of the Meridional Overturning Circulation and the North Equatorial Current which converge and accelerate through the Grenada Passage. The vertical shear of this inflow is enhanced by an eastward undercurrent, which flows along the south American Coast between 100 and 250 m depth. The shallow eddies (less than 200 m depth) formed in the vicinity of the Grenada Passage get rapidly deeper (down to 1000 m depth) and stronger by their interaction with the deep interior flow of the Subtropical Gyre, which enters through passages north of St. Lucia. These main eastern Caribbean inflows merge and form the southern Caribbean Current, whose baroclinic instability is responsible for the westward growth and strengthening of these eddies from the Venezuela to the Colombia Basin.(3) Eddies of lesser strength are produced in other regions of the Caribbean Sea. Their generation and growth is also linked with instability of the local currents. First, cyclones are formed in the cyclonic shear of the northern Caribbean Current, but appear to be rapidly dissipated or absorbed by the large anticyclones coming from the southern Caribbean. Second, eddies in the Cayman Sea, which impact the Yucatan region, are locally produced and enhanced by barotropic instability of the deep Cayman Current.(4) The role of the North Brazil Current (NBC) rings is mostly to act as a finite perturbation for the instability of the mean flow. Their presence near the Lesser Antilles is ubiquitous and they appear to be linked with most of the Caribbean eddies. There are some evidences that the frequency at which they form near the Grenada Passage is influenced by the frequency at which the NBC rings impinge the Lesser Antilles. But large Caribbean eddies also form without a close influence of any ring, and comparison between simulations shows that mean eddy kinetic energy and eddy population in the Caribbean Sea are not substantially different in absence or presence of NBC rings: their presence is not a necessary condition for the generation and growth of the Caribbean eddies.     

A key-formula to compute the gravitational potential of inhomogeneous discs in cylindrical coordinates

We have established the exact expression for the gravitational potential of a homogeneous polar cell??an elementary pattern used in hydrodynamical simulations of gravitating discs. This formula, which is a closed-form, works for any opening angle and radial extension of the cell. It is valid at any point in space, i.e. in the plane of the distribution (inside and outside) as well as off-plane, thereby generalizing the results reported by Durand (Electrostatique. Vol. I. Les Distributions, 1953) for the circular disc. The three components of the gravitational acceleration are given. The mathematical demonstration proceeds from the incomplete version of Durand??s formula for the potential (based on complete elliptic integrals). We determine first the potential due to the circular sector (i.e. a pie-slice sheet), and then deduce that of the polar cell (from convenient radial scaling and subtraction). As a by-product, we generate an integral theorem stating that ??the angular average of the potential of any circular sector along its tangent circle is ${\frac{2}{\pi}}$ times the value at the corner??. A few examples are presented. For numerical resolutions and cell shapes commonly used in disc simulations, we quantify the importance of curvature effects by performing a direct comparison between the potential of the polar cell and that of the Cartesian (i.e. rectangular) cell having the same mass. Edge values are found to deviate roughly like ${2 \times 10^{-3}\times N/256}$ in relative (N is the number of grid points in the radial direction), while the agreement is typically four orders of magnitude better for values at the cell??s center. We also produce a reliable approximation for the potential, valid in the cell??s plane, inside and close to the cell. Its remarkable accuracy, about ${5\times 10^{-4}\times N/256}$ in relative, is sufficient to estimate the cell??s self-acceleration.     

Diversité du métamorphisme éclogitique dans le massif ophiolitique du Monviso (Alpes occidentales,Italie)

Résumé

Le complexe ophiolitique du Monviso représente un témoin essentiel de la lithosphère océanique subduite puis exhumée dans les Alpes occidentales. Ce complexe est classiquement subdivisé en unités lithologiques, qui ont toutes subi une évolution structurale caractérisée par la succession de trois événements dans des environnements (1) éclogitique, (2) schistes bleus puis (3) schistes verts. Cependant la quantification des conditions physiques du métamorphisme éclogitique au sein de trois unités à lithologies comparables (Viso Mozzo, Passo Gallarino et Lago Superiore), montrent clairement l’existence d’une hétérogénéité des conditions éclogitiques enregistrée par l’ensemble des unités, indépendamment de la chimie de la roche initiale. Les conditions estimées sont de 450 ± 40 °C et de 12 ± 3 kb pour l’unité du Viso Mozzo et du Passo Gallarino contre 580 ± 40°C et 19 ± 2 kb pour l’unité du Lago Superiore. De plus l’analyse structurale combinée révèle que c’est au cours de l’exhumation, dans les conditions du faciès des schistes bleus, que les différentes unités vont être juxtaposées et vont suivre une histoire tectono-métamorphique commune. Ces nouvelles données, impliquent une réinterprétation des modèles géodynamiques existants et couramment admis pour le Monviso. Ce dernier doit être considéré comme un complexe résultant de l’accrétion de différents morceaux d’une lithosphère océanique subduite, qui se sont détachés à différentes profondeurs pour venir se stocker à 25 km de profondeur dans les conditions du faciès des schistes bleus. © 2000 Éditions scientifiques et médicales Elsevier SAS