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.

     

Approaches to analyse and model changes in impacts: reply to discussions of “How to improve attribution of changes in drought and flood impacts”*

ABSTRACT

We thank the authors, Brunella Bonaccorso and Karsten Arnbjerg-Nielsen for their constructive contributions to the discussion about the attribution of changes in drought and flood impacts. We appreciate that they support our opinion, but in particular their additional new ideas on how to better understand changes in impacts. It is great that they challenge us to think a step further on how to foster the collection of long time series of data and how to use these to model and project changes. Here, we elaborate on the possibility to collect time series of data on hazard, exposure, vulnerability and impacts and how these could be used to improve e.g. socio-hydrological models for the development of future risk scenarios.     

Palaeomagnetism of the Ordovician dolerites of the Crozon Peninsula (France)

Summary. In order to obtain a Lower Palaeozoic pole for the Armorican Massif and to test the origin of the Ibero-Armorican arc, the Ordovician dolerites of the Crozon peninsula have been palaeomagnetically studied. The samples show a multicomponent magnetization which has been revealed by AF and thermal demagnetization and thoroughly investigated with rock magnetic experiments, polished section examinations and K/Ar dating. Four groups of directions have been recognized, often superimposed on each other in an individual sample. One component (D) has always the lowest blocking temperatures and coercivities and is considered to be of viscous origin, acquired recently in situ or in the laboratory during storage. Two components (A and B) are interpreted to be of secondary origin and to correspond to the observed K/Ar age distribution between 300 and 190 Myr. These ages represent the time interval between two regional thermo-tectonic events, associated with the Hercynian orogeny and the intrusion of dykes related to the early opening of the Central Atlantic Ocean and the Bay of Biscay. A fourth component (C) could be of Ordovician or younger Palaeozoic age; it is not clear whether the age of the magnetization is pre- or post-folding, but a pre-folding age would yield a direction of magnetization similar to Ordovician results from the Iberian peninsula. The latter interpretation suggests a fairly high palaeolatitude, which is in agreement with a glacio-marine postulated for sediments overlying the dolerite sills.     

Approximate spectral analysis by least-squares fit

An approximate method of spectral analysis called successive spectral analysis based upon the mean-quadratic approximation of an empirical function by generalised trigonometric polynomial with both unknown frequencies and coefficients is developed. A few quotations describing some properties of the method as well as one of the possible methods for numerical solution are given.     

A dynamical investigation of the conjecture that Mercury is an escaped satellite of Venus

The possibility that Mercury might once have been satellite of a Venus, suggested by a number of anomalies, is investigated by a series of numerical computer experiments. Tidal interaction between Mercury and Venus would result in the escape of Mercury into a solar orbit. Only two escape orbits are possible, one exterior and one interior to the Venus orbit. For the interior orbit, subsequent encounters are sufficiently distant to avoid recapture or large perturbations. The perihelion distance of Mercury tends to decrease, while the orientation of perihelion librates for the first few thousand revolutions. If dynamical evolution or nonconservative forces were large enough in the early solar system, the present semimajor axes could have resulted. The theoretical minimum quadrupole moment of the inclined rotating Sun would rotate the orbital planes out of coplanarity. Secular perturbations by the other planets would evolve the eccentricity and inclination of Mercury's orbit through a range of possible configurations, including the present orbit. Thus the conjecture that Mercury is an escaped satellite of Venus remains viable, and is rendered more attractive by our failure to disprove it dynamically.     

The transition from elliptic to hyperbolic orbits in the two-body problem by slow loss of mass

Transition from elliptic to hyperbolic orbits in the two-body problem with slowly decreasing mass is investigated by means of asymptotic approximations.Analytical results by Verhulst and Eckhaus are extended to construct approximate solutions for the true anomaly and the eccentricity of the osculating orbit if the initial conditions are nearly-parabolic. It becomes clear that the eccentricity will monotonously increase with time for all mass functions satisfying a Jeans-Eddington relation and even for a larger set of functions. To illustrate these results quantitatively we calculate the eccentricity as a function of time for Jeans-Eddington functionsn=0(1) 5 and 18 nearly-parabolic initial conditions to find that 93 out of 108 elliptic orbits become hyperbolic.     

Deriving TDS values in coarse sediments from long normal and electromagnetic logs

This paper presents an empirical relationship of quantitatively linked electromagnetic (EM) borehole recordings of the total dissolved solids (TDS) in pore water in the Quaternary deposits of the Belgian coastal plain. First, the long normal (LN) logs are linked to EM logs, then the already developed relationships between LN resistivity measurements and the TDS values are rewritten for EM recordings. The main parameter in these equations is the formation factor, which is derived from ground water analyses and LN logs through Archie's law. The EM recording has several advantages compared to the LN logs. The EM analysis allows measuring in PVC-cased wells and is not hindered by the invasion zone around the well. Furthermore, it has a high vertical resolution. LN logs can be measured only once, after drilling a well; EM recordings can be repeated several times in monitoring wells, which allows the gathering of time-dependent data over a complete vertical cross section. Such data could be obtained with LN logs only in wells with screens over the full-depth interval, which causes a hydraulic short circuit. This short circuit can result in a large artificial flow through the well between different levels, resulting in a salinity profile, which is no longer representative for the studied site. Remediation against short circuiting is a reduction of the screened interval, which strongly reduces the gathered information. The application of the derived equations is one of setting up a monitoring network along the Belgian coast to monitor the trend in salinity levels and comparing present salinity levels with older LN recordings to investigate the salinity changes in the last 30 years. Deep wells already present in the Belgiancoastal plain can then be used to monitor both the fresh water head changes and the salt water evolution. The technique has also been used for parameter identification for which real concentration measurements were needed.     

An environmental assessment of the Charleston Ocean Dredged Material Disposal Site and surrounding areas after partial completion of the Charleston Harbor Deepening Project

A project to deepen shipping and entrance channels in Charleston Harbor was conducted from 1999 to 2002. This generated approximately 22 million cubic yards of sediment for offshore disposal. Assessments of biological and physical conditions in the Charleston Ocean Dredged Material Disposal Site and surrounding areas were conducted prior to deepening (1993-94), and partway through the disposal period (2000). Results from the 2000 survey are presented and compared to the baseline survey. The study area was composed of the disposal zone and surrounding areas and divided into 20 one square mile strata. Within each stratum, benthic grab samples were collected from ten random sites for analysis of sediment composition and contaminants and macrobenthic assemblages. No contaminant levels were above effects range low levels. Results revealed that sediments in the western strata had significantly higher silt/clay content in the 2000 survey when compared to baseline sediments, while sediments east of the disposal zone were similar to baseline. Analyses were performed on a subset of the benthic data that compared baseline to 2000 conditions in western and eastern strata. The benthic communities in western strata were altered following disposal operations. The benthic community east of the disposal area was not different from baseline conditions. These alterations in the benthic community were attributed to changes in bottom habitat characteristics rather than pollution effects.