Construction and analysis of higher order finite difference schemes for the 1D wave equation

In this article, we propose to: 1. Establish most of the properties conjectured in [2] about the higher order finite difference approximation of the 1D Laplace operator. 2. Generalize to any order the fourth-order accurate scheme in space and time of Shubin and Bell [20] and Cohen [6]. For this new family of 2m–2m schemes, we establish, via elementary mathematics, various stability and dispersion results that are helpful to compare these schemes to the 2–2m schemes of Anné et al. [2]. This revised version was published online in July 2006 with corrections to the Cover Date.     

Influence of uncertain boundary conditions and model structure on flood inundation predictions

In this study, the GLUE methodology is applied to establish the sensitivity of flood inundation predictions to uncertainty of the upstream boundary condition and bridges within the modelled region. An understanding of such uncertainties is essential to improve flood forecasting and floodplain mapping. The model has been evaluated on a large data set. This paper shows uncertainty of the upstream boundary can have significant impact on the model results, exceeding the importance of model parameter uncertainty in some areas. However, this depends on the hydraulic conditions in the reach e.g. internal boundary conditions and, for example, the amount of backwater within the modelled region. The type of bridge implementation can have local effects, which is strongly influenced by the bridge geometry (in this case the area of the culvert). However, the type of bridge will not merely influence the model performance within the region of the structure, but also other evaluation criteria such as the travel time. This also highlights the difficulties in establishing which parameters have to be more closely examined in order to achieve better fits. In this study no parameter set or model implementation that fulfils all evaluation criteria could be established. We propose four different approaches to this problem: closer investigation of anomalies; introduction of local parameters; increasing the size of acceptable error bounds; and resorting to local model evaluation. Moreover, we show that it can be advantageous to decouple the classification into behavioural and non-behavioural model data/parameter sets from the calculation of uncertainty bounds.     

Relationship between waterfowl and the seagrassRuppia maritima in a Southwestern Atlantic coastal lagoon

We evaluated the distribution of waterfowl in relation to a seagrass (Ruppia maritima) patch, to infauna, and on its relationship with substrate characteristics. An experiment performed in the Mar Chiquita coastal lagoon (37°46′S, 57°27′W; Argentina) was used to evaluate the effect of herbivory on widgeon grass,R. maritima. Control plots of equal size, located between bird exclosures, were exposed to herbivory. The experiment ran for 31 d, starting on December 1, 1994. Censuses showed that black-necked swan ( $\bar x = 50$ birds ha^?1, SD = 37, n = 10) and coots ( $\bar x = 42$ birds ha^?1, SD = 28, n = 10) were the most important (always present) of the waterfowl seen feeding onR. maritima. The results of the experiment showed greater leaf lengths, lower belowground (rhizomes and roots) biomass, greater aboveground (leaves and shoots) biomass, and greater abundance of the polychaeteHeteromastus similis in exclosure plots. There were no exclosure effects on total biomass (belowground plus aboveground), reproductive parts (fruits and pre- and postpollination flowers), or abundance of most benthic infauna. Topographic surveys showed that sediment surface was higher within theR. maritima patches, but there were no significant differences in granulometric composition. Surveys also showed that bird distribution was strongly associated with the presence ofR. maritima.     

Rainfall and the 6–9 day wave-like disturbance in West-Africa during summer 1989

Summary Using ECMWF analyses and daily rain amounts of 569 stations in Western Africa for summer 1989, the study documents the composite structure of the 6–9 day oscillation and its influence on rain. Rain is modulated by vorticity as displayed in the wave composite. There are rainfall maxima coincident with cyclonic vorticity and rainfall minima coincident with anticyclonic vorticity at the 700hPa level, at 17.5°N and 7.5°N.With 6 Figures     

Mais comment s'écoule donc un glacier ? Aperçu historique

Ice and snow have often helped physicists understand the world. On the contrary it has taken them a very long time to understand the flow of the glaciers. Naturalists only began to take an interest in glaciers at the beginning of the 19th century during the last phase of glacier advances. When the glacier flow from the upslope direction became obvious, it was then necessary to understand how it flowed. It was only in 1840, the year of the Antarctica ice sheet discovery by Dumont d'Urville, that two books laid the basis for the future field of glaciology: one by Agassiz on the ice age and glaciers, the other one by canon Rendu on glacier theory. During the 19th century, ice flow theories, adopted by most of the leading scientists, were based on melting/refreezing processes. Even though the word ‘fluid’ was first used in 1773 to describe ice, more the 130 years would have to go by before the laws of fluid mechanics were applied to ice. Even now, the parameter of Glen's law, which is used by glaciologists to model ice deformation, can take a very wide range of values, so that no unique ice flow law has yet been defined. To cite this article: F. Rémy, L. Testut, C. R. Geoscience 338 (2006).     

Coherent structure dynamics and sediment particle motion around a cylindrical pier in developing scour holes

Recent investigations on the dynamics of the turbulent horseshoe vortex system (THV) around cylindrical piers have shown that the rich coherent dynamics of the vortical structures is dominated by low-frequency bimodal fluctuations of the velocity field. In spite of these advances, many questions remain regarding the changes of the flow and sediment transport dynamics as scour progresses. In this investigation we carry out laboratory experiments to register the development of the scour hole around a cylindrical pier in a fine-sand bed (d ₅₀ = 0.36 mm). We use the bathymetry measured in the experiment to simulate the flow field employing the detached-eddy simulation approach (DES), which has shown to resolve most of the turbulent stresses around surface-mounted obstacles. From these simulations we compare the dynamics of the THV to the flat-bed case, and analyze the effects on particle transport and sediment flux using the Lagrangian particle model of Escauriaza and Sotiropoulos (2011b) to study the impact of the changes of the flow on the sediment dynamics.     

Apophis: the Story Behind the Scenes

On December 20, 2004 the Minor Planet Center issued the Minor Planet Electronic Circular (MPEC) 2004-Y25 announcing the discovery of a new Near Earth Asteroid (NEA) with designation 2004 MN₄. Only two days later, when the Christmas holidays were about to begin, it was already apparent that this asteroid, currently known as Apophis, would be notorious: our close-approach monitoring system, CLOMON2, was already showing a Virtual Impactor (VI) in 2029 reaching the level 2 in the Torino Scale, the first asteroid to reach that level since our monitoring system had been operational. However, this was just the beginning of what it was to come in the subsequent days. In this paper we will give an overview of the NEODyS-CLOMON2 system and provide the details on how Apophis’ collision scenario evolved, the way NEODyS’ team handled it and the crazy 2004’ Christmas holidays we had due to this unexpected guest.     

How do granitoid magmas mix with each other? Insights from textures,trace element and Sr–Nd isotopic composition of apatite and titanite from the Matok pluton (South Africa)

In plutonic systems, magma mixing is often modelled by mass balance based on whole-rock geochemistry. However, magma mixing is a chaotic process and chemical equilibration is controlled by non-linear diffusive–advective processes unresolved by the study of bulk samples. Here we present textural observations, LA-(MC-)ICP-MS trace element and Sr–Nd isotopic data of accessory apatites and titanites from a hybrid granodiorite of the Neoarchean Matok pluton (South Africa), collected in a zone of conspicuous mixing between mafic and felsic magmas. Apatite grains mostly show a pronounced zoning in CL images, corresponding to abrupt changes in REE and HFSE concentrations recording their transfer through compositionally different melt domains during mixing. These grains crystallized early, at temperatures of 950–1000 °C. Titanite grains crystallized at temperatures of 820–900 °C (Zr-in-sphene thermometry). They show limited intra-grain chemical variations but huge inter-grain compositional scatter in REE and HFSE, pinpointing crystallization within a crystal mush, from isolated melt pockets having different composition from one another owing to incomplete chemical homogenization and variable Rayleigh fractionation. These chemical–textural characteristics, in combination with partitioning models and Polytopic Vector Analysis, point to “self-mixing” between co-genetic dioritic and granodioritic/granitic magmas. Both resulted from differentiation of mantle-derived mafic melts, showing that mixing does not necessarily involve magmas from contrasted (crust vs. mantle) sources. Systematic variations in εNd _t (?4.5 to ?2.5) and ⁸⁷Sr/⁸⁶Sr_(i) (0.703–0.707) of titanite and apatite grains/domains crystallized from the two magmas point to an isotopically inhomogeneous mantle source, which is not resolved by bulk-rock isotopic data. Interaction between the two magmas must have occurred at relatively high temperatures (ca. 900°C) so that their viscosity contrast remained low, allowing efficient mechanical mixing. Despite this, chemical homogenization was incomplete, as recorded by diffusive fractionation between REE–HFSE and Sr. Modelling thereof reveals that chemical exchange between the liquid phases of the two mixed magmas did not last more than a few tens to hundreds of years. The chemical equilibration between mixed magmas thus strongly depends on the considered elements and observational length scales.