On the validity of Kraichnan scalings for forced two-dimensional turbulence

We examine the validity of the scaling laws derived by Kraichnan (1967) for forced two-dimensional turbulence. We use a new numerical technique (Dritschel & Fontane 2010) to reach higher Reynolds number than previously accessible with classical pseudo-spectral methods. No large scale friction or hypo-diffusion is used in order to avoid any distortion of the inverse cascade and to be in agreement with the theoretical framework used by Kraichnan. Both spectral and spatial forcing are considered and statistical convergence is obtained through large simulation ensembles. A steeper energy spectrum proportional to k^(-2) is observed for the inverse cascade in place of the classical k^(-5/3) prediction. This steepening is shown to be associated with a faster growth of energy at large scales, scaling like t^(-1) rather than Kraichnan's prediction of t^(-3/2). The deviation from Kraichnan's theory is related to the emergence of a vortex population dominating the distribution of energy across scales, and whose number density and vorticity distribution with respect to vortex area are related to the shape of the enstrophy spectrum

Implémentation et évaluation d’algorithmes parallèles de FFTs 3D à base de modèles de composants logiciels

International audienceThe Fast Fourier Transform (FFT) is a widely-used building block for many high-performance scientific applications. Efficient computing of FFT is paramount for the performance of these applications. This has led to many efforts to implement machine and computation specific optimizations. However, no existing FFT library is capable of easily integrating and automating the selection of new and/or unique optimizations.To ease FFT specialization, this study evaluates the use of component-based software engineering, a programming paradigm which consists in building applications by assembling small software units. Component models are known to have many software engineering benefits but usually have insufficient performance for high-performance scientific applications.This talk uses the L²C model, a general purpose high-performance component model, and studies its performance and adaptation capabilities on 3D FFTs. Experiments show that L²C, and components in general, enables easy handling of 3D FFT specializations while obtaining performance comparable to that of well-known libraries.La transformée de Fourier rapide (FFT) est un élément fondamentale fréquemment utilisé dans de nombreuses applications scientifiques de haute performance. Calculer efficacement des FFT est ainsi primordial pour la performance de ces applications. Cela a conduit à de nombreux efforts pour implémenter des optimisations spécifiques à un matériel ou à une classe d'algorithmes donnée. Cependant, aucune bibliothèque de FFT existante permet facilement d'intégrer et d'automatiser la sélection de nouvelles optimisations et / ou d'optimisations uniques.Cette étude vise à évaluer l'utilisation de techniques de génie logicielle à base de composants, un paradigme de programmation qui consiste à construire des applications en assemblant de petites briques logiciels. Les modèles de composants sont connus pour avoir de nombreux avantages de génie logiciel, mais ont généralement des performances insuffisantes pour les applications scientifiques de haute performance.Cette étude s'intéresse à l'utilisation du modèle L²C, un modèle de composants de haute performance, et étudie ses performances et sa capacités à pouvoir adapter les applications de FFT 3D. Les expériences montrent que L²C et les composants en général, permettent de manipuler facilement la structure des applications de FFT 3D via une spécialisations d'assemblage, tout en obtenant des performances comparables à celle des bibliothèques bien connues

Vortical control of forced two-dimensional turbulence

A new numerical technique for the simulation of forced two-dimensional turbulence (Dritschel and Fontane, 2010) is used to examine the validity of Kraichnan-Batchelor scaling laws at higher Reynolds number than previously accessible with classical pseudo-spectral methods,making use of large simulation ensembles to allow a detailed consideration of the inverse cascade in a quasi-steady state. Our results support the recent finding of Scott (2007), namely that when a direct enstrophy cascading range is well-represented numerically, a steeper energy spectrum proportional to k^(−2) is obtained in place of the classical k^(−5/3) prediction. It is further shown that this steep spectrum is associated with a faster growth of energy at large scales, scaling like t^(−1) rather than Kraichnan’s prediction of t^(−3/2). The deviation from Kraichnan’s theory is related to the emergence of a population of vortices that dominate the distribution of energy across scales, and whose number density and vorticity distribution with respect to vortex area are related to the shape of the enstrophy spectrum. An analytical model is proposed which closely matches the numerical spectra between the large scales and the forcing scale

Mapping ecosystem services provided by wetlands at multiple spatiotemporal scales : a case study in Quebec, Canada

Abstract : Wetlands are affected by climate and anthropogenic changes, which influence the ecosystem services (ES) they provide. This study presents a spatially explicit quantification of wetland ESs. The study site is the Yamaska river watershed located in Quebec, Canada. The proposed approach includes four main steps: (1) statistical selection of function indicators (FI) to build a composite ecosystem service indicator (ESI); (2) temporal land use mapping for past (1984), recent (2011) and future scenarios (2050); (3) mapping and quantification of FIs and ESIs at all temporal and spatial scales; and (4) synthesis of multispatial and multitemporal information using a diagram representation. Results present the spatiotemporal evolution of the maintaining habitat ES provided by wetlands in the studied watershed. The historical characterization shows a general degradation of this service on the entire territory for the last 30 years. Multi-scale analyses can target priority sectors in which this service has deteriorated or is lacking. Future scenarios show the urgency to act in order to preserve currently intact areas because even the optimistic scenario indicates that the studied ES would not return to its 1984 state. Finally, the synthesis analysis provides a decision support tool adapted to territory managers. Thus, this study shows that the proposed multi-scale method is reproducible, robust and that it provides simple procedures to assess ES over time and space

Effective stress in unsaturated granular materials: micro-mechanical insights

Stress transport in an unsaturated granular material is analytically derived. As such, an effective stress tensor related to the mechanical state governed by the interganular forces within the skeleton is identified together with a capillary stress tensor that accounts for the interactions due to the liquid and gaseous phases. Using a Discrete Element Method for modelling an unsaturated granular material, this capillary stress tensor is computed along different loading paths. Knowing the applied total stress, the effective stress tensor is then readily deduced and it is shown that it describes adequately the strength of the unsaturated granular material along various loading paths for any degree of saturation

Acquisition d’information dans un modèle intertemporel en temps continu

Cet article examine la demande d’information et la valeur de l’information dans un modèle intertemporel en temps continu. Le modèle étudié est un modèle à information incomplète où la technologie d’information est contrôlée par l’investisseur moyennant un coût. Le mécanisme bayésien continu de révision des croyances produit, pour cette structure, une distribution postérieure gaussienne à tout point du temps. Le contrôle de la technologie d’information est équivalent au contrôle de l’estimateur de la position de la variable d’état (espérance conditionnelle) ainsi que de la précision de cet estimateur (variance conditionnelle). La demande d’information, dans notre modèle, se compose de deux termes, qui résultent du conflit entre deux objets d’apprentissage. Sous l’hypothèse d’une offre de précision stochastique et inélastique, le prix d’équilibre de l’information est dérivé et sa structure analysée.In this paper we examine the demand for information and the value of information in an intertemporal continuous time model. The model analyzed is a model with incomplete information where the information technology is controlled by the investor at a cost. The continuous bayesian updating of beliefs yields, for the information structure postulated, a posterior conditional distribution that is Gaussian at any point in time. The control of the information technology is equivalent to the control of the estimator of the state variable (conditional mean) and of the precision of this estimator (conditional variance). The demand for information is composed of two terms which result from the conflict between two subjects of learning. Under an assumption on the supply of precision, we derive and analyze the equilibrium price of information

Is there an arms race in the Arctic?

To what extent does the military posturing of Arctic coastal states reflect an ongoing arms race for the control of the Arctic? This idea first emerged after the 2007 planting of a Russian flag at the North Pole, and is regularly quoted by the media and several political analysts as the most likely scenario. However, the fact that most countries are engaged in the restructuring of their navies does not mean they are engaged in an arms race, a behaviour where every country increases its military capacity in reaction to the neighbours’ developments. The overall picture of Arctic military evolution is one of limited modernization, limited increases or change in equipment. There has indeed been some modest military buildup by the Arctic states, and often the new equipment was replacement, not expansion. But that buildup hardly signals aggressive designs. Rather, it seems little more than a prosaic response to expanded jurisdictional space with the melting of the ice, and continued resource development

Le statut des expériences de pensée en philosophie

Les expériences de pensée sont des situations hypothétiques qui cherchent à critiquer ou défendre des théories et des concepts. Leur utilisation est répandue dans une multitude de disciplines, autant en science qu’en philosophie. Malgré sa popularité dans les débats philosophiques, l’usage des expériences de pensée est contesté. Par contre, en science elles sont acclamées. Est-ce que les expériences de pensée en science et en philosophie font partie de la même méthode? Nous avons examiné la thèse de Sorensen (1992) qui défend qu’il n’y a pas de différence disciplinaire entre les EP. Le premier chapitre est consacré à l’examen de la thèse de Sorensen. Le deuxième chapitre exposera les critiques de Sorensen. Dans le troisième chapitre, nous répondrons aux critiques établis dans le deuxième chapitre, ainsi qu’aux critiques sceptiques qui attaquent la légitimité de cette méthode. Nous défendrons une thèse expérimentaliste qui assure le caractère informatif et légitime des expériences de pensée, plus particulièrement en philosophie