On a mis au point des methodes de calcul permettant de determiner des grandeurs physiques moyennes (vitesse, pression) et turbulentes (énergie cinétique turbulente, tension de Reynolds, dissipation, etc.) dans un écoulement décollé turbulent incompressible, provoqué par l'élargissement brusque d'un conduit cylindrique. La première methode de calcul utilisant le concept de viscosité turbulente effective, avec des equations de type elliptique du fait de la recirculation, a permis la prevision de l'écoulement s'éten-dant depuis la section du décollement jusqu'au rétablissement complet de l'écoulement, loin en aval. La deuxième methode est consacrée plus particulièrement a la zone rétablissement de l'écoulement qui se développe a partir du recollement, le caractère parabolique des equations dans cette zone a permis par contre l'application des modèles contenant des equations de transport de la contrainte de Reynolds, sans le concept de viscosité turbulente. L'ensemble des calculs sera compare aux résultats expérimentaux obtenus d'une part au laboratoire, sur un modèle aérodynamique dans lequel on a étudié l'influence de plusieurs paramètres d'entrée (couche limite initiale, nombre de Reynolds, rapport d'élargissement) et d'autre part par divers auteurs. La comparaison calculs théoriques-mesures expérimentales a conduit a une description sur le mécanisme de transfert de l'énergie cinétique turbulente et du frottement turbulent.Summary Methods are developed for calculation of mean velocity and pressure and mean turbulent kinetic energy, Reynolds tension, dissipation, etc. in turbulent incompressible flow after separation at a sudden increase in the cross-section of a circular duct. One method, based on the concept of effective turbulent viscosity and elliptical equations (because of the recirculation taking place), has allowed prediction of flow conditions from the point of separation to that a long way downstream at which normal flow is restored. Another method is associated more especially with the area in which normal flow is restored after readhesion; as the governing equations in this zone are parabolic, it has been possible to apply models containing Reynolds stress transport equations without the turbulent viscosity concept. The overall calculated data are compared with experimental results determined on an aerodynamics model used to study the effect of the initial boundary layer, Reynolds number and the cross-sectional expansion factor, and with other authors' data. Turbulent kinetic energy and friction transfer mechanisms are described in terms of the results of the comparison between theoretical and experimental data. Recu le 9/4/76 et revise le 30/10/76 Ha Minh Hieu et Hebrard j Etude théorique et expérimentale d'un écoulement décollé 1 Downloaded by [University of Ulster Library] at 03:57 15 December 2014

The nexus between natural resources and environmental degradation has significant implications. Nevertheless, this domain is insufficiently examined. This paper therefore a examines the time-frequency influence of economic growth, human development, and urbanisation on Vietnam’s ecological footprint (EF) using wavelet analysis. The findings showed that the intercorrelation between EF and related variables is statistically significant at low, medium, and high frequencies. More importantly, the elationships between these variables occur at a high frequency, which means that EF, economic growth (GDP), human development index (HDI), and urbanisation (UB) have different fluctuations in the long run. These outcomes are also confirmed by the wavelet-based Granger causality test at various time scales, which supports our relationship results

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