Evolution de la fonction de répartition d'un gaz de tourbillons 2D en présence d'un bruitEvolution of the repartition function of 2D vortex gaz in presence of noise

In this work, we study the motion of N localized vortices in the presence of ‘noise’. To apply the methods of statistical mechanics, we determine the evolution equation for the probability density function of vortices in which the presence of the ‘noise’ is accounted for by as a term similar to viscosity. This equation is isomorph to the system of equations which describe 2D turbulence with viscosity. The advantage of this formulation is that it can be numerically implemented at very large Reynolds numbers. To cite this article: S. Decossin, V. Pavlov, C. R. Mecanique 331 (2003).     

Étude expérimentale des transferts de chaleur fluide-paroi induits par convection thermocapillaire : influence du nombre de PrandtlExperimental study of fluid-wall heat transfer induced by thermocapillary convection: influence of the Prandtl number

This article concerns heat transfer due to thermocapillary convection induced by an air bubble introduced under a heated wall into a silicone oil layer. An experimental study is carried out under normal gravity conditions with direct measurements by means of a heat fluxmeter. Effects of the bubble size and the temperature gradient are systematically investigated for two values of viscosity. The nature of the thermocapillary convection state (stationary or oscillatory) is determined by shadowgraphy. Two regimes of heat transfer are made evident. They depend on the Prandtl number but are independent of the state of the flow. To cite this article: C. Reynard et al., C. R. Mecanique 331 (2003).     

The mixing layer instability of wind over a flexible crop canopyInstabilité de couche de mélange dans le vent sur un couvert végétal souple

A coupled fluid-stucture model is proposed to study the dynamics of a flexible crop canopy exposed to wind. The canopy is represented by an elastic continuous medium and coupled to the wind mixing layer through a drag load. The mixing layer instability is shown to remain the principle instability mechanism but its characteristics are modified when taking into account the flexible canopy. The size of the coherent structures is decreased as well as the instability growth rate. To cite this article: C. Py et al., C. R. Mecanique 332 (2004).     

Dispersion de Taylor généralisée à un fluide à propriétés physiques variablesGeneralized Taylor dispersion for heterogeneous fluid

The investigation of non-reactive miscible solute dispersion in a vertical Hele–Shaw cell is considered. An asymptotic method is used to extend Taylor model to the case of the fluid density, the dynamic viscosity and the molecular diffusion coefficient are solute concentration-dependent. It is demonstrated that the averaged variables over the gap are governed by a convection–dispersion equation in which the dispersion tensor is concentration-dependent. To cite this article: C. Felder et al., C. R. Mecanique 332 (2004).     

On the nature of the boundary layers instabilities in a flow between a rotating and a stationary discSur la nature des instabilités de couche limite dans un écoulement entre un disque fixe et un disque tournant

Both theoretical linear stability analysis and direct numerical simulation are performed to study the transition flow between a stationary and a rotating disc. This paper concerns three-dimensional spiral and annular patterns computed with a high-order (spectral) numerical method and related to Bödewadt layer instabilities. The characteristic parameters of these boundary layer patterns are compared to the theoretical results and interpreted in terms of type I and type II generic instabilities. Moreover, the absolute instability regions are also theoretically identified and the critical Reynolds numbers of the convective/absolute transition in both layers are given. To cite this article: E. Tuliska-Sznitko et al., C. R. Mecanique 330 (2002) 91–99.     

Experimental observation of the straining field responsible for vortex ring instabilityObservation expérimentale du champ responsable de l'instabilité du tourbillon torique

The aim of this work is to show experimentally the straining field responsible for the vortex ring instability. To do so, the velocity field in the neighbourhood of the core is measured with Particle Image Velocimetry. This field is compared with the one coming from theoretical work on a thin vortex ring in an ideal fluid. Theoretical and experimental data fit well. This indicates that the linear phase of the instability is weakly influenced by viscosity. To cite this article: A. Dazin et al., C. R. Mecanique 332 (2004).     

Sur la réponse transitoire d'une couche solidaire d'un milieu semi-infini ; application à un impact sur le thoraxOn the transient response of a layer welded to a half-space; an insvestigation of impact on the thorax

The theory of generalized rays is dedicated to the investigation of the transient response of elastic layered media. It yields exact solutions, whatever the duration of the applied impulse (i.e., for any frequency content of the excitation). This Note is part of a research project on the modeling of non-penetrating impact on thorax. We investigate a simplified model of the thoracic wall – a layer welded to a semi-infinite medium – submitted to an impulse of variable duration. Among other things, it is found that the response computed for a “long” impulse is consistent with a result of the classical plate theory. To cite this article: Q. Grimal et al., C. R. Mecanique 331 (2003).     

Asymptotics at infinity of solutions to the Neumann problem in a sieve-type layerComportement asymptotique à l'infini d'un problème de Neumann dans une couche perforée

The Neumann problem is considered in a domain $\text{Ω}$, which can differ from a periodic layer inside a compact set. We prove the Fredholm property of the corresponding operator in step-weighted Sobolev spaces and determine its kernel and cokernel. All these results are based on the obtained asymptotic representation of solutions at infinity. To cite this article: S.A. Nazarov, G. Thäter, C. R. Mecanique 331 (2003).     

Simulation numérique directe de l'influence de la forme aval d'une plaque séparatrice sur une couche de mélangeDirect-numerical simulation of the splitting-plate downstream-shape influence upon a mixing layer

In this Note, we present direct numerical simulation results of a spatial mixing layer generated behind an upstream plate separating two boundary layers. The effect of the shape of the trailing edge of the plate is considered through comparisons between flows obtained from a bevelled or a blunt plate. In the former case, a spatial mixing layer consistent with previous experimental and numerical observations is obtained. In the latter case, the self-excited state that establishes in the near wake region dominates primary and secondary instability mechanisms while understating the importance of inflow perturbations. This behaviour is interpreted in terms of convective or absolute instability. The effects on turbulent statistics are also discussed. To cite this article: S. Laizet, E. Lamballais, C. R. Mecanique 334 (2006).     

Homogénéisation d'un milieu élastique fortement hétérogèneHomogenization of a strongly heteregeneous elastic medium

We consider the homogenization of an elastostatic problem in a strongly heterogeneous periodic medium made of two connected components having comparable tensors of elastic moduli, separated by a third medium (soft layer), the thickness of which is of the same order ε than the basic periodicity cell, and such that its elastic moduli tensor becomes infinitely small following a rate ε^r, r>0. If r?2, we identify the homogenized problem. Otherwise, we have to assume moreover that there are no volume forces in the third medium. To cite this article: M. Mabrouk, A. Boughammoura, C. R. Mecanique 330 (2002) 543–548.     

Effet de l'orientation d'un champ magnétique horizontal sur la stabilité de l'écoulement de HadleyEffet of the orientation of a horizontal magnetic field on the stability of Hadley flow

A numerical study based on the linear stability analysis is undertaken, in order to determine the influence of a horizontal magnetic field on the marginal modes occuring in a fluid layer subjected to a horizontal temperature gradient. A particular interest is devoted to the influence of the magnetic field orientation on both nature and critical values of the unstable modes. Calculations show, that when it is subjected to such a magnetic field, this type of flow, known as Hadley flow, can present oblique waves, hitherto non-existent when no magnetic field is applied and even when a vertical, a transverse or a longitudinal magnetic field is imposed. A new asymptotic behavior is also observed for the stabilizing effects. To cite this article: S. Kaddeche et al., C. R. Mecanique 331 (2003).     

Crack tip behavior in near-surface fluid-driven fracture experiments

This Note presents experimental results for the near-tip fracture opening of fluid-driven fractures. The effect of fluid viscosity, quantified by a dimensionless parameter, was varied between tests. The tip region closely followed the classical square-root behavior from linear elastic fracture mechanics when the viscosity parameter was small. Conversely, when the viscosity parameter was of order one and the lag between the fluid-filled region and the fracture front accounted for less than 30% of the fracture, the tip region behaved according to a known intermediate asymptotic solution which results from the solid/fluid coupling. To cite this article: A.P. Bunger et al., C. R. Mecanique 333 (2005).     

Boundary layer sensitivity and receptivitySensibilité et réceptivité d'une couche limite

The relation between the receptivity and the sensitivity of the incompressible flow in the boundary layer over a flat plate to harmonic perturbations is determined. Receptivity describes the birth of a disturbance, whereas sensitivity is a concept of larger breath, describing the modification incurred by the state of a system as a response to parametric variations. The governing equations ruling the system's state are the non-local stability equations. Receptivity and sensitivity functions can be obtained from the solution of the adjoint system of equations. An application to the case of Tollmien–Schlichting waves spatially developing in a flat plate boundary layer is studied. To cite this article: C. Airiau et al., C. R. Mecanique 330 (2002) 259–265.     

Active control of the aeroacoustics of cavity flows from the downstream edge

Active control of the aeroacoustics of flow-induced oscillations in a rectangular cavity using a vibrating plate inserted at the downstream edge is demonstrated. Pressure and phase-locked Particle Image Velocimetry measurements show that the oscillations of the mixing layer can be controlled in order to attenuate or amplify the radiated sound. Results obtained from a previously developed analytical model are used to characterize the effects of the control. To cite this article: L. Chatellier et al., C. R. Mecanique 334 (2006).     

Effets d'une modulation en phase de température à la frontière sur l'instabilité convective d'une couche liquide viscoélastiqueEffects of a temperature modulation in phase at the frontier on the convective instability of a viscoelastic layer

In this Note we study the effects of the temperature modulation, applied at the horizontal boundaries, on the onset of convection of a horizontal liquid Maxwellian layer. It is assumed that the temperature imposed features a steady component and a time dependent component. To analyse the effect of the temperature modulation, the study is restricted to a linear stability analysis. Thus the Floquet theory and a technique of converting a boundary value problem to an initial value problem are used to solve the system of equations corresponding to the onset of convection. Results obtained may be used to characterize the influence of modulation effects and that of the viscoelastic nature of liquid on the critical Rayleigh number. To cite this article: B. Oukada et al., C. R. Mecanique 334 (2006).     

Experimental study of a hypersonic shock layer stability on a circular surface of compressionL'étude expérimentale de la stabilité d'une couche de choc hypersonique sur une surface circulaire de compression

The method of electron-beam fluorescence is applied to study the evolution of natural and artificial periodic disturbances on a developed streaky structure in the shock layer on a circular compression surface model. The model is exposed to a hypersonic nitrogen flow with a Mach number M_∞=21 and unit Reynolds number Re_1∞=6×10⁵ m^?1. Data on the effect of surface curvature and temperature on disturbance characteristics are obtained. To cite this article: S.G. Mironov, V.M. Aniskin, C. R. Mecanique 332 (2004).     

Noise reduction of a Mach 0.7–0.9 jet by impinging microjetsRéduction du bruit d'un jet de Mach 0,7–0,9 par un système de microjets impactants

A global noise reduction of a high-subsonic jet is achieved by experimental use of an impinging microjets system. The microjet velocity relative to the main jet velocity, the longitudinal distance of injection and the number of microjets are the three parameters examined in order to obtain the maximum noise reduction. This optimized microjet configuration is obtained by a balance between low-frequency attenuation and high-frequency noise generation due to the interaction between the microjets and the main jet mixing layer. To cite this article: T. Castelain et al., C. R. Mecanique 334 (2006).     

Stability of a hypersonic shock layer on a flat plateStabilité d'une couche de choc hypersonique sur une plaque plane.

Stability of a hypersonic shock layer on a flat plate is examined with allowance for disturbances conditions on the shock wave within the framework of the linear stability theory. The characteristics of the main flow are calculated on the basis of the Full Viscous Shock Layer model. Conditions for velocity, pressure, and temperature perturbations are derived from steady Rankine–Hugoniot relation on the shock wave. These conditions are used as boundary conditions on the shock wave for linear stability equations. The growth rates of disturbances and density fluctuations are compared with experimental data obtained at ITAM by the method of electron-beam fluorescence and with theoretical data of other authors. To cite this article: A.A. Maslov et al., C. R. Mecanique 332 (2004).