Thermocapillary motion of a two-bubble cluster near a plane solid wall

The thermocapillary motion of two bubbles near a plane solid wall at uniform temperature is investigated by solving five boundary integral-equations. Preliminary computations show that wall–bubble interactions dictate the migration of equal bubbles with line of centers parallel to the wall. To cite this article: A. Sellier, C. R. Mecanique 333 (2005).     

Electrophoresis of a 2-particle cluster near a plane boundaryElectrophorèse de deux particules en présence d'une paroi plane

Particle–boundary and particle–particle interactions in Electrophoresis are examined by considering a 2-particle cluster near a plane boundary. The advocated treatment holds for two insulating particles of arbitrary shapes and zeta potential functions and resorts to 13 boundary-integral equations. Preliminary results reveal that, depending upon the addressed velocity nature (translational or angular), wall–particle may be stronger or weaker than particle–particle interactions. To cite this article: A. Sellier, C. R. Mecanique 331 (2003).     

On the slow motion of a cluster of bubbles under the combined action of gravity and thermocapillarity

The slow migration of N spherical bubbles under combined buoyancy and thermocapillarity effects is investigated by appealing solely to $3N+1$ boundary-integral equations. In addition to the theory and the associated implementation strategy, preliminary numerical results are both presented and discussed for a few clusters involving 2, 3, 4 or 5 bubbles with a special attention paid to the case of rigid configurations. To cite this article: A. Sellier, C. R. Mecanique 333 (2005).     

Gravitational motion of a two-particle cluster between two parallel plane solid wallsSédimentation de deux particules solides entre deux plans parallèles

The slow viscous settling migration of a 2-particule cluster between two solid and parallel plane walls is investigated by resorting to a Boundary Element Method. The procedure, valid for arbitrarily-shaped bodies, is presented and preliminary numerical results for both identical spheres and a spheroid-sphere cluster are discussed. To cite this article: L. Pasol, A. Sellier, C. R. Mecanique 334 (2006).     

On particle–particle interactions in solid,non-conducting impurity removalSur l'interaction particule–particule lors de l'extraction d'impuretés solides isolantes

A whole boundary-integral formulation is proposed to determine the rigid-body motions of two solid and insulating particles, freely-suspended in a metal liquid and subject to uniform ambient electric and magnetic fields. As revealed by our numerical results, particle–particle interactions may become significant for close enough bodies. To cite this article: A. Sellier, C. R. Mecanique 331 (2003).     

Turbulence from 1870 to 1920: The birth of a noun and of a concept

We consider here the works of French, British, and German researchers in fluid mechanics from 1870 to the beginning of the twentieth century. Our aim is to understand how the term “turbulence” introduced by William Thomson in 1887, which was not used by the main researchers of the time, including Joseph Boussinesq, Osborne Reynolds, Lord Rayleigh, Horace Lamb in the first editions of his book, became classical in the 1920s. We trace the first introductions of the terms “turbulence”, “turbulent flow” in the works of relatively unknown researchers between 1889 and 1903, until it reaches the vocabulary of mainstream researchers in fluid mechanics and physics. Our result is that the shift was in 1906–1908, when the term was used in the 1906 edition of the book of Horace Lamb, and in Lanchester's book, followed by a series of papers of German researchers before the First World War.The use of the word “turbulence”, a word used for a long time for crowds or for children, in a scientific context, corresponds to the introduction of a new concept, a new understanding of a scientific phenomenon clearly identified as being different from laminar motion. The study of the use of this term is also the study of the diffusion of a new concept among researchers of the time.     

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).     

On the slow gravity-driven migration of arbitrary clusters of small solid particles

A new approach is advocated to compute at a low cpu time cost the rigid-body motions of settling solid particles when inertial effects are negligible. In addition to the relevant boundary-integral equations, the numerical implementation and a few convincing benchmark tests we address two configurations of equivalent spheres and spheroids, i.e. that exhibit when isolated the same settling velocity. To cite this article: A. Sellier, C. R. Mecanique 332 (2004).

Résumé

On propose une approche originale pour déterminer le mouvement d'une assemblée de particules solides et de formes arbitraires soumise à l'action de la pesanteur dans l'approximation de Stokes. Outre les intégrales de frontière et la méthode numérique associées on présente quelques comparaisons et examine le cas de deux configurations de sphères et ellipsoides de révolution équivalents, c'est-à-dire dotés lorsqu'ils sont seuls de la même vitesse de sédimentation. Pour citer cet article : A. Sellier, C. R. Mecanique 332 (2004).     

Amelioration de technique d'intensimetrie hydroacoustiqueImprovement of hydro-acoustic intensity technique

For industrial applications, a transfer matrix model can be used to study pressure and flow rate fluctuations propagation within ducts. If none analytical model exists, this matrix has to be identified according to acoustic intensity techniques.Pressure waves exert forces, which cause a compliant system to move, the motion causes pressure waves in return (fluid–structure interaction). An extension of acoustic intensity technique using several transducers is presented. To cite this article: J. Charley, C. R. Mecanique 331 (2003).     

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).     

Instabilité non linéaire dans un milieu en expansionNonlinear instability in a expanding medium

We consider nonlinear acoustical phenomena, explosive instabilities and a formation of localized structures in nonstationary environment. An example of such a medium is our Universe in expansion considered as a fluid submissive to a gravitational self-concorded force field and governed by the classical hydrodynamics equations. We show that the taking into account of the nonlinear effects allow us to understand the causes of the appearance of the specific nonlinear instability, which is calling explosive instability. This type of instability is more fast, $～\ln [{(t_0?t)}^{\mathrm{?1}}]$ for density fluctuation, that the habitual instability (exponential, $～{\mathrm{e}}^{\gamma t}$): at the end of a finite time, all spatial inhomogeneity of the initials conditions lead to a formation of singularities in the fields. This phenomena will be appear if certains conditions for the initials amplitudes and wavelengths of the fluctuations are observed. To cite this article: F. Henon, V. Pavlov, C. R. Mecanique 334 (2006).     

Détermination de la résonance de Bragg et des largeurs des bandes interdites par le modèle d'onde plane corrigéDetermination of the Bragg resonance and line width of forbidden bands using the corrected plane wave model

During the interaction of the swell with a sea bottom composed of a set of steps, using the model of plane wave corrected by the effective length: (1) We determine the exact position of the Bragg resonance in case of a periodic bottom or containing a periodic part; (2) The determination of forbidden band widths is brought back to the study of the sign of the discriminant of the polynomial characteristic of the matrix of transfer of the generating motive of the periodic part of the bottom; (3) One can increase the width of the forbidden band while using some slightly increasing or decreasing length steps. To cite this article: S. Naasse et al., C. R. Mecanique 331 (2003).     

On the stability of a Bingham fluid flow in an annular channelSur la stabilité de l'écoulement d'un fluide de Bingham dans une conduite annulaire

Linear stability of a fully developed Bingham fluid flow between two coaxial cylinders subject to infinitesimal axisymetric perturbations is investigated. The analysis leads to two uncoupled Orr–Sommerfeld equations with appropriate boundary conditions. The numerical solution is obtained using fourth order finite difference scheme. The computations were performed for various plug flow dimensions and radii ratios. Within the range of the parameters considered in this paper, the Poiseuille flow of Bingham fluid is found to be linearly stable. To cite this article: N. Kabouya, C. Nouar, C. R. Mecanique 331 (2003).     

Drop impingement on a deep liquid surface: study of a crater's sinking dynamicsImpact d'une goutte sur une surface liquide profonde : étude de la dynamique d'enfoncement du cratère

When there is a drop impact on a liquid surface, two phenomena can appear depending on the impact Weber number: either vortex generation or jet formation; in this paper the second behavior is dealt with. Based on the comparison of experimental and theoretical results, the dynamic of splashing drops on deep liquid surfaces is analyzed; this work focuses on the crater's evolution and its maximum. The liquids used are water and ethyl-alcohol. Drop impacts are made with various impact velocities by creating drops from several heights above the liquid surface. A straightforward model to describe and predict the crater's sinking evolution is proposed and agrees well with the experimental results over a range of Weber numbers from 50 to 1500. To cite this article: D. Brutin, C. R. Mecanique 331 (2003).     

Dispersion de particules solides en mouvement de saltation dans un écoulement turbulentDispersion of solid saltating particles in a turbulent flow

The solid particle dispersion in saltating motion is studied in an homogeneous turbulence and in a turbulent boundary layer. The fluid velocity along the particle trajectory is estimated using a continuous stochastic differential equation in which the correlation integral time takes into account gravity and inertia effects. As far as the boundary layer is concerned, the aerodynamic entrainment of particles and the rebound are modelised as random variables with Gaussian probability density functions. Compared with experimental results, the numerical results show good agreement for dispersion, although velocity fluctuations are slightly under evaluated. To cite this article: C. Aguirre et al., C. R. Mecanique 332 (2004).     

Migration d'une particule ellipsoı̈dale conductrice sous l'action d'un champ électromagnétique uniformeMigration of a conducting ellipsoid subject to uniform ambient electric and magnetic fields

We obtain analytically, within a relevant framework, the rigid-body motion of a solid, conducting and ellipsoidal particle immersed in a liquid metal and subject to uniform ambient electric and magnetic fields. The motion experienced exhibits a few basic properties that are briefly discussed. To cite this article: A. Sellier, C. R. Mecanique 331 (2003).     

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).     

An optimality condition on the minimum energy threshold in subcritical instabilities

For flows subject to subcritical instabilities the stability of the basic flow can be guaranteed only for perturbations of energy lower than a critical threshold δ. The computation of this threshold for the Navier–Stokes equations is still out of reach. More surprisingly, this computation has not been attempted for low dimensional models of subcritical transition. In this Note guidelines are provided for the computation of the minimum energy threshold δ and of the corresponding nonlinear optimal perturbations. In particular it is demonstrated that nonlinear optimal perturbations are constrained by the requirement that they must satisfy a local minimum condition. These results are applied to the analysis of four-dimensional models proposed in F. Waleffe, Phys. Fluids 7 (1995) and Phys. Fluids 9 (1997). To cite this article: C. Cossu, C. R. Mecanique 333 (2005).     

Amortissement visqueux d'un résonateur mécanique en environnement gazeuxViscous damping of a mechanical resonator in a gaseous environment

We study dissipation phenomena due to the presence of a gaseous environment, leading to the damping of the oscillations in vibrating systems such as mechanical resonators. In the so-called “viscous” pressure region (p ranging between 10^?3 mbar and 1 bar), we suggest a simple model allowing an order of magnitude analysis of the dissipation mechanisms. This model, based on the classical form of the energy conservation equation in fluid mechanics, leads to a p^1/2 variation scale for the dissipation. In addition, we present experimental results that are found to be in good agreement with the predictions of the model. To cite this article: D. Perret et al., C. R. Mecanique 331 (2003).