Large-amplitude internal solitary waves in a two-fluid modelOndes solitaires internes de grande amplitude dans un modèle à deux fluides

We compute solitary wave solutions of a Hamiltonian model for large-amplitude long internal waves in a two-layer stratification. Computations are performed for values of the density and depth ratios close to oceanic conditions, and comparisons are made with solutions of both weakly and fully nonlinear models. It is shown that characteristic features of highly nonlinear solitary waves such as broadening are reproduced well by the present model. To cite this article: Ph. Guyenne, C. R. Mecanique 334 (2006).     

Accurate simple approximation for the solitary waveApproximation simple et précise de l'onde solitaire

This Note investigates the effect of a renormalization technique on high-order shallow water approximations of gravity waves. The method is illustrated for the solitary surface wave. Applied to the solution of a generalized KdV equation, it is shown that the renormalization significantly increases the accuracy. To cite this article: D. Clamond, D. Fructus, C. R. Mecanique 331 (2003).     

Selection of two-dimensional nonlinear strain waves in micro-structured mediaSelection d'ondes de déformation non linéaires à deux dimensions dans des milieux à microstructure

It is shown that the micro-displacement gradient allows the propagation of two-dimensional localized long nonlinear strain waves in a medium with microstructure. These waves may exist even in the presence of dissipation and energy input in the microstructured medium but with selected values of the wave amplitude and velocity. An increase or a decrease in the wave amplitude and velocity happens faster at the initial stage than that of the plane localized wave. However, their steady values selected by the energy input/output, are higher for the plane waves. To cite this article: A.V. Porubov et al., C. R. Mecanique 332 (2004).     

High-order evolution equation for nonlinear wave-packet propagation with surface tension accountingÉquation d'évolution d'ordre élevé de groupes d'ondes non linéaires en présence de tension superficielle

The nonlinear problem for propagation of wave-packets along the interface of two semi-infinite fluids is solved on the basis of multiple scale asymptotic expansions. Unlike all previous investigations dealing only with third-order approximations, here fourth-order approximation is developed. The corresponding solvability condition is obtained and the evolution equation in the case away from the cut-off wave number is derived. As a result, the nonlinear higher-order Schrödinger equation is obtained which contains the nonlinear part in a compact form. This equation is valid for a wide range of wave numbers. The stability diagram shows regions of stability and instability of capillary-gravity wave-packets. To cite this article: I. Selezov et al., C. R. Mecanique 331 (2003).     

Multi-shock structure of roll wavesStructure multi-chocs d'ondes à rouleaux

The special class of periodic travelling waves which is known as roll waves is investigated for nonhomogeneous hyperbolic equations of gas dynamics type. In this Note these equations are applied to shallow water flows in inclined open channels, but the results obtained are more general and far-reaching. The necessary conditions for the existence of a roll wave are derived. It is shown that for a nonconvex pressure term, multi-shock configurations of roll waves of finite amplitude exist. A new type of periodic travelling wave, which corresponds to the slug flow regime in two-layer flows, is found. To cite this article: A. Boudlal, V.Yu. Liapidevskii, C. R. Mecanique 332 (2004).     

An explicit asymptotic model for the Bleustein–Gulyaev waveUn modèle explicite pour l'onde de Bleustein–Gulyaev

The antiplane motion of a transversely isotropic piezoelectric half-space is considered. An explicit asymptotic model is derived for the far field of the surface wave. It involves, in particular, a 1D hyperbolic equation for surface shear deformation propagating with the finite wave speed predicted for the first time by J.L. Bleustein and Yu.V. Gulyaev. Neumann and Dirichlet problems are formulated to restore interior mechanical and electric fields. The derivation utilizes asymptotic arguments combined with Lourier symbolic integration. Comparison with the exact solution is presented for surface impact loading. To cite this article: J. Kaplunov et al., C. R. Mecanique 332 (2004).     

On the Navier–Stokes equations simulation of the head-on collision between two surface solitary waves

The scope of this Note is to show the results obtained for simulating the two-dimensional head-on collision of two solitary waves by solving the Navier–Stokes equations in air and water. The work is dedicated to the numerical investigation of the hydrodynamics associated to this highly nonlinear flow configuration, the first numerical results being analyzed. The original numerical model is proved to be efficient and accurate in predicting the main features described in experiments found in the literature. This Note also outlines the interest of this configuration to be considered as a test-case for numerical models dedicated to computational fluid mechanics. To cite this article: P. Lubin et al., C. R. Mecanique 333 (2005).     

Dynamics of irregularly shaped bodies in a flow behind a shock waveLa dynamique des corps de forme irrégulière dans un écoulement derrière une onde de choc

For the first time, the multi-frame shadow visualization technique coupled with a laser stroboscopic source of light has been used to obtain data on the dynamics of irregularly shaped bodies in the flow behind shock wave. A procedure for determining body acceleration from body trajectory is proposed, which, together with the diagnostic technique used, represents a kind of contactless aerodynamic balance. Drag data for spheres and irregularly shaped bodies in the flow behind shock wave with Mach number of 0.5 to 1.5 and Reynolds number of 10⁵ are reported. To cite this article: V.M. Boiko, S.V. Poplavski, C. R. Mecanique 332 (2004).     

Une méthode de calcul des coefficients de réflexion et de transmission d'une houle bidimensionnelle en milieu confinéA new method for the calculation of transmission and reflection coefficients for water waves in a small basin

This paper presents a method to estimate reflected and transmitted wave amplitude spectra in a bounded domain such as a wave tank, when available data signals must be shortened due to interferences and wall effects. This paper extends the well known Goda and Suzuki two-probe method to three probes. The paper also suggests solutions to compute reliable transmission and reflection coefficients in spite of problems linked to higher harmonics and to the interference between different wave trains propagating in the tank. To cite this article: G. Duclos, A.H. Clément, C. R. Mecanique 331 (2003).     

On the existence of the low-frequency surface waves in a porous mediumSur l'existence des ondes de surface basse fréquence en milieux poreux

The existence and propagation of the surface waves at a vacuum/porous medium interface are investigated in the low frequency range. Two types of surface waves are shown to be possible: the generalized Rayleigh wave, which always exists, and the Stoneley wave, which exists for a limited range of wave numbers. Moreover, within the k-domain of existence the Stoneley wave cannot appear for certain values of elastic parameters of the solid phase. The bifurcation behavior of both the Stoneley wave and the Biot (P2) bulk wave, depending on the wave number, is revealed. The asymptotic formulas for the phase velocities of the surface waves are derived. To cite this article: I. Edelman, C. R. Mecanique 332 (2004).     

Interaction soliton–sable dans un canal en eau peu profonde

Interaction between solitons and a sandy bed in shallow water is investigated. In our experiments, solitons are generated on the background of a harmonic wave, in a wave flume used in resonant mode. It is found that the sand ripples formed by the solitons propagation induce a significant decrease of solitons amplitude and of the phase shift between the soliton and the harmonic wave. However, the amplitude of the harmonic wave is approximately constant. The possible physical processes of such behaviour for the soliton amplitude and for the harmonic wave amplitude are discussed. To cite this article: F. Marin et al., C. R. Mecanique 333 (2005).     

On the impact of anisotropy on dispersion spectra of acoustic waves in platesImpact de l'anisotropie sur les spectres de dispersion des ondes élastiques dans des plaques

A brief overview is given of specific features that can (or cannot) appear in the dispersion spectra of traction-free elastic homogeneous plates due to anisotropy. Its effect on the overall spectral configuration and on the short and long wave trends is illuminated with a link to anisotropic traits of bulk and surface waves. Relevant classical and recent results are put together, and new points are established. To cite this article: A.L. Shuvalov, C. R. Mecanique 334 (2006).     

Self-demodulation acoustic signatures for nonlinear propagation in glass beadsSignatures acoustiques de l'auto-démodulation basse fréquence lors de la propagation non linéaire dans des billes de verres

The present Note describes some experimental work related to the nonlinear propagation of acoustic waves in granular media such as unconsolidated glass beads. The studied nonlinear effect is a self-demodulation process performed with the operation of the so-called parametric transmitting antenna. The pump (or carrier) wave is generated by a high power ultrasonic broad-band transducer (100 kHz central frequency) which is LF (low frequency, i.e., a few kHz) amplitude modulated. As the attenuation of acoustic waves increases with frequency, only the LF demodulated wave can be transmitted. A parametric study is performed where the HF central frequency is monitored between 60 and 300 kHz. The LF demodulation profile versus the HF frequency is modified, its shape being temporally derived almost twice. A numerical analysis of the order of temporal derivation is done in the Fourier domain, its value varying from 1.25 to 2.7. Qualitative agreement with current theoretical models is described, and an advanced theoretical analysis by the same authors [Phys. Rev. E 66 (2002) 041303], taking into account absorption, nonlinearity, dispersion and scattering, is briefly discussed. To cite this article: V. Tournat et al., C. R. Mecanique 331 (2003).     

Phénomènes de vacillation d'amplitude pour un écoulement d'air en cavité tournante différentiellement chaufféeAmplitude vacillation phenomena in an air-filled differentially heated rotating annulus

A direct numerical simulation is carried out to describe the amplitude vacillation phenomena appearing between two successive steady regular waves flows in an air-filled differentially heated rotating annulus. For a fixed temperature difference, ΔT=30 K, when varying progressively the rotation rate, we have obtained the occurrence of the two amplitude vacillation instabilities observed experimentally by Read et al. (J. Fluid Mech. 238 (1992) 599–632) with a high Prandtl number fluid. The first one, denoted AV is characterized by a doubly periodic temporal behaviour with a periodic variation of wave amplitudes, while the second one corresponds to a torus-3 quasi-periodic or chaotic motion with the presence of a modulation in the wave amplitudes evolution. To cite this article: P. Maubert, A. Randriamampianina, C. R. Mecanique 331 (2003).     

Non-propagating solitary waves with the consideration of surface tension

In this paper, the governing equation for the non-propagating solitary waves, similar to the cubic Schrödinger equation, is derived by the multiple scales with the consideration of surface tension. The non-propagating solitary wave solution is given. It is explained by the capillary-gravity wave theory that the crests are sharpened and the troughs are flattened in the transversal harmonic of the non-propagating solitary waves. On σ～kh plane, two parameter regions are obtained in which the non-propagating solitary wave can occur, but all existing experimental parameters are in region 1 (Fig. 1).     

Propriétés élastiques non linéaires d'un milieu mésofissuréNonlinear elastic properties of a mesocracked medium

It is shown that the influence of closed frictionless cracks on overall elasticity can be evaluated by estimates based on Eshelby's theory. The idea consists in replacing the closed cracks by a ficticious material with shear modulus equal to 0 and a bulk modulus identical to that of the solid. Progressive crack closure is responsible for the nonlinearity of the overall elasticity. From this phenomenon, the distribution of crack density as a function of the initial aspect ratio can be determined. To cite this article: V. Deudé et al., C. R. Mecanique 330 (2002) 587–592.     

Modélisation probabiliste d'une expérience ultrasonore : calcul de la dispersion sur les mesures de célérité

This Note presents a probabilistic model of transient wave reflection at a fluid–solid interface. The configuration represents an ultrasonic experiment used for bone tissue evaluation. The parametric method is used to derive the probabilistic model for the mechanical parameters of the solid (bone); the associated random variables are derived according to the maximum entropy principle. A Monte Carlo simulation, associated with the Cagniard–de Hoop method to calculate the acoustic response, yields the probability density for an output ultrasonic parameter similar to the velocity of longitudinal waves in the solid. Results demonstrate the sensitivity of the probability density of this parameter to the experimental setup. To cite this article: K. Macocco et al., C. R. Mecanique 333 (2005).     

Modélisation thermodynamique du frottement interne et de l'hystérésis d'un élastomèreThermodynamics modelling of internal friction and hysteresis of elastomers

The study of the physical structure of filled elastomers makes us able to identify the state variables needed to model the behavior of elastomeric materials. We build a thermodynamics potential (written for finite strains and in 3D) which accounts for the nonlinearity of the behavior, for a hysteresis independent of the time and of the loading rate and for Mullins effect, this without introducing damage. The model can be coupled with damage to predict the crack initiation conditions under monotonic and/or cyclic loading. To cite this article: S. Cantournet, R. Desmorat, C. R. Mecanique 331 (2003).