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Thomas R.,Institute Of Recherche Sur Les Phenomenes Hors Equilibre | Kharif C.,Ecole Centrale Marseille | Manna M.,Montpellier University | Manna M.,CNRS Charles Coulomb Laboratory
Physics of Fluids | Year: 2012

A nonlinear Schrödinger equation for the envelope of two dimensional surface water waves on finite depth with non-zero constant vorticity is derivedthe influence of this constant vorticity on the well-known stability properties of weakly nonlinear wave packets is studied. It is demonstrated that vorticity modifies significantly the modulational instability properties of weakly nonlinear plane waves, namely the growth rate and bandwidth. At third order, we have shown the importance of the nonlinear coupling between the mean flow induced by the modulation and the vorticity. Furthermore, it is shown that these plane wave solutions may be linearly stable to modulational instability for an opposite shear current independently of the dimensionless parameter kh, where k and h are the carrier wavenumber and depth, respectively. © 2012 American Institute of Physics.


Meunier P.,Institute Of Recherche Sur Les Phenomenes Hors Equilibre
Journal of Fluid Mechanics | Year: 2012

This experimental and numerical study considers the two-dimensional stability of a circular cylinder wake, whose axis is tilted with respect to a stable density gradient. When the Reynolds number increases, the wake transitions from a steady flow to a periodic von Kármán vortex street as in a homogeneous fluid. However, the presence of a moderate stratification delays the appearance of the von Kármán vortex street, in agreement with the stabilization of shear flows by a density gradient. This stabilization, which does not occur for a vertical cylinder, increases with the tilt angle of the cylinder and is maximum for a horizontal cylinder. The critical Reynolds number increases when the stratification increases and diverges at a Froude number of order one for a horizontal cylinder. This critical Reynolds number can be predicted using the Richardson number based on the projection of the gravity and the density gradient in the direction of the shear, as was proposed by Candelier (J. Fluid Mech., vol. 685, pp. 191-201) for a tilted stratified jet. This picture is completely different for a strongly stratified wake since a new unstable mode appears, creating a von Kármán vortex street with a smaller Strouhal number. This surprising result is due to the presence of tilted vortices with no vertical velocity, i.e. with horizontal elliptic streamlines. This mode occurs in a band of Froude numbers which becomes smaller and smaller when the tilt angle increases, and eventually disappears for a horizontal cylinder. The presence of the tilt has thus a large impact on the structure of the wake at small Froude numbers and might need to be taken into account in geophysical flows. © 2012 Cambridge University Press.


Meunier P.,Institute Of Recherche Sur Les Phenomenes Hors Equilibre
Journal of Fluid Mechanics | Year: 2012

This experimental, numerical and theoretical study considers the lee internal waves generated by the wake of a circular cylinder, whose axis is tilted with respect to a stable density gradient. The main difference with the case of a horizontal cylinder is that the lee waves contain a large axial velocity, which are located in a row of lobes extending downstream from the cylinder. At small tilt angles, the wavelength is equal to 2π U/N, U being the velocity of the cylinder and N the Brunt-Väisälä frequency, which can be explained by the fact that the group velocity of the waves is small. The amplitude of the waves can be predicted using the Lighthill theory for dispersive waves applied to the case of a tilted bluff body. The flow around the cylinder is modelled empirically in order to reach a quantitative prediction in good agreement with the experimental and numerical results. The spatial structure of the predicted internal waves is qualitatively correct although some discrepancies arise because the advection by the flow around the cylinder is neglected. © 2012 Cambridge University Press.


Mercier F.,IRSTEA | Bonelli S.,IRSTEA | Pinettes P.,GeophyConsult | Golay F.,University of Toulon | And 2 more authors.
Journal of Hydraulic Engineering | Year: 2014

The jet erosion test (JET) is an experimental device increasingly used to quantify the resistance of soils to erosion. This resistance is characterized by two geotechnical parameters: the critical shear stress and the erosion coefficient. A previously published JET interpretation model provides an estimation of these erosion parameters. But the existing model is simplified and semiempirical and several assumed hypotheses can be discussed. The aim of this study is to determine the relevance of the JET interpretation model. Therefore, a numerical model was developed that is able to predict the erosion of a cohesive soil by a turbulent flow. The numerical model was first validated on a benchmark: erosion of an erodible pipe by a laminar flow. The numerical results were satisfactorily compared with the theoretical solution. Then, three JETs were modeled numerically with values of erosion parameters obtained experimentally. A parametric study was also conducted to validate the accuracy of the numerical results and a good agreement was observed. The erosion parameters found experimentally permit the numerical prediction of the evolution of the erosion pattern within good accuracy. This result contributes to the validation of the JET's semiempirical model. The numerical model also gives a complete description of the flow, including vortices which can be observed in the cavity created by erosion. The entire erosion pattern evolution was given by the numerical results. This numerical model gives information that is not available otherwise. © 2014 American Society of Civil Engineers.


Faranda D.,CEA Saclay Nuclear Research Center | Pons F.M.E.,University of Bologna | Dubrulle B.,CEA Saclay Nuclear Research Center | Daviaud F.,CEA Saclay Nuclear Research Center | And 3 more authors.
Physics of Fluids | Year: 2014

We introduce a novel way to extract information from turbulent datasets by applying an Auto Regressive Moving Average (ARMA) statistical analysis. Such analysis goes well beyond the analysis of the mean flow and of the fluctuations and links the behavior of the recorded time series to a discrete version of a stochastic differential equation which is able to describe the correlation structure in the dataset. We introduce a new index Y that measures the difference between the resulting analysis and the Obukhov model of turbulence, the simplest stochastic model reproducing both Richardson law and the Kolmogorov spectrum. We test the method on datasets measured in a von Kármn swirling flow experiment. We found that the ARMA analysis is well correlated with spatial structures of the flow, and can discriminate between two different flows with comparable mean velocities, obtained by changing the forcing. Moreover, we show that the Y is highest in regions where shear layer vortices are present, thereby establishing a link between deviations from the Kolmogorov model and coherent structures. These deviations are consistent with the ones observed by computing the Hurst exponents for the same time series. We show that some salient features of the analysis are preserved when considering global instead of local observables. Finally, we analyze flow configurations with multistability features where the ARMA technique is efficient in discriminating different stability branches of the system. © 2014 AIP Publishing LLC.

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