Ondes internes dans un sillage incliné

Structure des ondes générées par le sillage d'un objet incliné par rapport à la stratification

Van Hove singularities in Probability Density Functions of scalars

A general theory for the Probability Density Function (PDF) of a scalar stirred in an axisymmetric time-dependent flow is derived. This theory reveals singularities, discontinuities and cusps occurring as soon as the spatial gradient of the scalar concentration vanishes somewhere in the field. These singularities are similar to the Van Hove singularities obtained in the density of vibration modes of a crystal. This feature, ubiquitous in convection–diffusion problems, is documented experimentally for the mixing of a dye in a Lamb–Oseen vortex

Stratified Propelled Wakes

This paper presents experimental results on the wake of a propelled bluff body towed at a constant horizontal speed in a linearly stratified fluid. Three regimes of the wake have been found, depending on the angle of attack and on the ratio of drag force to propeller thrust. Most of the experiments were obtained in a first regime where a strong momentum flux is created in the wake, which can be oriented backward or frontward depending on the ratio of drag force to thrust of the propeller. The velocity amplitude, wake width and Strouhal number of the wake can be predicted by defining a momentum thickness based on the drag coefficient of the bluff body and the thrust of the propeller. A second regime is obtained on a narrow band of towing velocities, with a relative width of 4%, in which the momentum flux is found to vanish. The wake is characterised by the velocity fluctuations; the scaling exponents of the velocity, vorticity and width of the wake are measured. A third regime is obtained for wakes with a small angle of attack, with a null momentum flux. The mean profile of the wake is found to be asymmetric and its amplitude and wake width are measured. Finally, the relevance of these results to the case of a real self-propelled bluff body is discussed. The presence of weak internal waves or of weak fluctuations of background velocity would lead to a wake in the regime with momentum flux, and would allow prediction of the amplitude, width and Strouhal number of the wake

Analysis and treatment of errors due to high velocity gradients in particle image velocimetry

International audienceThis paper deals with errors occurring in 2D cross-correlation PIV algorithms (with window shifting), when high velocity gradients are present. A first bias error is due to the difference between the Lagrangian displacement of a particle and the real velocity. This error is calculated theoretically as a function of the velocity gradients, and is shown to reach values up to 1 pixel if only one window is translated. However, it becomes negligible when both windows are shifted in a symmetric way. A second error source is linked to the image pattern deformation, which decreases the height of the correlation peaks. In order to reduce this effect, the windows are deformed according to the velocity gradients in an iterative process. The problem of finding a sufficiently reliable starting point for the iteration is solved by applying a Gaussian filter to the images for the first correlation. Tests of a PIV algorithm based on these techniques are performed, showing their efficiency, and allowing the determination of an optimum time separation between images for a given velocity field

How vortices mix

International audienceThe advection of a passive scalar blob in the deformation field of an axisymmetric vortex is a simple mixing protocol for which the advection-diffusion problem is amenable to a near-exact description. The blob rolls-up in a spiral which ultimately fades away in the diluting medium. The complete transient concentration field in the spiral is accessible from the Fourier equations in a properly chosen frame. The concentration histogram of the scalar wrapped in the spiral presents unexpected singular transient features and its long time properties are discussed in connection with mixtures from the real world

Mixing in a vortex breakdown flow

International audienceThis paper presents experimental and theoretical results on the mixing inside a cylinder with a rotating lid. The helical flow that is created by the rotation of the disk is well known to exhibit a vortex breakdown bubble over a finite range of Reynolds numbers. The mixing properties of the flow are analyzed quantitatively by measuring the exponential decay of the variance as a function of time. This homogenization time is extremely sensitive to the asymmetries of the flow, which are introduced by tilting the rotating or the stationary disk and accurately measured by Particle Image Velocimetry (PIV). In the absence of vortex breakdown, the homogenization time is strongly decreased (by a factor 10) with only a moderate tilt angle of the rotating lid (of the order of 15 degrees). This phenomenon can be explained by the presence of small radial jets at the periphery which create a strong convective mixing. A simple model of exchange flow between the periphery and the bulk correctly predicts the scaling laws for the homogenization time. In the presence of vortex breakdown, the scalar is trapped inside the vortex breakdown bubble, and thus increases substantially the time needed for homogenization. Curiously, the tilt of the rotating lid has a weak effect on the mixing, but a small tilt of the stationary disk (of the order of 2 degrees) strongly decreases (by a factor 10) the homogenization time. Even more surprising is that the homogenization time diverges when the size of the bubble vanishes. All these features are recovered by applying the Melnikov theory to calculate the volume of the lobes that exit the bubble. It is the first time that this technique has been applied to a 3D stationary flow with a non-axisymmetric perturbation and compared with experimental results, although it has been applied often to 2D flows with a periodic perturbation

Self-preservation in stratified momentum wakes

A general model is described for drag wakes in a linearly stratified fluid, based on the self-preservation of the flow. It is assumed that the buoyancy-controlled self-similar wake expands in the horizontal direction due to turbulent diffusion and in the vertical direction due to viscous diffusion. The mean characteristics of the wake (height, width and velocity defect) are analytically derived and show good agreement with existing data from experimental and numerical results. Moreover, the three regimes previously found in the literature that characterise different dynamical phases of the wake evolution are recovered, and two new regimes are found. The model allows for prediction of characteristic length and velocity scales at the high Reynolds numbers of large-scale applications of geophysical and naval origin

Empirical scaling of antisymmetric stratified wakes

Proceedings of the "Bluff Body Wakes and Vortex-Induced Vibrations - BBVIV-4"Initially turbulent wakes of a propelled cylinder at nonzero angles of yaw to the mean flow were measured in the horizontal centerplane plane up to approximately 100 buoyancy times, where vertical velocities are very small. The profiles of mean velocity were found to be antisymmetric throughout their lifetime, with both width and maximum velocity decaying at the same rate as previously studied momentum wakes. The maximum velocity of the profile is proportional to the angle of yaw, but the width is constant. Both the mean flow and fluctuating quantities show that the late wake is self-similar, with scaling laws that are consistent with previous work on propelled and drag wakes

Physics of vortex merging

20 p.This article deals with the interaction of co-rotating vortices, in configurations similar to those found in the extended near-wake of typical transport aircraft. The fundamental process of vortex merging is analyzed and modeled in detail in a two-dimensional context, giving insight into the conditions for merging and its physical origin, and yielding predictions for the resulting flow. Three-dimensional effects, in the form an elliptic short-wave instability arising in the initial co-rotating vortex flow, are described and analyzed theoretically. They are found to cause significant changes in the merging process, like earlier merging and larger final vortex cores. Illustrations from recent experimental, numerical and theoretical studies are given, and the relevance of the results for applications to real aircraft wakes is discussed

Response of a stratified boundary layer on a tilted wall to surface undulations

International audienceThe structure of a stratified boundary layer over a tilted bottom with a small streamwise undulation is studied theoretically and numerically. We show that the tilt of the boundary can induce strong density variations and wall-transverse velocities in the critical layer when the frequency of the forcing by the topography kU(z c) is equal to the transverse Brunt–Väisälä frequency N sin α (N being the vertical Brunt–Väisälä frequency). The viscous solution in the critical layer, obtained and compared with direct numerical simulation results, is in good agreement for both the scaling and the spatial structure. The amplitude of the transverse velocity response is also shown to exhibit quasi-resonance peaks when the stratification strength is varied