Papers by Pierre Brancher
To improve the understanding of mud suspension in estuaries, a parametric stability analysis of a... more To improve the understanding of mud suspension in estuaries, a parametric stability analysis of a two-dimensional shear flow was carried out with a model of two miscible fluid layers of different mass density and dynamic viscosity. The direct numerical simulation code JADIM of IMFT (Institut de Mecanique des Fluides de Toulouse) is used to compute the temporal evolution of these flows. This study is completed by a linear stability study realized with the code LiSa developed at IMFT. A critical Richardson number close to 0.25 is observed. Results show that the characteristics of the most unstable modal wave number and the location of the interface instability, depend on the ratio of two fluid viscosity values. The model is initialized with continuous erf(z) vertical profiles for all quantities. Likely outcomes of this stability study are new parameterizations for realistic modelling of estuaries.
Physics of Fluids, 2017
We present a linear optimal perturbation analysis of streamwise invariant disturbances evolving i... more We present a linear optimal perturbation analysis of streamwise invariant disturbances evolving in parallel round jets. The potential for transient energy growth of perturbations with azimuthal wavenumber m 1 is analyzed for different values of Reynolds number Re. Two families of steady (frozen) and unsteady (diffusing) base flow velocity profiles have been used, for different aspect ratios ↵ = R/✓, where R is the jet radius and ✓ is the shear layer momentum thickness. Optimal initial conditions correspond to infinitesimal streamwise vortices, which evolve transiently to produce axial velocity streaks, whose spatial structure and intensity depend on base flow and perturbation parameters. Their dynamics can be characterized by a maximum optimal value of the energy gain G opt , reached at an optimal time ⌧ opt after which the perturbations eventually decay. Optimal energy gain and time are shown to be, respectively, proportional to Re 2 and Re, regardless of the frozen or diffusing nature of the base flow. Besides, it is found that the optimal gain scales like G opt / 1/m 3 for all m except m = 1. This quantitative difference for azimuthal wavenumber m = 1 is shown to be based on the nature of transient mechanisms. For m = 1 perturbations, the shift-up effect [J. I. Jiménez-González et al., "Modal and non-modal evolution of perturbations for parallel round jets," Phys. Fluids 27, 044105-1-044105-19 (2015)] is active: an initial streamwise vorticity dipole induces a nearly uniform velocity flow in the jet core, which shifts the whole jet radially. By contrast, optimal perturbations with m 2 are concentrated along the shear layer, in a way that resembles the classical lift-up mechanism in w with all-shear optimal flows. times The m = considerably 1 shift-up shorter effect in is the more case of ener m getic 2 than the disturbances. m 2 This lift-up, b suggests ut it is that slo these wer, perturbations may emerge very quickly in the flow when injected as initial conditions. When the base flow diffuses, the large time scale for m = 1 disturbances allows the shear layer to spread and the jet core velocity to decrease substantially, thus lowering the values of corresponding optimal gain and time. For m 2, results are less affected, since the shorter transient dynamics does not leave room for significant modifications of the base flow velocity profiles, and the scaling laws obtained in the frozen case are recovered. Nevertheless, base flow diffusion hinders the transient growth, as a consequence of a weaker component-wise non-normality and a smoother, radially spread structure of optimal disturbances.
Physical Review Letters, 1997
The generic problem of the spatiotemporal instability of a periodic basic flow (Stuart vortices) ... more The generic problem of the spatiotemporal instability of a periodic basic flow (Stuart vortices) is considered in order to interpret the sequence of bifurcations observed in open shear flows. Using a novel numerical technique, we show that the more concentrated the vortices, the smaller the backflow needed to trigger absolute instability. These results allow us to propose an alternative interpretation for the subharmonic resonance observed in forced shear flows, which is classically attributed to an acoustic feedback. [S0031-9007(96)02213-2]
Environmental Fluid Mechanics, 2014
OATAO is an open access repository that collects the work of Toulouse researchers and makes it fr... more OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible.
Three-dimensional measurements of an inclined vortex ring interacting with a density stratification
Physical Review Fluids, 2021
Vortex rings are self-propagating structures that can transport mass and momentum to locations re... more Vortex rings are self-propagating structures that can transport mass and momentum to locations remote from the ring creation. We focus on the reorganization of a light vortex ring impinging, at a given angle to the vertical, a layer of fluid stably stratified in density, as in many environmental applications. We also examine the stratified layer response with regard to baroclinic vorticity and internal gravity wave generation. The symmetry of both the flow and wave field is preserved over time for normal impacts. For inclined impacts, the flow reorganizes into a vertically flattened dipolar structure and internal gravity waves radiate from two sources that match with the dipole cores.
OATAO is an open access repository that collects the work of Toulouse researchers and makes it fr... more OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in:
We extend the linear stability analysis of the inviscid Lamb-Chaplygin dipole (LCD) carried out b... more We extend the linear stability analysis of the inviscid Lamb-Chaplygin dipole (LCD) carried out by Brion et al. to a family of viscous Lamb-Oseen dipoles (LOD) for varying aspect ratios a/b, where a is the characteristic radius of the vortices and b their separation distance. Brion et al. have recently discovered a new family of modes which correspond to a large-wavelength instability with a maximum growth rate in the two-dimensional (2D) limit. Their study suggests that vortex shedding in the wake of the dipole is the leading physical mechanism of those instabilities. Though the LCD is a peculiar model of vortex dipole, since it does not exhibit any viscous trail and presents a singular vorticity distribution, Brion et al. compared their results with the more regular LOD defined by Sipp et al. and confirmed the existence of a 2D instability of vortex dipoles. Despite a similar structure, the instability of the LOD presents an oscillating symmetric mode and growth rates that are sig...
L’analyse de stabilite lineaire du dipole de Lamb-Chaplygin (LCD) menee par Brion et al. [1] est ... more L’analyse de stabilite lineaire du dipole de Lamb-Chaplygin (LCD) menee par Brion et al. [1] est etendue a une famille de dipoles visqueux de Lamb-Oseen (LOD) de plus petit rapport d’aspect a/b, ou a est le rayon caracteristique des deux tourbillons et b leur distance de separation. En ce qui concerne le LCD, une famille d’instabilites a grande longueur d’onde, presentant un taux de croissance maximal a la limite bidimensionnelle, a recemment ete decouverte par Brion et al. [1]. Ces auteurs suggerent que la fuite de vorticite de perturbation dans le sillage du dipole est le principal moteur de l’instabilite. Or le LCD est un modele de dipole particulier, qui n’exhibe pas de traine visqueuse et presente une distribution de vorticite a derivee discontinue a la frontiere de la zone de recirculation. Brion et al. [1] ont donc egalement procede a un premier examen de la stabilite bidimensionnelle du LOD, qui presente une traine visqueuse et une distribution de vorticite reguliere, associ...
Bulletin of the American Physical Society, 2014
The present study investigates the stability of a family of quasi-steady two-dimensional vortex d... more The present study investigates the stability of a family of quasi-steady two-dimensional vortex dipoles resulting from the adaptation to the mutual deformation and viscous diffusion of counter-rotating Lamb-Oseen vortices of equal size and circulation. For sufficiently large Reynolds numbers, the internal structure is set by the dipole aspect ratio a/b (radius versus separation distance), giving rise to a family of smooth quasi-steady solutions. These base flow solutions consist of self-propagating dipoles with a vorticity trail leaking from the dipole during the self-adaptation process and from diffusion across the dipole Kelvin oval. The present work is a generalization of the recent study by Brion et al. (2014), who found that a specific kind of vortex dipole, the Lamb-Chaplygin dipole, was unstable with respect to two-dimensionnal perturbations. We show how the growth rate and spatial structure of the unstable modes vary with aspect ratio a/b and Reynolds number. The growth rate...
Journal of Fluid Mechanics, 2001
A computational study is reported of the close interaction of nominally anti-parallel vortex tube... more A computational study is reported of the close interaction of nominally anti-parallel vortex tubes with unequal strengths, Γ1 and −Γ2, where Γ2/Γ1 [les ] 1. The computations are performed using a spectral method, with periodic boundary conditions and vortex Reynolds number Re ≡ Γ1/v = 1500, and the vortices are perturbed by a wavelength for which the pair is unstable because of their mutual interaction. The numerical method is tested for the case of equal-strength vortices, which exhibits the classic vortex reconnection phenomenon typified by bridging between the vortex cores and formation of thin vorticity threads as the bridged sections advect away under their self-induced velocity. Computations for vortices of unequal strengths are reported for cases with small, moderate and large strength differences, for which Γ2/Γ1 = 0.82, 0.54 and 0.25 are chosen as representative values. The bridges between the vortex structures form loops that twist owing to the unequal vortex strengths. In...
Interation of unequal anti-parallel vortex tubes
Journal of Fluid Mechanics, 2008
The aim of the present paper is to analyse the dynamics of the Lamb–Oseen vortex when continuousl... more The aim of the present paper is to analyse the dynamics of the Lamb–Oseen vortex when continuously forced by a random excitation. Stochastic forcing is classically used to mimic external perturbations in realistic configurations, such as variations of atmospheric conditions, weak compressibility effects, wing-generated turbulence injected into aircraft wakes, or free-stream turbulence in wind tunnel experiments. The linear response of the Lamb–Oseen vortex to stochastic forcing can be decomposed in relation to the azimuthal symmetry of the perturbation given by the azimuthal wavenumber m. In the axisymmetric case m = 0, we find that the response is characterized by the generation of vortex rings at the outer periphery of the vortex core. This result is consistent with recurrent observations of such dynamics in the study of vortex–turbulence interaction. When considering helical perturbations m = 1, the response at large axial wavelengths consists of a global translation of the vorte...
Flow, Turbulence and Combustion, 2006
The present paper investigates the dynamics of a laminar plane jet impinging on a flat plate in a... more The present paper investigates the dynamics of a laminar plane jet impinging on a flat plate in a channel. An experimental parametric study is carried out to determine the flow regimes at different levels of confinement and Reynolds numbers. For very confined jets, the flow is steady whatever the Reynolds number. The overall structure of the flow is symmetric with respect to the jet axis and is characterized by the presence of recirculation zones at the channel walls. The dynamics is radically different for less confined jets. Above a critical Reynolds number, the flow bifurcates in the form of an oscillating flapping mode of the impinging jet. Analyses of the experimental results provide with a quantitative characterization of this regime in terms of amplitude, wavelength and frequency. This selfoscillating bifurcated flow induces strong sweepings of the target plate by the jet and intense vortex dipole ejections from the impacted wall. Such a regime is expected to be particularly useful in the enhancement of the local heat transfer at relatively low cost in terms of flow rate.
Experiments in Fluids, 2009
Experimental results on the dynamics of a vortex dipole evolving in a shallow fluid layer are pre... more Experimental results on the dynamics of a vortex dipole evolving in a shallow fluid layer are presented. In particular, the generation of a spanwise vortex at the front of the dipole is observed in agreement with previous experiments at larger Reynolds numbers. The results show that this secondary vortex is of comparable strength to the dipole. The present physical analysis suggests that the origin of this structure involves the stretching induced by the dipole of the boundary-layer vorticity generated by the dipole's advection over the no-slip bottom.
Nonmodal stability analysis of the Lamb-Oseen vortex
Two physical mechanisms of transient energy growth identified : theanti-lift-up (axisymmetric case... more Two physical mechanisms of transient energy growth identified : theanti-lift-up (axisymmetric case) and a resonance drivenmechanism leading to the emergence of vortex waves(m > 0).Robustness of the mechanisms : both mechanisms are selected underexternal unbiased realistic perturbation field.Importance of sub-optimals : in the m = 2 case, the dominantstructure is not the optimal perturbation. Need to lookat the sub-optimal perturbations in that case.Good candidate for the vortex meandering phenomenon : emergenceof the D-wave under external continuous forcing.
ANR VORTEX'Instabilités de tourbillons: applications aux sillages d'avions
Physics of Fluids, 1999
This paper investigates the three-dimensional stability of the Lamb-Chaplygin vortex pair. Short-... more This paper investigates the three-dimensional stability of the Lamb-Chaplygin vortex pair. Short-wavelength instabilities, both symmetric and antisymmetric, are found. The antisymmetric mode possesses the largest growth rate and is indeed the one reported in a recent experimental study ͓J. Fluid Mech. 360, 85 ͑1998͔͒. The growth rates, wave numbers of maximum amplification, and spatial eigenmodes of these short-wavelength instabilities are in good agreement with the predictions from elliptic instability theory. A long-wavelength symmetric instability similar to the Crow instability of a pair of vortex filaments is also recovered. Oscillatory bulging instabilities, both symmetric and antisymmetric, are identified albeit their growth rates are lower than for the short-wavelength instabilities. Their behavior and eigenmodes resemble those of the oscillatory bulging instability occurring in the mixing layer.
Une analyse de stabilite generalisee d’une famille de tourbillons ecrantes a ete menee pour les f... more Une analyse de stabilite generalisee d’une famille de tourbillons ecrantes a ete menee pour les faibles nombres de Reynolds. L’etude de stabilite temporelle modale permet de determiner la courbe neutre. Ensuite, pour le cas particulier du tourbillon de Taylor, une etude en perturbation optimale dans le cas sous-critique revele des amplifications transitoires a differents nombres d’onde azimutaux. Une etude au-dessus du seuil complete l’analyse aux temps courts. En dernier lieu, les effets de la diffusion de l’ecoulement de base sont quantifies pour un nombre de Reynolds de 100 : on montre que le mode le plus instable predit par l’analyse de stabilite classique n’est pas necessairement le plus dangereux aux temps courts.
Physical Review Fluids
The dynamics of perturbed aircraft wake models is investigated in the two-dimensional limit by me... more The dynamics of perturbed aircraft wake models is investigated in the two-dimensional limit by means of a linear stability analysis. The base flow, computed by a direct numerical simulation of the incompressible Navier-Stokes equations, is a viscous counter-rotating vortex dipole obtained from an initial condition which is either a superposition of two Lamb-Oseen vortices or a vorticity sheet with elliptical vorticity distribution. The former, referred to as the Lamb-Oseen dipole (LOD), is a model for the far field of the wake and gives rise to a family of quasisteady dipoles parametrized by their aspect ratio only. The later approaches the near-field wake of a wing during the rolling phase which eventually converges towards the LOD model at later times. First, a modal stability analysis of the LOD under the assumption of a frozen base flow is performed for aspect ratios a/b ranging from 0.05 to 0.36 at various Reynolds numbers. Several families of unstable antisymmetric and symmetric modes are observed. The maximal growth rates are reached at low Reynolds numbers. The results are consistent with those obtained by Brion et al. [Phys. Fluids 26, 064103 (2014)] for the higher aspect ratio inviscid Lamb-Chaplygin dipole (LCD). However, the a posteriori verification of the validity of the frozen base flow assumption shows that, except for a few modes occurring at the highest aspect ratios and large Reynolds numbers, these two-dimensional instabilities do not survive the base flow unsteadiness due to viscous diffusion. They are thus not likely to develop in the flow. Second, we focus on the transient dynamics of the dipoles by looking for the optimal perturbations through a nonmodal stability analysis based on a direct-adjoint approach. The observed energy gains are substantial and indicate the potential of transient mechanisms. In the short time dynamics, the optimal perturbation consists of intertwined vorticity layers located within each vortex core and leading to a m = 2 deformation Kelvin wave excited by the Orr mechanism. For moderate to large horizon times, the optimal perturbation takes the form of vorticity layers localized outside the vortex core which eventually give rise to the two-dimensional unstable mode unveiled by the modal analysis through a combination of Orr mechanism and velocity induction. The robustness of these modes is examined by considering the initial stage of the development of aircraft wakes. The optimal perturbations developing on an elliptic and a double-elliptic vorticity sheet present a similar structure and rely on the same mechanisms as the ones observed for the LOD but come with lower energy gains. It is concluded that the rolling-up of the vorticity sheet in the near-field of the wake does not influence significantly the linear development of these two-dimensional perturbations.
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Papers by Pierre Brancher