Patrice Le Gal Home Page

Institut de Recherche sur les Phénomènes Hors Equilibre (IRPHE)
UMR 6594, CNRS - Universités d'Aix-Marseille I et II.

Recent Publications

Wakes    Rotating Flows     Turbulence    Vortices   Geophysics  Bioluminescence     Liquid Crystal     Amateur Astronomy

1. Wakes

• Coupled wakes of cylinders
  Isabelle Peschard and Patrice Le Gal.

  Abstract
  This paper is devoted to the experimental study and theoretical modeling of the coupled wakes of a pair of cylinders placed side by side in a constant flow. We propose here a dynamical system which models the behavior of these coupled wakes. This model is constituted by two coupled Landau equations whose coefficients are estimated from experimental observations. A stability diagram is analytically and numerically computed. Finally, we present some new experiments which complete previous observations of locked and unlocked wakes.
  In phase wakes
  Out of phase wakes
  Asymmetric wakes
  Asymmetric wakes

  Physical Review Letters, volume 77, Number 15, p 3122, 7 October 1996.

• Collective behavior of wakes downstream a row of cylinders
  Patrice Le Gal, Isabelle Peschard, Marie-Pierre Chauve and Yasushi Takeda.

  Abstract
  This experimental study is devoted to visualisation and ultrasonic velocity measurement of the wakes formed behind a row of parallel cylinders placed side by side, perpendicular to an incoming flow at low Reynolds numbers. When the distance separating the cylinders is small compared to their diameter, two instability mechanisms, associated with different patterns and dynamics compete. A first spatial symmetry breaking appears when the stationary wakes behind each cylinder are deviated towards one side or the other and form large clusters containing from 2 to sometimes more than 10 wakes.(Figure 1). These clusters are separated by intense recirculating zones. When the Reynolds number is increased, the wakes belonging to the widest clusters experience a secondary temporal oscillatory bifurcation. Classical Benard-Von Karman vortex streets are thus shed in phase by these cylinders (acoustic mode), by contrast with the wakes outside these cells which stay stationary(Figure 2) (Figure 3). Finally, the flow around far appart cylinders is also investigated. The primary instability does not occur in this case and a perfect optical mode of vortex shedding, with neighbours in phase opposition, takes place in the flow.(Figure 4).

  Physics of Fluids, volume 8, Number 8, p 2097, August 1996.

• Identification of parameters in amplitude equations describing coupled wakes
  Jose Maria Fullana, Patrice Le Gal, Maurice Rossi and Stephane Zaleski.

  Abstract
  We study the flow behind an array of equally spaced parallel cylinders. snapshot, space-time diagram. A system of Stuart-Landau equations with complex parameters is used to model the oscillating wakes. Our purpose is to identify the 6 scalar parameters which most accurately reproduce the experimental data of Chauve and Le Gal [{Physica D {\bf 58}}, pp 407--413, (1992)]. To do so, we perform a computational search for the minimum of a distance $\calj$. We define $\calj$ as the sum-square difference of the data and amplitudes reconstructed using coupled equations. The search algorithm is made more efficient through the use of a partially analytical expression for the gradient $\nabla \cal J$. Indeed $\nabla \cal J$ can be obtained by the integration of a dynamical system propagating backwards in time (a backpropagation equation for the Lagrange multipliers). Using the parameters computed via the backpropagation method, the coupled Stuart-Landau equations accurately predicted the experimental data from Chauve and Le Gal over a correlation time of the system. Our method turns out to be quite robust as evidenced by using noisy synthetic data obtained from integrations of the coupled Stuart-Landau equations. However, a difficulty remains with experimental data: in that case the several sets of identified parameters are shown to yield equivalent predictions. This is due to a strong discretisation or ``round-off" error arising from the digitalization of the video images in the experiment.This ambiguity in parameter identification has been reproduced with synthetic data subjected to the same kind of discretisation.

  Physica D, 102,37,1997.

• On the spatio-temporal structure of cylinder wakes
  Isabelle Peschard, Patrice Le Gal and Y. Takeda.

  Abstract
  The wake of a short aspect ratio cylinder placed in a uniform flow is experimentally investigated. After having characterized the temporal behavior of the Benard-Von Karman vortex shedding by the use of a classical hot-wire anemometer, an ultrasound anemometry technique is applied to study the spatial critical behavior of the envelope of the transverse velocity of the wake (tranverse velocity profiles). It is shown that this envelope which represents the spatial form of the global mode of the wake, follows universal scaling laws which are in agreement with second order phase transition. In a second set of experiments, the behavior of the longitudinal velocity fluctuations is also investigated (longitudinal velocity profiles). It is discovered that there is a special point several diameters behind the cylinder, which plays a role of a wave maker. Finally for very small aspect ratio cylinders, symmetric vortex shedding (symmetric shedding)is reported and modeled using system of coupled oscillators.

  Exp. Fluids, volume 26, number 1, p. 12, 1999.

• Bi-Orthogonal Decomposition analysis and reconstruction of spatio-temporal chaos generated by coupled wakes
  J.F. Ravoux and P. Le Gal.

  Abstract
  Very often in hydrodynamics, the description of the complexity of flows can only be achieved by the use of simple models. These models, obtained usually by phenomenological arguments, need in general the knowledge of some parameters. The challenge is then to determine the values of these parameters from experiments. Here, our concern is the description of a coupled wakes experiment using a complex Ginzburg-Landau Equation (GLE). Our analysis is based on a proper decomposition of experimental spatio-temporal chaotic flow fields, followed by a projection of the GLE onto the proper directions. We show that our method is able to recover the parameters of the model which permit to reconstruct the spatio-temporal chaos observed in the experiment. As it is based on a general projection principle, this method is general and could be applied to other systems.

  Physical Review E, volume 58, number 5, p R5233, November 1998.

• Stability analysis of plane wave solutions of the discrete Ginzburg-Landau equation
  J. F. Ravoux, S. Le Dizès, and P. Le Gal

  Abstract
  The discrete Ginzburg-Landau model for a family of oscillators linearly coupled with their first neighbors is studied. The full linear stability analysis of the nonlinear plane wave solutions is performed by considering both the wavenumber ($k$) of the basic states and the wavenumber ($q$) of the perturbations as free parameters. In particular, it is shown that nonlinear plane waves can be destabilized not only by long ($q\rightarrow 0$) or short ($q=\pi$) wave perturbations, but also by intermediate wavenumbers ($0&ltq<\pi$). Finite size effects are also considered and discussed in connection with experiments on coupled oscillating wakes.

  Physical Review E, volume 61, number 1, January 2000.

• Visualization of the space-time impulse response of the subcritical wake of a cylinder
  P. Le Gal and V. Croquette

  Abstract
  The well-known Benard-Von Karman cylinder wake is one of the most challenging phenomena of fluid mechanics. As the Reynolds number of the flow around a cylinder passes through a critical value, alternating vortex shedding appears via a Hopf bifurcation. Theoretical studies of the wake have described the appearance of this self-sustained oscillation as the result of a convective to absolute transition resulting in the formation of a global mode. We illustrate here the convective global regime of the sub-critical wake by analyzing visualizations of its impulse response.

  Physical Review E, volume 62, number 3, pp. 4424-4426, September 2000.

• Hysteresis in the Forced Stuart-Landau Equation: Application to Vortex Shedding from an Oscillating Cylinder
  Patrice Le Gal, Ali Nadim and Mark Thompson

  Abstract
  The complex Stuart-Landau equation models a prototypical Hopf bifurcation in which, when the control parameter exceeds a critical value, the null solution bifurcates into a finite amplitude time-periodic solution. We study the response of this equation to time-harmonic forcing in the subcritical regime (i.e., before the bifurcation). We show that when a second parameter in the Stuart-Landau equation passes a critical value, a portion of the solution surface as a function of forcing frequency and amplitude becomes multivalued. For instance, at a fixed forcing amplitude, one finds a well-defined range of frequencies over which two stable periodic responses may coexist, having different amplitudes. We apply this result to predict the behaviour of the wake downstream of an oscillating cylinder, and compare the predictions with experimental (Re-Rec =-10) and computational observations of such a wake.

  forced wake 0.52 Hz.     forced wake 0.70 Hz.     forced wake 0.95 Hz.     forced wake 1.4 Hz.
  
  J. Fluids Struct. 15 (3/4), pp. 445-457, 2001.

• Recovering the coefficients of the Complex Ginzburg-Landau equation from experimental spatio-temporal data: Two examples from Hydrodynamics
  P. Le Gal, J.F. Ravoux, E. Floriani, T. Dudok de Wit

  Abstract
  There are many examples where the description of the complexity of flows can only be achieved by the use of simple models. These models, obtained usually from phenomenological arguments, need in general the knowledge of some parameters. The challenge is then to determine the values of these parameters from experiments. We will give two examples where we have been able to evaluate the coefficients of the complex Ginzburg-Landau equation from space-time chaotic data applied to first a row of coupled cylinder wakes and then to wave propagation in the Ekman layer of a rotating disk. In the first case, our analysis is based on a proper decomposition of experimental chaotic flow fields, followed by a projection of the CGLE onto the proper directions. We show that our method is able to recover the parameters of the model which permits to reconstruct the spatio-temporal chaos observed in the experiment. The second physical system under consideration is the flow above a rotating disk and its cross-flow instability. Our aim is to study the properties of the wavefield through a Volterra series equation. The kernels of the Volterra expansion, which contain relevant physical information about the system, are estimated by fitting two-point measurements via a nonlinear parametric model. We then consider describing the wavefield with the complex Ginzburg-Landau equation, and derive analytical relations which express the coefficients of the Ginzburg-Landau equation in terms of the kernels of the Volterra expansion.

  Physica D, 174 (1-4), p. 114-133,2003.

• The Stuart-Landau Model applied to Wake Transition revisited
  Mark C Thompson and Patrice Le Gal

  Abstract
  Following previous experimental and computational studies, this article further investigates the applicability of the Stuart-Landau equation to describe the Hopf bifurcation occurring for flow past a circular cylinder. It is shown that when the amplitude variable is taken as the transverse velocity component at a point in the wake, the so-called Landau constant varies considerably with position and importantly is generally far from constant during the saturation phase of wake development. The variation with downstream distance is quantified. However, it is found that the Landau constant at saturation is indeed a position-independent constant and this value is close to that generally measured previously both experimentally and numerically. It is shown that if the amplitude variable is taken as the lift coefficient of the cylinder (a global variable) then the same Landau constant is measured at saturation and the zero amplitude Landau constant corresponds to that for the transverse velocity at the back of the cylinder. These findings are used to interpret the wake behaviour of a transversely oscillating circular at subcritical Reynolds numbers.

  European Journal of Mechanics - B/ Fluids 23, pp. 219-228 (2004)  

• Flow-induced vibrations of high mass ratio flexible filaments freely hanging in a flow
  Lionel schouveiler, Christophe Eloy and Patrice Le Gal

Abstract

The behavior of high mass ratio flexible filaments freely hanging in steady horizontal uniform flows is experimentally and theoretically investigated. When the flow velocity is small, static equilibrium states (image) , where the filaments are inclined to the flow, are observed. Then, above a critical value of the wind velocity, the filaments exhibit periodic oscillations in the vertical plane (image). The problem is theoretically addressed considering the beam theory equations for the filament dynamics where the action of the flowing fluid is modeled using semi-empirical expressions. These equations are first solved for the stationary equilibrium states. Then, the stability of these steady solutions relatively to small perturbations is analyzed. A good agreement between experimental and theoretical results is found.

Physics of Fluids 17, 047104 (2005)

• Hysteretic mode exchange in the wake of two circular cylinders in tandem
  Yuji Tasaka, Seiji Kon, Lionel schouveiler and Patrice Le Gal

Abstract

Our experimental study is devoted to the analysis of the °ow past two tandem circular cylinders near the vortex shedding threshold. A recent bi-dimensional numerical analysis of this flow [Mizushima and Suehiro, Phys. Fluids 17, 104107 (2005)] has predicted that the bifurcation diagram should become complex in the vicinity of the instability threshold. Subcritical and saddle node bifurcations that lead to hysteretic exchanges between two different modes of vortex shedding were detected for particular distances of separation of the cylinders. We present here visualizations (image) and velocity measurements of this floow in a water channel that prove the robustness of the complexity
of the bifurcation diagram in real flows.

Physics of Fluids 18, 084104 (2006)

1. Rotating flows

• Experimental study of rotating disk flow instability. I. Natural flow
  Sandrine Jarre, Patrice Le Gal and Marie-Pierre Chauve.

  Abstract
  This article is devoted to the study of rotating disk flow instability. This inflectional-type instability, called cross-flow instability (image), is exemplary of transition to turbulence in the three-dimensional boundary layers. In a first part, we present the experimental marginal stability curve of unstable waves obtained by hot-film probe measurements and compare it with the theoretical results available in the literature. The experiment is in accordance with the different theoretical determinations of the linear threshold but we note a difference between experimental and theoretical critical wave number values. The unstable waves dynamics is then investigated by means of experimental dispersion curves (linking frequencies to the wave number vector components) determined by two-probe measurements. The results show in particular the existence of travelling dispersive waves, in the boundary layer of the rotating disk. Finally, we show that the emergence of non-linear effects occurs very early in the system, far from the transition point.

  Physics of Fluids, volume 8, number 2, p 496, February 1996.

• Experimental study of rotating disk flow instability. II. Forced flow
  Sandrine Jarre, Patrice Le Gal and Marie-Pierre Chauve.

  Abstract
  The destabilization of the rotating disk flow subject to a forcing is experimentally investigated. An isolated roughness element of order $\delta$ (the constant boundary layer thickness) is placed under the linear threshold of the cross-flow instability in order to create a hydrodynamic pattern of finite amplitude and localized in space. The experimental neutral stability curve is first established. The resulting double parabolic curve exhibits two minima: one of which is due to the amplification of fundamental modes, the other one is linked to the emergence of superharmonic modes. Dispersion curves determined by means of two-point measurements appear to be shifted away from those measures in the natural case (without forcing). We show that this discrepancy is due to the presence of weak nonlinear effects which can be described by a Ginzburg-Landau amplitude equation. Lastly, we present an original method that enables to determine both components of the group velocity vector using the measured dispersion relations and wave packet propagation angle.

  Physics of Fluids, volume 8, number 11, p 2985, November 1996.

• Spiral and circular waves in the flow between a rotating and a stationary disk
  Lionel Schouveiler, Patrice Le Gal and Marie-Pierre Chauve.

  Abstract
  Circular and spiral waves are observed in the flow between a rotating and a stationary disk. These waves are generated by instabilities of the stationary disk boundary layer. This experimental work is devoted to their study by means of flow visualization (circular waves) (travelling spiral waves) (stationary spiral waves)and measurements of the associated velocity fields. In particular, instantaneous velocity profiles (axial profiles of circular waves) (axial profiles of spiral waves) (radial profiles of circular waves and spiral waves)are measured by ultrasonic Doppler anemometry (ultrasound pulse). The spatio-temporal characteristics of the waves are studied with the help of Fourier transforms of these velocity signals.

  Exp. Fluids, volume 26, p.179, 1999.

• Stability of a traveling roll system in a rotating disk flow
  Lionel Schouveiler, Patrice Le Gal and Marie-Pierre Chauve.

  Abstract
  The stability of a traveling roll system, which results from the development of the flow between a stationary and a rotating disk, is experimentally studied. The characteristics of this traveling pattern and of the bifurcation from which it results are obtained. We show in particular that the band of the stable roll modes is limited by the Eckhaus secondary instability.
  
  Phys. Fluids, volume 10, number 11, p.2695, 1998.

• Nonlinear interactions in a rotating disk flow: from a Volterra model to the Ginzburg-Landau equation
  Elena Floriani, Thierry Dudok de Wit and Patrice Le Gal

  Abstract
  The physical system under consideration is the flow above a rotating disk and its cross-flow instability, which is a typical route to turbulence in three-dimensionnal boundary layers. Out aim is to study the nonlinear properties of the wavefield through a Volterra series equation. The kernels of the volterra expansion, which contain relevant physical information about the system, are estimated by fitting two-point measurements via a nonlinear parametric model. We then consider describing the wavefield wit hthe complex Ginzburg-Landau equation, and derive analytical relations which express the coefficients of the Ginzburg-Landau equation in terms of the kernels of the volterra expansion. These relations must hold for a large class of weakly nonlinear systems, in fluid as well as in plasma physics.

  Chaos, vol.10 (4), p. 834, 2000.

• Instabilities of the flow between a rotating and a stationary disk
  Lionel Schouveiler, Patrice Le Gal and Marie-Pierre Chauve

  Abstract
  This experimental study is devoted to the description of the different patterns resulting from instabilities which appear in the flow between a rotating and a stationary disk enclosed by a stationary sidewall. With the help of visualisations we describe the different flow regimes as functions of two control parameters: the Reynolds number and the aspect ratio of the gap separating the disks, which are varied on large continuous ranges. Moreover visualizsations and ultrasonic anemometry lead to the description of the different instabilities and to the construction of a transition diagram that summarizes the domains of existence of the various patterns. Two different scenarios of transition are maimly followed by the flow. When the gap between the two disks is more than the thickness of the two disk boundary layers, circular and spiral waves destabilize the stationary disk boundary layer. transition occurs in this case by the mixing of these waves. On the contrary, when the two boundary layers are merged, finite size turbulent structuress can appear. They consist of turbulent spots or turbulent spirals which invade the laminar domains as the Reynolds number of the flow is increased.

  J.Fluid Mech. 443, pp. 443-350, 2001

• Instabilities of the flow between a rotating and a stationary disk
  Anne Cros, Patrice Le Gal

  Abstract
  This work is devoted to the experimental study of the transition to turbulence of a flow confined in a narrow gap between a rotating and a stationary disk. When the fluid layer thickness is of the same order of magnitude as the boundary layer depths, the azimuthal velocity axial gradient is nearly constant and this rotating disk flow tends to be a torsional Couette flow. As in the plane Couette flow or the Taylor-Couette flow, transition to turbulence occurs via the appearance of turbulent domains inside a laminar background. In the rotating disk case, the nucleation of turbulent spirals, previously called "solitary waves" in the rotating disk flow literature, is connected to the birth of structural defects in a periodic underlying roll pattern. As the rotation rate is increased, the lifetime of these turbulent structures increases until a threshold is reached where they then form permanent turbulent spirals arranged nearly periodically all around a circumference. However, since the number of these turbulent spirals decreases with the rotational frequency, the transition to a fully turbulent regime is not achieved. Thus the turbulent fraction of the pattern saturates to a value lower than 0.5. After a geometrical description of the structures, we present a statistical analysis of sizes and lifetimes of the turbulent and laminar domains in order to compare this transition to already observed spatiotemporal intermittent behavior. (Spatio-temporal intermittency in the rotating frame)

  Phys. Fluids 14 (11), pp. 3755-3765, 2002

• Effects of wall compliance on the laminar-turbulent transition of torsional Couette flow
  A. Cros , R. Ali , P. Le Gal , P.J. Thomas , L. Schouveiler , P.W. Carpenter and M.P. Chauve

  Abstract
  Torsional Couette flow between a rotating disk and a stationary wall is studied experimentally. The surface of the disk is either rigid or, alternatively, covered with a compliant coating. The influence of wall compliance on characteristic flow instabilities and on the laminar-turbulent flow transition is investigated. Data obtained from analysing flow visualisations are discussed. It is found that wall compliance favours two of the three characteristic wave patterns associated with the transition process and broadens the parameter regime in which these patterns are observed. The results for the effects of wall compliance on the third pattern are inconclusive. However, the experiments indicate that the third pattern is not a primary constituent of the laminar-turbulent transition process of torsional Couette flow.

  J. Fluid Mech. 481, 177 (2003)

• Defect Turbulence in a spiral wave pattern in the torsional Couette flow
  A. Cros and P. Le Gal

  Abstract
  Our experimental study is devoted to the transition to defect turbulence of a periodic spiral wave pattern occurring in the flow between a rotating and a stationary disk. As the rotation rate $\Omega$ of the disk is increased, the radial phase velocity of the waves changes its sign: the waves that propagate first outward on average, then become stationary and finally propagate inward. As they become stationary, the nucleation of topological defects breaks the periodicity of the pattern. For higher $\Omega$, more and more defects are generated in the flow pattern. This article presents the statistical study of this defect mediated turbulence.

  Phys. Rev. E.,70, 016309, pp. 1-7 (2004)

• Turbulent rotating disk flow with inward through flow
  S. Poncet, M.P. Chauve and P. Le Gal

  Abstract
  The evolution of the entrainment coefficient K of the rotating fluid in a rotor-stator cavity with an imposed centripetal flux and pre-rotation is studied according to the flow parameters. Measurements are realized in water for a turbulent Batchelor type of flow by the means of a two component laser Doppler anemometer (LDA) and the results are compared to those performed by pressure transducers. We show that the entrainment coefficient $K$ depends on a local flow rate coefficient $Cq_r$ according to a 5/7 power law, whose coefficients depend on the boundary conditions. A theoretical analysis confirms the asymptotic behavior of K.

    J. Fluid Mech.522, pp 253-262 (2005)

• Transition to turbulence of the Batchelor flow in a rotor:stator device
  A. Cros, E. Floriani, P. Le Gal and R. Lima

  Abstract
  This experimental study is devoted to the transition to turbulence of the flow confined between a stationary and a rotating disk.
  Using visualization and video image analysis, we describe the different transitions occurring in the flow as the rotating velocity
  of the disk is varied. The space–time behavior of the wave patterns is analyzed using the Bi-Orthogonal Decomposition (BOD)
  technique. This decomposition of the experimental signals on proper modes permits to project the dynamics of the waves in a
  reduced embedding phase space. By this means, a torus doubling bifurcation is revealed before its complete destruction during
  the transition to a weak turbulence. Finally, a more classical 2D-Fourier analysis completes our description of the transition and
  shows for higher rotation rates, the appearance of a more developed turbulence issued from the former chaotic waves.

  Eur. J. Mech. B/ Fluids  24, pp. 409–424 (2004)

• A statistical study of spots in torsional Couette flow
  Patrice Le Gal, Yuji Tasaka, Jotaro Nagao,  Anne Cros and Kohei Yamaguchi

  Abstract
  This article presents some results on the statistical behavior of localized structures—called
  “spots”—that propagate in the flow between a rotating and a stationary disk when those are very close
  one to the other. Under these conditions the rotating-disk flow belongs to the Couette-flow family and is
  called the torsional Couette flow. Some visualizations of its transition to turbulence have already revealed
  the propagation of these spots (Schouveiler et al., J Fluid Mech 443:329–350, 2001) from the rim of the disk
  towards its center.Using flow visualizations and an original image analysis, the present study aims to better
  describe the characteristics of the spots whose number continuously increases with the Reynolds number
  until they invade the whole flow. Moreover, we propose a statistical model that predicts an error-function
  shape for the probability to observe a spot at a given radial position. This prediction is confirmed by an image
  analysis of the flow and the stability curve of torsional Couette flow is deduced from these observations.

  J. Eng. Math.  57, pp. 289–302 (2007)

1. Turbulence

• Turbulence Modelling low order statistics of temperature increments in fully developed turbulence.
  Stefan Bounoua, Myriem Ould-Rouis, Patrice Le Gal and Fabien Anselmet.

  Abstract
  This paper reports an experimental data analysis which clearly emphasizes the complex nature of the mechanisms governing the mixing of passive scalars such as temperature in fully developed turbulence. for that purpose, we compare our measurements of temperature increments and their probability density functions (pdfs) to theoretical predictions available in the literature for a scalar field evolving within a fully developed turbulent field. The observed disagreements lesd us to propose some improvements of the existing models. This in fact underlines the tremendous evolution through the scales of turbulence of the statistics of temperature increments, whose coupling with the velocity field appears to be an essential feature of the mixing process.

  Int. J. Heat and Mass Trans., volume 41, number 13, p. 2049, 1998.

• Predictions of small-scale Statistics for a passive scalar in turbulent mixing.
  Luminita Danaila, Fabien Anselmet, Patrice Le Gal, Jan Dusek, Cedric Brun and Alain Pumir .

  Abstract
  This letter presents some quantitative predictions for the small-scale statistics for a passive scalar mixed in a fully turbulent flow. Our method uses an equation (Vaienti et al. Physica D 73D, 99, 1994) which controls the evolution through the scales of the probability density function of temperature increments. This equation, which needs some closure as well as initial data, uses results from direct numerical simulations or from exeriments. for the dissipative and small inertial range scales, our predictions are in excellent agreement with the measured or numerically calculated probability density functions. The associated Yaglom equation is also well verified for the same range of scales.

  Phys. Rev. Lett. 79, 23, 4577, 1997.

• On velocity and passive scalar scaling laws in a turbulent swirling flow.
  J.F. Pinton, F. Plazza, L. Danaila, P. Le Gal, F. Anselmet.

  Abstract
  We analyze experimentally the statistical properties of velocity and temperature fluctuations, considered as a passive scalar, in a turbulent flow generated in the gap between coaxial disks. One of the disk is heated at a temperature higher than ambient, while the other one is cooled. With this arrangement one obtains a flow with either positive, negative or null temperature-velocity correlations. The velocity, temperature and heat flux fields are measured locally and studied via the moments of their increments. we find that the velocity field characteristics are independent of the large scale anisotropy, with scaling laws in agreement with the ones generally observed in fully developed turbulence. In contrast, the scalar field is strongly affected by the injection conditions at large scale; only in the central well-mixed region does one observe a behavior consistent with the existence of scaling. In the same region, the heat transport dudt^2 follows the same scaling laws as the kinetic energy flux du^3.

  Physica D, 122, 187, 1998.

• Some new features of the passive scalar mixing in a turbulent flow.
  L. Danaila, P. Le Gal, F. Anselmet, F. Plazza, J.F. Pinton.

  Abstract
  We analyze experimentally the statistical properties of a turbulent mixing created in the gap between two counter-rotating disks at a Taylor Reynolds number R_l = 400. Local isotropy is investigated for the inertial and dissipative scales r, using two tests, one applied on C(r), the correlation coefficient between temperature increments and velocity increments, and the other one on S(r), the temperature increment skewness factor. When heating one of the disks and cooling the other one, either positive, negative or almost null values of C and S can be obtained at small scales as a direct result of the presence of several temperature sources. In particular, we emphasize the fact that null or small values for these quantities in the inertial range are an evidence of local isotropy of the temperature field. In these cases, we use the Vaienti et al. equation [Physica D 73, 99 (1994)] for the evolution of the temperature increments probability density functions (PDFs) to predict the inertial and dissipative range PDFs, using an initial PDF, and two measurable closure functions. The intermittent behaviour quantified through these statistics is well reproduced by the numerical integration of this evolution equation.

  Physics of Fluids, 11, p.1, 1999.

1. Vortices

• Experimental study of the multipolar vortex instability
  Christophe Eloy, Patrice Le Gal, and Stèphane Le Dizès

  Abstract
  The instability of a vortex subject to a stationary dipolar or tripolar constraint is studied experimentally using a rotating deformable cylinder on which two or three rollers are applied. As the Reynolds number and the aspect ratio of the cylinder are varied, different modes of instability are observed and their wavelength and frequency are compared to theoretical predictions. Secondary instability and cyclic break up are also evidenced in the elliptic geometry.

  (Mode 1,3)      (Mode -1,1)      (Mode 0,2)

  16 October 2000, Physical Review Letters, Volume 85, Number 16

• Elliptic and triangular instabilities in rotating cylinders
  Christophe Eloy, Patrice Le Gal, and Stèphane Le Dizès

  Abstract
  In this article, the multipolar vortex instability of the flow in a finite cylinder is addressed. The experimental study uses a rotating elastic deformable tube filled with water which is elliptically or triangularly deformed by two or three rollers. The experimental control parameters are the cylinder aspect ratio and the Reynolds number based on the angular frequency. For Reynolds numbers close to threshold, different instability modes are visualized using anisotropic particles, according to the value of the aspect ratio. These modes are compared with those predicted by an asymptotic stability theory in the limit of small deformations and large Reynolds numbers. A very good agreement is obtained which confirms the instability mechanism: for both elliptic and triangular configurations, the instability is due to the resonance of two normal modes (Kelvin modes) of the underlying rotating flow with the deformation field. At least four different elliptic instability modes, including combinations of Kelvin modes with azimuthal wavenumbers m=0 and m=2 and Kelvin modes m=1 and m=3 are visualised. Two different triangular instability modes which are combination of Kelvin modes m=-1 and m=2 and combination of Kelvin modes m=0 and m=3 are also evidenced. The nonlinear dynamics of a particular elliptic instability mode, which corresponds to the combination of two stationary Kelvin modes m=-1 and m=1, is examined in more detail using Particle Image Velocimetry (PIV). The dynamics of the phase and amplitude of the instability mode is shown to be well-predicted by the weakly nonlinear analysis for moderate Reynolds numbers. For larger Reynolds number, a secondary instability is observed. Below a Reynolds number threshold, the amplitude of this instability mode saturates and its frequency is shown to agree with the predictions of Kerswell (1999). Above this threshold, a more complex dynamics develops which is only sustained during a finite time. The flow then relaminarises and the destabilisation process starts again. Experimental visualizations:

  (Mode 0,2)      (Secondary Instability of mode -1,1)

  Journal of Fluid Mechanics 476 (2003), p. 357-388

1. Geophysics

• Elliptical instability in a rotating spheroid
  Lacaze L., Le Gal P., Le Dizès S.

  Abstract
  This paper concerns the elliptical instability of a flow in a rotating deformed sphere. The aim of our work is to observe and measure the characterics of this instability in experiments and to compare them with theorical predictions. For this purpose, an elastic and transparent hollow sphere has been moulded. The flow is visualised using Kalliroscope flakes as the sphere is set into rotation and compressed by two rollers. The elliptical instability occurs by the appearance of the so-called 'spin-over' mode whose growth rates and saturations are measured for different Eckman numbers by video image analysis. These growth rates compare avantageously to theorical calculations which are performed using classical asymptotic expansions. The linear analysis is then completed by a non linear model which predicts correctly the asymptotic regimes for high Eckman numbers. Experimental visualization:

  (Spin over mode in a spheroid) (Movie of spin over mode in a spheroid)

  
  Journal of Fluid Mechanics 505, pp. 1-22 (2004)

• Elliptical instability of the flow in a rotating shell
  Lacaze L., Le Gal P., Le Dizès S.

Abstract
A theoretical and experimental study of the spin-over mode induced by the elliptical instability of a flow contained in a slightly deformed rotating spherical shell is presented. This geometrical configuration mimics the liquid rotating cores of planets when deformed by tides coming from neighboring gravitational bodies. Theoretical estimations for the growth rates and for the non linear amplitude saturations of the unstable mode are obtained and compared to experimental data obtained from Laser Doppler anemometry measurements. Visualizations and descriptions of the various characteristics of the instability are given as functions of the flow parameters.

Physics of the Earth and planetary interiors 151, pp. 194-205 (2005)

• Magnetic field induced by elliptical instability in a rotating spheroid
  Lacaze L., Herreman W., Le Bars M., Le Dizès S. and Le Gal P.

Abstract
The tidal or elliptical instability of rotating fluid flows is generated by the resonant interaction of
inertial waves. In a slightly elliptically deformed rotating sphere, the most unstable linear mode is
called the spin-over mode and is a solid body rotation versus an axis aligned with the maximum strain
direction. In the non viscous case, this instability corresponds to the median moment of inertia insta-
bility of solid rotating bodies. This analogy is furthermore illustrated by an elliptical top experiment, (Movie of the elliptical top),
which shows the expected inviscid heteroclinic behaviour. In geophysics, the elliptical instability may
appear in the molten liquid cores of rotating planets, which are slightly deformed by tidal gravitational
effects of close bodies. It may then participate to the general outer core dynamics and possibly to the
geodynamo process. In this context, Kerswell and Malkus (Kerswell, R.R. and Malkus, W.V.R., Tidal
instability as the source for Io's magnetic signature, Geophys. Res. Lett., 1998, 25, 603-606) showed
that the puzzling magnetic field of the Jovian satellite Io may indeed be induced by the elliptically
unstable motions of its liquid core that deffect Jupiter magnetic field. Our magnetohydrodynamics
experiment is a toy-experiment of this geophysical situation and demonstrates for the first time the
possibility of an induction of a magnetic field by the flow motions due to the elliptical instability.
A full analytical calculation of the magnetic dipole induced by the spin-over is presented. Finally,
exponential growths of this induced magnetic field in a slightly deformed rotating sphere filled with
Galinstan liquid metal are measured for different rotating rates. Their growth rates compare well with
theoretical predictions in the limit of a vanishing Lorentz force.

Geophysical and Astrophysical Fluid Dynamics (100), pp. 299-317 (2006)

• Coriolis effects on the elliptical instability in cylindrical and spherical rotating containers
    Le Bars M., Le Dizès S. and Le Gal P.

Abstract
The effects of the Coriolis force on the elliptical instability are studied experimentally in cylindrical and spherical rotating containers placed on a table rotating at a fixed rate . For a given set-up, changing the ratio Ω^G of global rotation to flow rotation leads to the selection of various unstable modes due to the presence of resonance bands , in close agreement with the normal-mode theory. No instability occurs when Ω^G varies between −3/2 and −1/2 typically. On decreasing Ω^G toward −1/2, resonance bands are first discretized for Ω^G<0 and progressively overlap for −1/2 Ω^G < 0. Simultaneously, the growth rates and wavenumbers of the prevalent stationary unstable mode significantly increase, in quantitative agreement with the viscous short-wavelength analysis. New complex resonances have been observed for the first time for the sphere, in addition to the standard spin-over. We argue that these results have significant implications in geo- and astrophysical contexts.

Journal of Fluid Mechanics (585), pp. 323-342 (2007)

• 
    Experimental analysis of the Strato-rotational Instability in a cylindrical Couette flow Le Bars M. and Le Gal P.

Abstract
This study is devoted to the experimental analysis of the stratorotational instability (SRI). This
instability affects the classical cylindrical Couette flow when the fluid is stably stratified in the axial
direction. In agreement with recent theoretical and numerical analyses, we describe for the first time in
detail the destabilization of the stratified flow below the Rayleigh line (i.e., the stability threshold without
stratification). We confirm that the unstable modes of the SRI are nonaxisymmetric, oscillatory, and take
place as soon as the azimuthal linear velocity decreases along the radial direction. This new instability is
relevant for accretion disks.

Phys. Rev. Lett.  99, 064502 (2007)

• Law of spreading of the crest of a breaking wave
  Pomeau Y., Jamin T., Le Bars M., Le Gal P and Audoly B.
  Abstract
  In a wide range of conditions ocean waves break. This can be seen as the manifestation of a singularity in the dynamics of the fluid surface, moving under the effect of the fluid motion of the underlying fluid. We show that, in the real world,
  at the onset of breaking, the wave crest expands in the span-wise direction as the square root of time. This is first derived from a theoretical analysis and then compared with experimental findings. The agreement is excellent.

shadowgraphic movie of a breaking wave

Proc. Roy. soc. (2008)

1. Bioluminescence

• Bioluminescence du plancton marin
  Anne-Sophie Cussat-Legras, Patrice Le Gal et Brigitte Berland

  Résumé
  Le phénomène de bioluminescence est bien connu des marins ou des nageurs nocturnes. Il provient de l'excitation de certains organismes planctoniques, notamment des dinoflagellés, provoquée par les mouvements de l'eau occasionnés par le passage de bateaux ou de nageurs. Ces organismes uni-cellulaires possèdent une taille de quelques dizaines à quelques centaines de microns, et quand leur densité est suffisamment importante, cette bioluminescence naturelle pourrait devenir un moyen de visualisation et d'études originales des écoulements hydrodynamiques. Il semble donc interressant de réaliser des expériences de stimulation de la bioluminescence en laboratoire afin de comprendre et calibrer la réponse du plancton à des stimuli contrôlés. Plusieurs espèces de dinoflagellés sont actuellement cultivées: Pyrocystis lunula, P. noctiluca et Gonyaulax polyedra. Une fois les densités des cultures de dinoflagellés suffisantes, ces solutions sont transférées sur des installations expérimentales, afin de procéder aux essais de bioluminescence stimulée par différents écoulements. Le stimulus naturel de la bioluminescence des dinoflagellés est mécanique; les cellules répondent à une déformation de la membrane cellulaire produite par des forces "brusques", induites par une forte agitation forte agitation de l'eau (içi dans un flacon de culture), comme dans le cas du brisement des vagues ou la nage rapide des mammifères, des poissons ou des invertébrés.

  Proceedings of the 13th International Couette-Taylor Workshop, Nonlinear Dynamics in fluids, pp. 10-13, Barcelona, July 3-5, 2004.

• Bioluminescence of the dinoflagellate Pyrocystis noctiluca induced by laminar and turbulent Couette flow
  Cussatlegras Anne-Sophie and Patrice Le Gal

  Abstract
  The excitation of bioluminescence by different flow regimes generated within a Couette chamber was examined using the dinoflagellates Pyrocystis noctiluca. Cultured cells of Pyrocystis noctiluca were gently transferred into a cylindrical Couette chamber in a dark room. In initial experiments, the velocity of the outer Couette cylinder was then gradually increased. The bioluminescence emissions in response to stationary-laminar and turbulent flows were quantified using a photomultiplier tube. Video images were also recorded in order to identify the location of bioluminescence emissions within the Couette chamber. Reflective flake flow visualizations were used to correlate these locations to the flow regimes in those parts of the chamber. These experiments clearly demonstrated that the strongest bioluminescence emissions were only triggered by the onset of turbulence at high rotation speeds. Below the turbulence threshold, much lower bioluminescence emissions were detected, and appeared to be in response to a non-homogeneity in the stationary-laminar flow (end cap effects and Ekman cells). In a second set of experiments, the excitation of bioluminescence in response to acceleration was studied by abrupt starts of the rotating Couette cylinder. These experiments also triggered massive bioluminescence emissions. We conclude that pure laminar-stationary, homogenous shear flow excites very little bioluminescence in Pyrocystis noctiluca. The bulk of bioluminescence emissions primarily occurred under non homogenous or non stationary flow conditions, where the cells experience velocity changes as they move through the flow. These findings are discussed in relation to the theory that bioluminescence in dinoflagellates is an anti-predation mechanism. (bioluminescence in the turbulent Couette flow)

  Journal of Exp. Marine Biology and Ecology 310/2, pp. 227-246 (2004)
  Voir également La bioluminescence marine par A.S. Cussatlegras.

• Dinoflagellate bioluminescence in response to mechanical stimuli in water flows
  Cussatlegras Anne-Sophie and Patrice Le Gal

Abstract
Bioluminescence of plankton organisms induced by water movements has long been observed and is still under
investigations because of its great complexity. In particular, the exact mechanism occurring at the level of the cell has
not been yet fully understood. This work is devoted to the study of the bioluminescence of the dinoflagellates plankton
species Pyrocystis noctiluca in response to mechanical stimuli generated by water flows. Several experiments were performed
with different types of flows in a Couette shearing apparatus. All of them converge to the conclusion that stationary
homogeneous laminar shear does not trigger massive bioluminescence, but that acceleration and shear are both
necessary to stimulate together an intense bioluminescence response. The distribution of the experimental bioluminescence
thresholds is finally calculated from the light emission response for the Pyrocystis noctiluca species.

Non linear processes in Geophysics, 11, pp. 1-7 (2004)

• Variability in the bioluminescence response of the dinoflagellate Pyrocystis lunula
  Cussatlegras Anne-Sophie and Patrice Le Gal

Abstract
Light emission in dinoflagellates is induced by water motions. But although it is known that mechanical stimulations of these
organisms trigger the bioluminescent response, the exact mechanism that involves some cell membrane excitations by fluid
motions is not yet fully understood and is still controversial. We show in this experimental study that the accelerated shear flow,
created by abrupt rotations of one or both co-axial cylinders of a Couette shearing chamber excites the light emission from cultured
dinoflagellates Pyrocystis lunula. Following our first results published earlier that state that pure laminar shear does not excite the
main bioluminescent response in dinoflagellates, our present experiments show that both shear and acceleration in the flow are
needed to trigger the bioluminescent response. Besides, the probability to stimulate this bioluminescent response under acceleration
and shear is deduced from the response curves. This response follows a Gaussian distribution that traduces a heterogeneity in
individual cell thresholds for the stimulation of bioluminescence in a dinoflagellate population. All these results will have a
repercussion in the possible applications of dinoflagellate bioluminescence in flow visualizations and measurements. Moreover,
this study opens a new way in studying mechanically-induced stimulus thresholds at the cell level.

Journal of Experimental Marine Biology and Ecology, 343, pp. 74-81 (2007)

1. Liquid Crystal

• Cisaillement de cristaux liquides (recherche en cours)
  Patrice Le Gal, Leon Fronzoni et Ricardo Lima

  Résumé
  Contrairement aux molécules d'un fluide classique tel que l'eau, les longues molécules d'un cristal liquide peuvent être orientées lorsqu'elles sont soumises à une contrainte extérieure. Dans notre expérience, le champ appliqué à la couche de nématiques (orientée préalablement perpendiculairement au rotor et au stators) est dû à un cisaillement créé par la rotation d'une des deux plaques (le rotor) entre lesquelles est contenue la couche de nématiques d'une épaisseur de 100 microns. Le cristal liquide utilisé lors de ces expériences est le MLC-6610 de la société Merck. Ses caractéristiques physico-chimiques le rendent proche d'un nématique phase 9A. L'effet d'un cisaillement sur une couche de nématiques est un sujet qui a reçu beaucoup d'attention il y a quelques dizaines d'années car l'étude de la réponse de telles couches fluides cisaillées permet de mesurer les coefficients visco-élastiques du cristal liquide. Ainsi plusieurs expériences se sont attachées à l'étude de l'orientation des molécules (observée entre polariseurs croisés) dans des configurations d'écoulement de Couette plan ou de type rotor-stator. Nous avons alors noté que dans ces dernières expériences, des réseaux de lignes de disinclinaisons avaient été observées, mais qu'elles avaient été considérées comme néfastes compte tenu des objectifs de la recherche menée. Notre étude expérimentale montre en effet que le cisaillement provoque le basculement des molécules appartenant à certaines régions de l'espace séparées du fond homogène par des lignes de disinclinaison et dont l'organisation spatio-temporelle est fonction du taux de rotation appliqué. En particulier, nous avons mis en évidence à fort taux de cisaillement une forme de turbulence que nous appelons Turbulence d'orientation qui fond à l'arrêt du rotor. Les propriétés des textures observées ont été alors étudiées: taille des structures, vitesse de propagation des fronts séparant les domaines lors des régimes de fonte ou de croissance... Mais, si le rotor est mis à nouveau en mouvement avant la totale disparition des derniers domaines, les quelques gouttes qui n'ont pas encore fondu, vont constituer des germes où la nouvelle phase va pouvoir s'établir. Étonnement, comme le montrent les clichés successifs de la figure suivante, seuls les domaines ayant une double structure peuvent survivre; les ``mono-domaines'' sont tout d'abord étirés par le cisaillement puis ils disparaissent.

  3ième Colloque sur le chaos temporel et le chaos spatio-temporel, pp. 178-181, Le Havre, 24-25 sept. 2001.     Voir également ZIF

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