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In turbulent rough-walled flows, the 2D friction-roughness relation differs from its 3D counterpart., The friction f is the property of wall-bounded flows that sets the pumping cost of a pipeline, the draining capacity of a river, and other variables of practical relevance. For highly turbulent rough-walled pipe flows, f depends solely on the roughness length scale r, and the f − r relation may be expressed by the Strickler empirical scaling f ∝ r1/3. Here, we show experimentally that for soap film flows that are the two-dimensional (2D) equivalent of highly turbulent rough-walled pipe flows, f ∝ r and the f − r relation is not the same in 2D as in 3D. Our findings are beyond the purview of the standard theory of friction but consistent with a competing theory in which f is linked to the turbulent spectrum via the spectral exponent α: In 3D, α = 5/3 and the theory yields f ∝ r1/3; in 2D, α = 3 and the theory yields f ∝ r.

Numerical simulations of rotating two-dimensional turbulent thermal convection on a hemisphere are presented in this paper. Previous experiments on a half soap bubble located on a heated plate have been used for studying thermal convection as well as the effects of rotation on a curved surface. Here, two different methods have been used to produce the rotation of the hemisphere: the classical rotation term added to the velocity equation, and a non-zero azimuthal velocity boundary condition. This latter method is more adapted to the soap bubble experiments. These two methods of forcing the rotation of the hemisphere induce different fluid dynamics. While the first method is classically used for describing rotating Rayleigh&ndash, B&eacute, nard convection experiments, the second method seems to be more adapted for describing rotating flows where a shear layer may be dominant. This is particularly the case where the fluid is not contained in a closed container and the rotation is imposed on only one side of it. Four different diagnostics have been used to compare the two methods: the Nusselt number, the effective computation of the convective heat flux, the velocity and temperature fluctuations root mean square (RMS) generation of vertically aligned vortex tubes (to evaluate the boundary layers) and the energy/enstrophy/temperature spectra/fluxes. We observe that the dynamics of the convective heat flux is strongly inhibited by high rotations for the two different forcing methods. Also, and contrary to classical three-dimensional rotating Rayleigh&ndash, nard convection experiments, almost no significant improvement of the convective heat flux has been observed when adding a rotation term in the velocity equation. However, moderate rotations induced by non-zero velocity boundary conditions induce a significant enhancement of the convective heat flux. This enhancement is closely related to the presence of a shear layer and to the thermal boundary layer just above the equator.

International audience; This work is devoted to a numerical study of two-dimensional incompressible flows in afluid-porous medium system placed on an impermeable wall. Flow in the whole system is studiedeither at the pore scale or at the Darcy scale (using a one-domain approach) and the models atboth scales are solved with a penalization method using the same formal Navier-Stokes equationsmodified by a Darcy-like term. Several effective medium penalized models are considered for thesimulations. Various flow regimes are investigated ranging from laminar to turbulent. The velocityprofiles inside and outside the porous medium show significant discrepancies between the differentpenalization models compared to the direct numerical simulations. This work motivates furtherstudies about the spatial variations of the penalization coefficient to be introduced in the effectivemedium models in order to better reproduce the physics near the fluid-porous medium boundaries.

Many far field boundary conditions are proposed in the literature to solve Navier-Stokes equations. It is necessary to distinguish the streamwise or outlet boundary conditions and the spanwise boundary conditions. In the first case the flow crosses the artificial frontier and it is required to avoid reflections that can change significantly the flow. In the second case the Navierslip boundary condition is often used but if the frontier is not far enough the boundary is both inlet and outlet. Thus the Navier-slip boundary condition is not well suited as it imposes no flux through the frontier. The aim of this work is to compare some well-known boundary conditions, to quantify to which extend the artificial frontier can be close to the bodies in two-and three-dimensions and to take into account the flow rate through the spanwise directions.

International audience; The aim of this work is to study the platooning of square-back vehicles on top of a road. When two or three bodies are following each other with a short distance between them, the presence of the preceding body changes significantly the pressure force in front of the following one as a weak flow is present in between. The preceding body plays the role of a buckler and so the following body has to face completely different flow conditions. Therefore the drag coefficient of the following bodies can be drastically reduced as shown on the results. But the reduction is strongly linked to the distance between the bodies and the differences are significant. The numerical simulations are performed around simplified vehicles, namely the square back Ahmed body and the simplified European tractor-trailer geometry. The results are also linked to the shape of the bodies.

An efficient method to capture an arbitrary number of fluid/structure interfaces in a level-set framework is built, following ideas introduced for contour capturing in image analysis. Using only three label maps and two distance functions we succeed in locating and evolving the bodies independently in the whole domain and get the distance between the closest bodies in order to apply a collision force whatever the number of cells is. The method is applied to rigid solid bodies in order to compare to the results available in the literature. In that case, a global penalization model uses the label maps to follow the solid bodies all together without a separate computation of each body velocity. Numerical simulations are performed in two- and three- dimensions. An application to immersed vesicles is also proposed and shows the capability and efficiency of the method to handle numerical contacts between elastic bodies at low resolution. Two-dimensional simulations of vesicles under various flow conditions are presented.

Two-phase immiscible fluids in a two-dimensional micro-channels network are considered. The incompressible Stokes equations are used to describe the Newtonian fluid flow while the Oldroyd-B rheological model is used to capture the viscoelastic behavior. In order to perform numerical simulations in a complex geometry like a micro-channels network, the volume penalization method is implemented. To follow the interface between the two fluids, the level-set method is used and the dynamics of the contact line is modeled by Cox law. Numerical results show the ability of the method to simulate two-phase flows and to follow properly the contact line between the two immiscible fluids. Finally, simulations with realistic parameters are performed to show the difference when a Newtonian fluid is pushed by a viscoelastic fluid instead of a Newtonian one.

A vortex generated behind a simplified vehicle induces a pressure force at the back wall that contributes to a significant part of the drag coefficient. This pressure force depends on two parameters: the distance of the vortex to the wall and its amplitude or its circulation. Therefore there are two ways to reduce the drag coefficient: pushing the vortices away from the wall and changing their amplitude or their dynamics. Both analytical studies and numerical simulations show that these two actions decrease the pressure force and consequently reduce the drag coefficient. The first action is achieved by an active control procedure using pulsed jets and the second action is achieved by a passive control procedure using porous layers that change the vortex shedding. The best drag coefficient reduction is obtained by coupling the two procedures.

International audience; Viscoelastic non-Newtonian fluids can be achieved by adding a small amount of polymer additives to a Newtonian fluid. In this paper, numerical simulations are used to investigate the influence of such polymer additives on the behavior of flow past a circular cylinder. A numerical method is proposed that discretizes the non-linear viscoelastic system on a uniform Cartesian grid, with a penalization method to model the presence of the cylinder. The drag of the cylinder and the flow behavior under the effect of different Reynolds numbers (), Weissenberg numbers (Wi) and polymer viscosity ratios (ε) are studied. Numerical results show that different flow characteristics are exhibited in different parameter zones. The polymer viscosity ratio plays an important role at low Weissenberg and Reynolds numbers, but as the Reynolds and Weissenberg numbers increase, the influence of ε weakens. The drag force of the cylinder is mostly affected by the Reynolds and Weissenberg numbers. At low Reynolds numbers, the drag of the cylinder and the flow fields are only affected by a large value of Wi when the elastic forces are strong. Non-trivial drag reduction occurs only when there is vortex shedding in the wake flow, whereas drag enhancement happens when the vortex shedding is inhibited.

In this paper, diphasic flows driven by pressure gradient in channels of a few hundred of micrometres square sections are studied. At this scale, the interfacial effects are dominating and the instabilities processes are generally studied from the experimental point of view. The instability is a well-known hydrodynamic instability due to surface tension namely the Plateau-Rayleigh instability. In this work, tridimensional numerical simulations are presented to understand this phenomenon and more generally to study the behaviour of diphasic fluids evolving in square microchannels.

The control of two-dimensional flows around the Ahmed body with a rear window on top of a road is achieved using porous devices added on some parts of the body. The modelling of the flow in different media is performed by means of the penalisation method. A good choice of the location of the porous interfaces yields an improvement of the aerodynamic parameters. To cite this article: C.-H. Bruneau et al., C. R. Mecanique 335 (2007).

A square back Ahmed body is used to mimic a heavy vehicle, bus or truck, in order to derive control processes that yield a significant drag reduction. The first step is to analyse carefully the structures in the flow that have a strong impact on the drag forces. Then, active and passive controls using blowing jets or porous medium layers are presented and discussed. The results are analyzed showing the direct impact of the control on the flow behaviour.

In this work, a viscosimeter implemented on a microfluidic chip is presented. The physical principle of this system is to use laminar parallel flows in a microfluidic channel. The fluid to be studied flows side by side with a reference fluid of known viscosity. By using optical microscopy, the shape of the interface between both fluids can be determined. Knowing the flow rates of the two liquids and the geometrical features of the channel, the mean shear rate sustained by the fluid and its viscosity can thus be computed. Accurate and precise measurements of the viscosity as a function of the shear rate can be made using less than 300 microL of fluid. Several complex fluids are tested with viscosities ranging from 10(-)(3) to 70 Pa.s.

Numerical simulations of the 2D lid-driven cavity flow are performed for a wide range of Reynolds numbers. Accurate benchmark results are provided for steady solutions as well as for periodic solutions around the critical Reynolds number. Numerous comparisons with the results available in the literature are given. The first Hopf bifurcation is localized by a study of the linearized problem.

SUMMARY The aim of this paper is to model and simulate the displacement of radioactive elements in a saturated heterogeneous porous medium. New schemes are proposed to solve accurately the convection-diusion- reaction equations including nonlinear terms in the time derivative. Numerical tests show the stability and robustness of these schemes through strong heterogeneities of the medium. Finally the COUPLEX 1 benchmark concerning the fareld simulation of a pollutedow by a leak of a nuclear waste disposal is performed and compared with the results available in the literature. Copyright ? 2005 John Wiley & Sons, Ltd.

The passive control of bluff body flows using porous media is investigated by means of the penalization method. This method is used to create intermediate porous media between solid obstacles and the fluid in order to modify the boundary layer behaviour. The study covers a wide range of two-dimensional flows from low transitional flow to fully established turbulence by direct numerical simulation of incompressible Navier-Stokes equations. A parametric study is performed to illustrate the effect of the porous layer permeability and thickness on the passive control

A proper orthogonal decomposition based model is considered for two-dimensional vortex shedding past a confined square cylinder. The aim is to study the validity of such a model for Reynolds numbers and blockage ratios that are different from those for which the model was derived. Using a calibration procedure it is shown that reliable results can be obtained in terms of short-term (one period) dynamics. Long-term dynamics are accurately captured with a variation of the Reynolds number, whereas the error becomes large when the blockage ratio changes. The controllability and observability of vortex shedding at a slightly supercritical Reynolds number is investigated relying on the accurate low-order models obtained.

A splitting method is used for the temperature and the velocity–pressure unknowns to solve the time-dependent thermal convection problem in an 8:1 enclosure (International Journal for Numerical Methods, this issue). High performance is obtained by means of incomplete Cholesky conjugate gradient for the temperature equation on one hand and a multigrid procedure for Navier–Stokes equations on the other hand. The approximation is achieved by second- and third-order finite differences on staggered grids. The stability of the steady solution is analysed by the computation of the first Lyapunov exponent. The periodic flow at Ra=3.4×105 is widely discussed and some investigations have been done for some higher Rayleigh numbers. Copyright © 2002 John Wiley & Sons, Ltd.

A two-dimensional backward facing ramp is used to represent a car simplified rear window. Direct numerical simulations are performed to describe the flow behavior over the ramp. Constant blowing jets and synthetic jets are applied on the body to control the flow. The results presented in this work show a significant reduction of the recirculation zone.

A new artificial boundary condition for two-dimensional subsonic flows governed by the compressible Navier–Stokes equations is derived. It is based on the hyperbolic part of the equations, according to the way of propagation of the characteristic waves. A reference flow, as well as a convection velocity, is used to properly discretize the terms corresponding to the entering waves. Numerical tests on various classical model problems, whose solutions are known, and comparisons with other boundary conditions (BCs), show the efficiency of the BC. Direct numerical simulations of more complex flows over a dihedral plate are simulated, without creation of acoustic waves going back in the flow. Copyright © 2001 John Wiley & Sons, Ltd.

Resume Le controle passif de l'ecoulement derriere un obstacle est obtenu en integrant a l'obstacle des zones poreuses. La methode de penalisation est utilisee pour modeliser les differents milieux qui sont tous consideres comme des milieux poreux. Le fluide est identifie a un milieu poreux de permeabilite infinie et le solide a un milieu poreux de permeabilite nulle. Ceci permet de representer simultanenement des milieux fluide, solide et poreux en fonction d'un meme parametre. La presence du milieu poreux a l'interface entre le solide et le fluide permet de regulariser l'ecoulement et de reduire de facon significative l'enstrophie et la trainee.

Hydrodynamic stability during advection combined with diffusion and adsorption of a binary gas mixture in porous media is considered in this work. The general framework is that of pressure swing adsorption (PSA) on beds of zeolite beads. The dispersion/adsorption problem is studied at Darcy's scale on a 1D porous column from a numerical point of view while complete time-periodic cycles are considered. The regular solution of the problem is first sought using a finite volume scheme and stability analysis is performed on this time-dependent solution. While instability evidence is shown on a direct 2D numerical simulation of the problem with pressure and concentration disturbances at the entrance of the column, the stability analysis is carried out in 1D by making use of the linear amplitude equation method. Results clearly show the stability conditions which are quite different depending on whether pressure or concentration disturbances are considered as initial conditions or maintained as boundary conditions at column entrance.

Non reflecting boundary conditions on articial frontiers of the domain are proposed for both incompressible and compressible Navier-Stokes equations. For incompressible flows, the boundary conditions lead to a well-posed problem, convey properly the vortices without any reflections on the articial limits and allow to compute turbulent flows at high Reynolds numbers. For compressible flows, the boundary conditions convey properly the vortices without any reflections on the articial limits and also avoid acoustic waves that go back into the flow and change its behaviour. Numerical tests illustrate the eciency of the various boundary conditions. R esum e. Les equations de Navier-Stokes pour des fluides incompressibles ou compressibles sont r e- solues avec des conditions aux limites non r efl echissantes. Dans le cas incompressible, les conditions aux limites conduisent a un probl eme bien pos e, permettant de convecter correctement les tourbil- lons sans cr eer de r eflexions et de faire des simulations directes de la turbulence a grands nombres de Reynolds. Dans le cas compressible, les conditions aux limites permettent aussi de convecter correcte- ment les tourbillons et surtout d' eviter la remont ee d'ondes acoustiques qui changent le comportement de l' ecoulement. Des tests num eriques illustrent l'ecacit e des conditions aux limites propos ees.

Schrodinger-like equations play an essential role in the modeling of plasmas created by laser beams, and taking into account of relativistic terms yields a new kind of nonlinearity in them, as compared to the classical case. A numerical scheme involving a new handling of absorbing conditions suitable for Schrodinger-like equations is given, and several general models are studied: the classical cubic case linked to the Kerr effect for an anharmonic plasma, where numerical experiments prove the efficiency of our code applied to the computation of solitons and explosive solutions. Furthermore, new kinds of explosive solutions are computed, and we numerically show the essential role of the ground state to get approximations of the cubic explosive solution by global ones. A multiphotonic ionization model is also studied including higher-order terms in the nonlinearity. In this case, we obtain stable structures physically explained by competing saturation processes. These structures have been experimentally detected. Finally, a relativistic model involving the Lorentz kinematic factor in the evolution equations is investigated numerically; filamentary structures are found in agreement with predicted relativistic phenomena. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 672–696, 1999

This paper is devoted to the numerical approximation of the elliptic-hyperbolic form of the Davey–Stewartson equations. A well-suited finite differences scheme that preserves the energy is derived. This scheme is tested to compute the famous dromion 1–1 and dromion 2–2 solutions. The accuracy of Crank–Nicolson scheme is discussed and it is shown that it induces a phase error. The qualitative behaviour of the solutions is then studied; in particular the influence of the initial datum and of the various parameters is pointed out. Finally, numerical experiments show the existence of blow-up solutions.

Le but de ce papier est de mettre l'accent sur les difficultes majeures que l'on rencontre pour simuler des ecoulements transitoires de fluides incompressibles derriere des obstacles ainsi que pour analyser les solutions obtenues. Il est hors de question de pretendre a l'exhaustivite, seuls certains aspects sont presentes ici. En premier lieu les conditions aux limites artificielles du domaine de calcul et la prise en compte des obstacles. Ces deux points conditionnent pour beaucoup le choix de l'approximation selon le maillage utilise et l'aptitude a calculer des solutions a nombres de Reynolds eleves. C'est a dire des solutions transitoires vers la turbulence. La reside un nouvel ecueil car il est tres difficile de qualifier precisement une solution avec des outils d'analyse classique des qu'elle n'est plus strictement periodique.

An original method to implement cartesian computations to solve a spherical problem is introduced in this paper. The problem consists in performing the numerical simulations of a half soap bubble located on a heated plate. The gradient of temperature between the base and the top of the bubble generates plumes at the base that move up. These plumes give rise to eddies that survive for several minutes eventually creating a two-dimensional turbulent thermal convective flow. Our method consists in defining an appropriate stereographic projection in order to use classical numerical scheme defined for two-dimensional Navier–Stokes equations. The results are then analyzed through spherical harmonics decompositions and compared to data obtained with soap bubble experiments.

International audience; By using a half soap bubble heated from below, we obtain large isolated single vortices whose properties as well as their intensity are measured under different conditions. By studying the effects of rotation of the bubble on the vortex properties, we found that rotation favors vortices near the pole. Rotation also inhibits long life time vortices. The velocity and vorticity profiles of the vortices obtained are well described by a Gaussian vortex. Besides, the intensity of these vortices can be followed over long time spans revealing periods of intensification accompanied by trochoidal motion of the vortex center, features which are reminiscent of the behavior of tropical cyclones. An analysis of this intensification period suggests a simple relation valid for both the vortices observed here and for tropical cyclones.

The aim of this work is on the one hand to show that the drag coefficient of a bluff body is mainly linked to the vortical structures in the close wake of the body. Thus an active control can be used to push away these structures to decrease the pressure forces at the back and consequently to reduce the drag coefficient. On the other hand a study of the platooning is performed. When two bodies are following each other with a short distance between them, the presence of the first body changes significantly the pressure force in front of the second one as a weak flow is present in between. The first body plays the role of a buckler and so the second body has to face completely different flow conditions. Therefore the drag of the second body is drastically reduced as shown on the results. Finally a control of the flow around the first body gives promising and surprising results.Copyright © 2013 by ASME

Efficient natural condition s on open boundaries for incompressible flows are derived from a weak formulation of Navier-Stokes equations. Energy estimates in velocity-pressure are established from a mixed formulation and a rigourous proof of existence of solutions is given. As an illustration the conditions are written down for the flow behind an obstacle in a channel. Moreover numerical tests have shown the accuracy and robustness of such conditions.

International audience; In this paper, we use a simple Oldroyd B constitutive model to study the role of the viscoelasticity of dilute polymer solutions in two-dimensional flows past a bluff body using numerical simulations. This investigation is motivated by the numerous experimental results obtained in quasi two dimensional systems such as soap film channels. The numerical modeling is novel for this case and therefore a comprehensive comparison is carried out to validate the present penalization method and artificial boundary conditions. In particular we focus on flow past a circular object for various values of the Reynolds number, Weissenberg number, and polymer viscosity ratio. Drag enhancement and drag reduction regimes are discussed in detail along with their flow features such as the pattern of vortex-shedding, the variation of lift as well as changes in pressure, elongational rates, and polymer stress profiles. A comprehensive study of the flow behavior and energy balance are carefully carried out for high Reynolds numbers. Flow instabilities in both numerical and experimental results are discussed for high Weissenberg numbers

The aim of this work is to show that the drag coefficient of a bluff body is mainly linked to the circulation and the distance of the vortices in the close wake of the body. Thus an active control can be used to push away the vortices to decrease the pressure forces at the back. For the size of the vortices a passive control by means of porous layers is used taking benefit of the Kelvin-Helmholtz instability to change the vortex shedding. For two bodies with a short distance between them, the presence of strong vortices in the wake of the first body changes significantly the pressure force in front that governs the drag of the second body. The results of the control processes are illustrated on a single Ahmed body and on two Ahmed bodies following each other on top of a road.

Direct numerical simulations of a two-dimensional channel flow in the presence of a polymeric fluid are presented. The flow is perturbed by an array of cylinders which generates a turbulent flow downstream and whose statistical properties are studied in detail. Several features emerge from this study such as the reduction of turbulent fluctuations at large scales, the reduction of the energy transfer rate, and the reduction of the fluctuations of the enstrophy and energy transfer rates. These features are in excellent agreement with previous experimental measurements and show that despite the possible limitations of the model used to describe the polymeric fluid (an Oldroyd-B model), the changes observed here and in experiments may be generic to two-dimensional turbulent flows. An examination of the stress and elongation fields shows that the stresses are important in strong elongation zones pointing out that the effects due to polymers may have their origin in the large elongation zones which develop between vortices.

The vortices generated behind a simplified vehicle induce presssure forces at the back wall that contribute to a significant part of the drag coefficient. The study shows the strong relationship between the distance of the vortices to the back wall and these pressure forces. In particular, control process can modify the trajectory of the vortices to accelerate their removal from the wall and consequently reduce the drag coefficient.Copyright © 2011 by JSME

International audience; We here use direct numerical simulations to describe the flow of a viscoelastic fluid, modeled using the so-called Oldroyd B model, around a cylinder in two dimensions. A wide range of flow parameters is covered in these simulations allowing to draw definitive conclusions as to the effect of viscoelasticity on such a flow situation. Both drag enhancement and drag reduction are observed and a phase diagram is proposed in the parameter space Reynolds number vs. Weissenberg number. While only drag enhancement is observed below a Reynolds number of 40, both drag enhancement and drag reduction are observed for higher Reynolds numbers indicating that drag reduction is a feature associated with the shedding of vortices behind the cylinder. An interesting observation accompanies the onset of drag enhancement in the vortex-shedding regime: the shedding is suppressed.

Several active and passive control techniques are used to reduce the drag coefficient of the square back Ahmed body. The results are carefully analyzed and compared to each other. The final goal of this paper is to show that it is possible to couple passive and active control techniques to improve the flow control. In the present study, a drag reduction of 30% is achieved, almost corresponding to the goal of automotive industry.

The goal of this work is on the one hand to simulate the flow around a simplified ground vehicle called Ahmed body in order to identify the structures that contribute strongly to the drag coefficient and on the other hand to control the flow by an action on these main structures to reduce the drag forces.

The aim of this work is to analyse one of the mechanisms that contributes to the drag forces, namely the distance of the vortices to the back wall of a bluff body. The study shows the strong relationship between this distance and the pressure forces at the back. Indeed, the active control processes modify the trajectory of the vortices to accelerate their removal from the wall and consequently reduce the drag coefficient.Copyright © 2010 by ASME

The aim of this work is to control the flow around ground vehicles by active or/and passive strategies. The active control is achieved by steady, pulsed or closed-loop jets located at the back of the simplified car model. The passive control is performed using porous layers between the solid body and the fluid in order to modify the shear forces. Then, the two previous control methods are coupled to improve the drag reduction.Copyright © 2009 by ASME

Two-dimensional turbulence admits two different ranges of scales: a direct enstrophy cascade from the injection scale to the small scales and an inverse energy cascade at large scales. It has already been shown in previous papers that vortical structures are responsible for the transfers of energy upscale while filamentary structures are responsible for the forward transfer of the enstrophy. Here we propose an original mathematical tool, the interaction function, for studying the space localization of the enstrophy fluxes. It is defined using an orthogonal two-dimensional wavelet decomposition.

The aim of this work is to combine penalization and level-set methods to solve inverse or shape optimization problems on uniform cartesian meshes. Penalization is a method to impose boundary conditions avoiding the use of body-fitted grids, whereas level-sets allow a natural non-parametric description of the geometries to be optimized. In this way, the optimization problem is set in a larger design space compared to classical parametric representation of the geometries, and, moreover, there is no need of remeshing at each optimization step. Special care is devoted to the solution of the governing equations in the vicinity of the penalized regions and a method is introduced to increase the accuracy of the discretization. Another essential feature of the optimization technique proposed is the shape gradient preconditioning. This aspect turns out to be crucial since the problem is infinite dimensional in the limit of grid resolution. Examples pertaining to model inverse problems and to shape design for Stokes flows are discussed, demonstrating the effectiveness of this approach.

Two-dimensional turbulence admits two different ranges of scales: a direct enstrophy cascade from the injection scale to the small scales and an inverse energy cascade at large scales. It has already been shown in previous papers that vortical structures are responsible for the transfers of energy upscale while filamentary structures are responsible for the forward transfer of the enstrophy. Here we introduce an original wavelet-based new mathematical tool, the interaction function, for studying the space localization of the enstrophy fluxes. It is based on twodimensional orthogonal wavelet decompositions of the two terms involved in the transport term in the Navier-Stokes equations.

Numerous direct numerical simulations of soap film flows yield a large amount of data on two-dimensional turbulence. The analysis of such data is very sensitive to the analysis tools and the way they are used. On the one hand, some of the possible errors obtained by a misuse of the analysis tools are reported. On the other hand, a rigorous use of wavelet packets analysis reveals surprising results that slightly differ from the KLB theory for the flow considered. A careful wavelet packets filtering and a good computation of the energy and enstrophy fluxes show the role of the solid rotation vortices and the vorticity filaments to both the inverse energy cascade and the direct enstrophy cascade.