 Okay, thank you here, okay, so I try to give you a panorama of the different fluid and stabilities and structure, coherent structure, wakes, vortex when we work in our lab and are related to different problems of physics. So as said by Professor Sweeney, my main activity is experimental, so I try to give you an explanation of how we do in our experiments and our work. I am in the so first of all, thank you a lot for the organizer to give me this opportunity to be with you. I really am very happy and very sensitive to the interests of this particular school. I came from a called the Physique de Chimi of Paris. In Paris, in France, the ingenious faculties in the university are normally in what is called a big school. Our is a small big school because we have only no more than 70 students but many many teachers and professor and we have especially an experimental activity to produce physicists and chemists as engineering and with a lot of innovation but also a lot of history because it's the place where Pierre and Marie Curie discover radium and they discover radium essentially because there are very good experimentalists. In this picture you see here, this is the apparatus built by Pierre Curie to measure the activity because after Becquerel was observed this first natural activity, he put an apparatus to obtain and quantitative measurements of the activity and as this was Marie Curie, they found new chemical elements but essentially because they had in their hand a very strong instrument and this is very important to know this history of Pierre and Marie Curie and also the school with Sorio Curie, Frederick, Paul and Gervand was the head of the school as Pierre Gilles and other important scientists. I go to speak about fluid mechanics. I suggest you to take, I think it's not not more than ten dollars, this multimedia fluid mechanics CD with a lot near 500 or 400 movies of the different fluid mechanics experiments and explanation. So many times I go to use movies and concepts from these very interesting activity for a lot of very good colleagues many from our SPCI to show what happened with fluid mechanics. First of all, remember Navier-Stokes equation for fluid mechanics. Navier-Stokes has special equation with a non-linear part and a linear one, the Laplacian, with given the diffusive transport and this non-linear term giving you the convective transport or inertia. So it is important that these two combinations of linear and non-linear phenomena go to go ways, separate ways many times when you go to analyze fluid mechanics phenomena. Okay, remember an important point is the kinematical viscosity, which I remember is dynamic viscosity divided by the density and this is the reason and the hair is more viscous than water in terms of kinematical viscosity, what we go to use many times. So first of all, concepts about typical size, typical times. When you have diffusive phenomena and diffusive phenomena remember that the typical distance is related to the square root of the time and the pre-factor is the kinematical viscosity. Kinematical viscosity is the coefficient of diffusion of vorticity for this is very useful in duty problems. So a typical time is the square of the typical distance in your problem divided the kinematical viscosity. For example, you have a sharp profile of velocity, this profile goes to diffuse with this typical time and with this typical size. For the opposite, when you have convective phenomena, you have mixing by vortex, for example, in this case, you need to consider another time with its wheel with the typical velocity and the distance with, for example, returning and vortex, the time of return of vortex. So with this, those typical times, we go to explore all the phenomena of fluid mechanics. And for this, if you take Navier-Stokes equation, you go to be a dimensionalized with the typical size, with the typical velocity, you can form the Reynolds number, which is the product of the typical velocity, the typical distance divided by the kinematical viscosity. And this Reynolds number is no more than the ratio of these two typical times, the time of diffusion and the time of convection. By example, if the diffusive time is low, you have the low Reynolds behavior with more diffusion. And so normally, if the smaller time gives the dominant mechanism with this small introduction, because I think that people was not came necessarily or don't remember the time of when you learn about fluid mechanics. Another important point of fluid mechanics, many times you have strong velocities, you have inertia, you have separation, especially when you have an adverse gradient of velocity, so higher velocity, lower velocity, and you produce this kind of separation. This is a very important problem, for example, in the airplanes. If you take an higher angle of inclination of the wings, you produce this separation, and you have a problem with lift. So this is an important problem in aerodynamics in fluid mechanics. So I go to use this separation, what happened here? Here I have a ratio of deep wall with fluid, and I go to use this to produce fluid and stability. Why? Because I have higher velocity here and very low velocity here, nearly and slow motion. So I have the condition for the flow instability. If I grow the Reynolds number in this flow visualization in our water tunnel, I go to come back after, you can show one, two important points. First of all, the recirculation length, the size of the recirculation, grows with the Reynolds number, grows, grows, grows. But in one moment you have fluid and stability. And this fluid and stability, you observe this vortex with vorticity normal to the wall, and what you can observe in another point, more intense as the vorticity, more intense as the recirculation length shrinks. So we have essentially this kind of behavior with the recirculation length in the beginning for a stationary wall flow grow, and after in the end is constant because you have this shrink of the velocity. How I can understand phenomenological concept, this phenomena. In the beginning, what happened? In the beginning I suppose I have slow velocities, and the diffusing phenomena is more important. So if I have velocity here by diffusion, the velocity came to the, this is the backward facing step, 8 h, higher velocity here, new velocity here. By diffusion, the velocity came from here until here. What is, what time take by diffusion to came from here until here, then this is the square root of new t. But what is, what is delta, delta is this distance. What is the time? There's the time to go from here until the end of the recirculation length. So it is L divided u. So I put here inside, I transform with the Reynolds number, and I found that L, the longer length of the recirculation length, grow with linearly with the Reynolds number, what is I observe. So for this diffusive mechanism, explain me the growing in the beginning of the recirculation length. What happened in the end? In the end, I have strong vorticity. So the typical time now is the time to return this, this vortex. What is this, this, this time is the wavelength with the size, the wavelength, the, the size of the, the length divided by the 2 or the size of the vortex divided the typical velocity with this, the order of magnitude of the free stream velocity because I have free stream velocity and zero here. Okay? So the typical time is this, and in this time I need to go from here until here, from the recirculation length divided by the velocity. So I observe in this case that L is proportional to h. So the L divided h is constant. So I have the two behaviors, a small Reynolds number, diffusive, a big Reynolds number, convective, inertial, but in the middle is the problem because it's not very clear how is the low for in between these two states. And this is an open subject on such a very active, there are on paper last year from the group of Swiss, how to understand the very non-linear phenomena to take in consideration the two extremes. Okay. I, I speak about water tunnel. Water tunnel, it is, it is not an top, it's not an terrible experiment, but nearly. It's the smaller water tunnel in the world. Normally, you have in your universities a lot of mechanical engineering, aerodynamics, or aerodynamics, and you have a building for a water tunnel. First I thought we are in the center of Paris. It's very expensive, the square meter. So our water tunnel is no more than this, half of this size. So a small water tunnel you can build in your institute because if you have a workshop, it's only plexiglass. You have holes and plexiglass, no more than this. And it's very efficient because you do basic physics and you can do application. You can do, to study the phenomena of many problems, you can do small reduction models to study what happened by example flow control in the TGV, in the train of the Great Velocity in France. They are not in a position. Okay. So after I can help if you have ideas, there are another water tunnel, water, small, in the London Pinks University, but it is important, important point. What you see in free mechanics, attention. What you see not necessarily is what you exist. Why? Because one is the streamlines. Streamlines is the tangent to the velocity vector. Okay. It is an institutionary flows. No problem. What you see here, but with particles, with the trajectory, the stick lines I go to speak after is what is really the streamline. What is important is the velocity. After we use PIV, the method to measure the velocity, I will take pictures and it's very important to try to measure this tangent vector to the velocity of the flow. Okay. But what happened? Normally we put dye in one point. We put dye here. The dye is transported until here. If the system is not stationary, at each time, this molecular of dye observed different emotions. In one moment, this dye here was up here, but the particle here, this particle came from one time before from here, and this from other times, shorter here. Each particle, what you see here, has the history, the history from the exit of the dye until the moment you take the picture. It's very complicated. This picture is really very complicated because it's this integration of the past. Okay. There are an un-stationary flow. It is called a strict lines. Strict lines is not streamlined. Remember this. Okay. This is a typical error of the people doing numerical work. For example, see up. Okay. Try to show this. No, you don't show this except you put particles in your code, and you follow the particles. Okay. But normally, if you like to see what happened, what you see in visualization seems similar to vorticity. Okay. The flow visualization was very old. You know, Mare was the people in the, in this time, in the end of the nineties, he built this wind tunnel. He is the same guy who invented the cinematography. And at the same time, he was interested in studying the flow, to flow visualization. Okay. I'll come back to the backward phase type. What happened? The backwriters say, I have this profile of velocity. I have this inflection. I have this strong vorticity here in the, here is the recirculation, the freeways. Okay. And this is the, I try to understand why, why there are these instabilities. This is some kind of shear instability. A typical example of shear instability, if you have two flows as this, you incline this, this tube, and you can see this typical Kelvin-Helmholtz instability or shear instability. Okay. It is very, very typical in many problems of fluid mechanics. For example, many times you have this, this, this flow with this strong gradient in the case of quasi flow, in the case of a new shed, in the case of the, the wake in the, after a cylinder, the mixing layer. This is very typical. What you do to try to study this, you study linear stability. So you take the flow equation, for example, the 2D equations, you separate the flow in the basic state and you add small perturbations. And after you take, as the perturbations are very small, you take linear approximation, that is, this is the linear problem of the interstock. You suppose that this perturbation has this normal form. What is this? It's an owned, if you want, with some wavelength, one wave number k, with 2p divided by the wavelength, and an frequency, imaginary frequency real part is, if this part is this, is this imaginary frequency here, this is imaginary here, is positive, the flow explodes. It is what, what you try to see is the dispersion, the relation is the relation between the wavelength and the wave number, the wave and the frequency for each Reynolds number to see what happened. So what you do, you take the basic flow, you put in the equation here, you take this basic flow by example, the mixing layer, or even this particular approximative basic flow, you do the, the dispersion relation and you obtain this. What is this? This gives the growth rate positive, if this negative flow is stable, positive between this wave number and this wave number, the inverse of the wavelength. So it is, and there are maximum, there are maximum. So normally I expect to see this wave number or this wavelength, remember, very important. Almost the calculation in this flows, if I do a tangent hyperbolic adhesion here, or this piece of, this mixing layer, normally this value is 0.39, 0.41, very near 0.4. If you need the order of magnitude, remember 0.4 as the typical wave number. And as this, I go to the more typical problem of the vortex shedding, or the more typical open flow and stability, which is the Benard-Fonkermann, because Benard was observed this in 98 and Fonkermann gave the theory in, in, in 1911. Oh, so before Reynolds number 47, nearly 50, you have two waves, stationary waves behind the cylinder. But in one moment, from Reynolds bigger than Reynolds critical, you have this alternative vortex shedding with emission of the vortex. And this is the important point. This is the cylinder, in infinite cylinder. And these, these are the vortex, okay? The vorticity parallel to the object, span-wise, not stream-wise. I go to, came back this, okay? So this was observed by Leonardo, very nice picture of Leonardo, who was observed in nature, nature, and nature is a lot of this kind of vortex behind a bridge. And you can observe this by satellite, because you have a small bond time, and you have nil and 2D problem in the atmosphere, and you can this, the emission in the atmosphere with clues. So what have, what is? Essentially, you have an uniform profile, you have the object, the cylinder, and you have the wake, okay? So this wake, go to produce this shear and stability. And this is the, the, the stability. An important point. If you see here, there are a very small change in the basic flow by the existence of the stability. And this is an important point, but I need after, okay? So I have an experiment in the water channel, okay? About with fluorescein as dye, okay? And you can see it is really a hydrodynamic, or rather a hydrodynamic clock, okay? Because if you are very clear, this is an absolute instability, very clear frequency, and we, attention. The, the wake, not grow, grow, grow, grow until, I know. It is what you observe, what you see. But in reality, reality, if you take measurements, the perturbation grow and after decrease, okay? So, and the typical size where there is the maximum is the correlation length in this hydrodynamic instability, okay? So, and in this case, you have the dispersion relation, I remember one point. Why there are a cutoff wave number? Because if the rolls are very big, by example here is small wave number, the shear is very small. So, small growth rate. If the wave number, the wave length is small, big wave number, you don't see the shear. So it is the reason there are cutoff and this part is stable. Another situation, by example, if you have no miscible interface between the shear, you have the cutoff is given by the capillarity, by example. So the cutoff is given by the capillary wave length. But here the cutoff is given by the geometry of the flow. Order of magnitude of the frequency, order of magnitude. Remember, the point 4 is the maximum growth of the wave number with the maximum growth. So 2p delta light. What is the typical size? The typical size of the shear is the half of the diameter, okay? So you can observe that the wave length follow the dispersion relation of the shear and stability is the order of 18. It is order of magnitude. So if the frequency is the phase velocity of the wave length and the phase velocity is smaller than the velocity u, you arrive to obtain that the frequency is this value. Normally, the frequency is measured with the struer number, which is the dimensional alliance of frequency multiplied by distance divided by the u is 0.12. It is not exactly, but if you have an instability and you observe when the struer number is 1, sure it is not a shear instability. The order in magnitude, when you have this typical struer number of 0.2, you can do the calculation so you can observe you are in the good kind of instability. Okay, the real struer number is this. The struer number grows in the beginning from this onset and after goes to this constant and it is a nonlinear oscillator with the wave length proportional to the square of the amplitude, but the amplitude is proportional to the square root to the distance of the onset. So you have the low of the frequency. It's important because it's an industrial application because if you put in your pipe, for example, an cylinder and you take a capture of pressure, you can measure the pressure of the vortex shedding and you relate the frequency of the frequency to the Reynolds to the velocity to the flow rate. As this you have many, many sensors to measure flow rates in the industry. But another big problem is it is what we observe this frequency, but if you do the calculation of the linear theory, it is this low. So there are these crepants of you calculate the global calculation of the frequency and what you observe it and what is the reason? Because these measurements are calculated on the basic of the basics flow at each Reynolds number. But I say normally the fluctuation by nonlinearities can develop what is called a zero mode. So one is stationary modification of the mean flow. And this modification of the mean flow has a strong importance. If you do the calculation, as we do many people, do the calculation, not taking the real basic flow, the basic flow estimate, but the mean flow, you obtain the good. And this was many years ago, Marcus suggested to understand turbulence, take the mean flows from the linear theory. This is a very important subject of discussion today. And one important moment to observe that these nonlinearities are real exist is you see the recirculation length behind the cylinder. What happened? The recirculation length grow as I showed you before, linearly with the Reynolds number. And afterwards the stability begins shrink. And the difference between the length before and this length is the fact, sorry, is the fact as the perturbation grows, put an additional mean flow who stopped the recirculation. And this is the more macroscopic effect of the nonlinearity. You can see this, the stronger reaction. One point about force. These vortex produce force on the objects. You can estimate if you take by Safman the moment of vorticity in the vortex street and you can approximate, and you can see the velocity, the force is proportional to the derivative of the product of the circulation and the distance to the central line. So bigger is the circulation, bigger is the force. Smaller is the distance of the central line, smaller is the drag, by example. But, but, but, but, by example, if you change the sign of the circulation, you go to the, change the sign of the force. And you are in the case of the fish, for example, propulsion. Because it has the emission of vortex, but unreversed, but, but it is the Benarphone Carman who produced drag. But now if you change the same, oh, sorry. If you change, in this case, you have not more drag, but you have thrust. Okay. And this is one mechanism to go, to give propulsion. So, by example, this is the PIV measurements. We have this drag, we have some flap and the function of the frequency of the flap, we can modify the distance between the street. And when one moment the street is zero here, as in Kolmogorov problem, okay. And you can change this. And this is interesting because what happened? Many bills, many bills have a number calculate about the amplitude. You take this amplitude of the flapping, okay. And multiply by the velocity, and divided by the period, almost the bit are around 0.2. And what happened? We have measurements with some flap, okay. So we have, in this kind of frequencies, we have a Benarphone Carman, but we can observe, we can observe, but higher frequency, this reverse. And this reverse, we can measure force. And this is the line which goes to change to drag to thrust. And this is the line to strewell 0.2, as the observed. Okay. I speak about vortex shedding about, if you want, two dimensional objects. But what happened with, when you have the vortex shedding become behind 3D bodies, by example in sphere? I go to my water channel, I put in sphere here, okay. And we try to study what happened. First of all, I compare the 2D problem to the 3D. In the 2D, we have two recirculations. In the case of the sphere, I have a tour of recirculation. An azimuthal recirculation. In one moment, in one moment, this azimuthal recirculation slows symmetry. One part of the tour, by example here, is bigger than one this part of the tour. And it is, and this go to produce two counter-rotating vortex, stationary. So the first instability in the case of an sphere, or an disk, are the existence of the breaking of the axisimethic symmetry. And I produce two counter-rotating small, very weak, two small vortex, okay. And after, and after we have, this is the situation, by example in the case of this sphere between 212 and 270, this stationary instability, and after we have vortex shedding in the form of herpes, okay. And this is what you observe, this is the typical herpes, okay. So if you come from the side, from the top, or you can see in front, okay. It is the typical vortex shedding. One important point, one important point for free mechanics. What is important in the herpes is the legs, this part. Because these legs go to mix up very well. The head of the, the head of the herping is, seems not very important. I see, seems because it's a very strong discussion today, okay. Okay. To give an idea what happened, perhaps you can see in the drops in spark water. Imaginate a bubble. It's a sphere. I suppose the bubble is rigid. So in the beginning, the bubble grows, the Reynolds-Gernamel grows until 212 and appear the two counter-rotating vortex to produce lift. So this lift put an angle. So the bubble arrived here and deviate here stationary. And after, there are the herpes. So I have the zigzag. And a higher instability is this kind. So you can observe this when you have and drop the, this sequence of instability. Perhaps you can observe this in a bottle, okay. Good. And then it's important because I come back to the head. Now we have experiments when we turn this sphere because the interest is to study the wind turbines, okay. So, but it's very similar, okay. The, the interest is, and what happened here is, okay, is I add, if I put rotation, I add vorticity at one of the legs and diminish the other. So the herping disappears and you have an helical, helical mode. And almost the, the, the situation, you, the, the herping up is very short region and you have different helical, higher order helical modes. Okay. Good. Attention. What I explained is valuable all the time for all the shear flows? Not. Because if I apply this concept to Poisson flow, plane, quake, pipe, flow, even boundary layers, what happened is you can calculate the critical Reynolds number and it is a critical Reynolds number, example in the case of quake plane, say, all the time is stable and pipe all the time is stable. But the reality you can observe or the critical, you can observe transition are Reynolds less than the critical linear one, even if it all the time is stable. And it is why? Because it exists in so critical transition to turbulence with the existence of very localized structure with the spots. It is one spot in our channel. Okay. With these spots are essentially with three wide vorticity, no span wise at the men are from Garmin. Okay. And it is very, is sensitive to finite amplitude perturbation. Okay. So in the case of world confined shear flows, we have different situation. And why? Because if I am wall, I have strong gradient, the stream wise vortex, vortex in the direction, go to mix and put the high momentum from here until the wall and the opposite. And it's not the same scenario I discussed in the beginning with the men are from Garmin. And this is the reason why you have a very different situation even when you have shear, but the existence of wall wounded. Okay. But in this case, now we do an experiment and to produce quite a Poisson stability. So we have a moving back here and fix a wall here, the quit go from put water from one side to other side, the cable came back. And we can see laminar, the exit on spot, the existence of a band or the full turbulence here. And it is what the one of the subject to understand the existence of this kind of transitions. Okay. Another important point to the stream wise vortex is what occur also in reality. By example, take objects as your car. You have behind behind this part, you have a span wise electroculation. But as the sphere, as the disk, there are many very strong constrain wise vortex behind your car. And this varies behind are weak of the simulation, but important because 45% of the drug, the pressure drug in your car came from the the artistic you have behind. So it's important to modify this hydrodynamics. And for this, we can put counter rotating vortex in vortex generators. By example, we have here is solid vortex generator who go to produce pair of counter rotating vortex who go to interact with the body to modify these big structures and have a very important effect. Normally, you cannot use, you cannot use these because it's not useful when a car, but you put shed in a cross flow you blow and this shed produce two counter rotating vortex. And this is what is today the vortex generator applied in names in very small apparatus. Okay. To finish, I come back to the Kelvin Helmholtz stability, shear instability as I say before the cutoff was given by the size of the boundary layers. But, but you come if you have an interface, the capillary effect try to like don't like to put very small radius. Okay. So I go to show you and Helmholtz instability and shear instability, but with interface. But in this case, I go to produce this in the following. I have two flows here, no miscible, water in the here and in the top very, very viscous oil. And I try to produce this oscillation. And what happened with this oscillation? I go to generate Stokes layer. So, you know, by skin effect, when you have rotation and proportional to the frequency, you can induce a wave boundary layer here. Inversal and proportional, higher is the frequency, smaller is the thickness. Okay. So if I can produce this, now I have a shear instability, even the function of the time. And this shear instability, go, go, go, go, go, go to produce these frozen waves. Okay. And it is what an easy phase, what is the reason? Because one of the, the oil here is very viscous, very big wave boundary layer. So it, it turns with the reservoir, with the box. And the other not. So it is equivalent to shear one layer, shear the other, but it's nearly, not no motion. Okay. It's very easy to do. Okay. If you take this and you go to, to, to observe what do you have here, perhaps after you turn. Okay. And you can produce. We have here two liters of this oil. If you want, you take, to come back to your lab and do this, this small toy to show you this kind of surface instability which can be here much. It's interesting because it's this code with this kind of stability, you can see the linear phenomena, the non-linear desaturation, and even the very interesting problem of, of wave breaking. By example, if this, you remember the, the finger doing this kind, it's very similar to the problem of wave breaking. And we study now how is the typical distance and function of time and compare with the recent theoretical prediction of, of, of, of promo. And you can do even the same with sun. Okay. You have sun, water, and you can do this, but in this case it's not shear stability, but you arrive to produce underwater dunes by modulation of the interface with the same concepts. Okay. Good. I think as this you have an idea of what you can do in flow, flows, even if they're not exactly thyroid experiments, in other, in many cases, yes, but I suggest you to build your water tunnel in your laboratory up to finish. I am very happy today, even with emotion, because I was studying Argentina in Buenos Aires and one of my teacher was Jambiashi. And here we are in the hall at Jambiashi. So really I am very happy. He was a fantastic teacher and he is very recognized. It's just the, this hall of lecture at the Jambiashi hall. So it's a good moment for me. I was the student here, I was Jambiashi, my teacher of thermodynamics many, many years ago. Thanks to all my collaborators of the laboratory.