 So, hello everybody. My name is Sergey Chernyshov. I work for Central Aerohydrodynamic Institute in Moscow. Area of my study is acoustic radiation by subsonic turbulent jet. There are many important applications. Most known of them is aviation noise control. It is a classic problem. Nevertheless, there are unsolved questions like this. What aspect of turbulent pulsation in a jet is responsible for the sound radiation? After brief introduction, I will stop on the standard approach to the problem, then measurements and then proposed stochastic model to overcome some problems. A general solution of our acoustic problem was done in 1970 by Krow for the low Mach number and acoustically compact flow. He showed that the turbulent flow as a whole can be regarded as a source of sound with quadrupole moment calculated from incompressible dynamics. So, the task divided in two parts. First of all, in calculation of incompressible dynamics and then calculation of sound. But of course, we can interested in the details of sound sources. So, can we extract local turbulent events as independent sound sources? The answer is yes, but there is some problem because local event in vortex dynamics in some point is accompanied by in-phase disturbances of surrounding vaticity field in mixing layer. Both of them radiate sound, the self-sound by the event itself and the secondary, the so-called share noise, radiated by in-phase disturbances. So, aim of our study is correct modeling of the share noise, this part, radiated by turbulent mixing layer. Let's continue with the standard approach to this problem. In this approach, the first step is averaging of turbulent mixing flow and as a result, we have average share flow. Then, we look at the disturbances excited with some unsteady source in this flow and noise generated by the disturbances of the flow is regarded as share noise. It can be represented in terms of disturbances of vaticity. Then, the quadruple moment of all this situation can be departed in two parts. The quadruple moment of the self-noise, the event itself and the quadruple moment of share noise that can be represented as a function of disturbances of vaticity. The result for the point external source in the mixing layer, the harmonic end time, is presented here. In 2D flow, we have two different possible quadruples and one of them produces the share noise and the other no. Then, we continue with the measurements. There are a lot of measurements of jet noise, but most interesting and detailed of them are obtained with arrays of microphones. For example, with circular air, we can decompose the jet noise on different azimuthal harmonics and it is very interesting information. For example, here we can see the acoustic noise directivity for different harmonics. Here, acoustic radiation power depending on jet axial coordinate x. This is three azimuthal harmonics and different curves correspond to different frequency band. This is very good rich data for theory validation. Of course, theory that we can compare with the measurements is a little bit more complicated than I spoke about. Nevertheless, we can in 3D green function for different quadruples, 3D quadruples, we can separate the self-noise radiated by the source itself and the share noise components that relates with the disturbances in the surrounding vaticity field. Only two quadruples have share noise tom and the other node. If we compare the model prediction and the measurements, then we can see a very good agreement in a wide range of parameters for different velocities, for different angles and so on. This is a model without share noise. Share noise is not included here. If we include the share noise term, then the comparison is corrupted. Do we understand right the share noise phenomenon? To make this more clear, we consider the stochastic model of the share noise. When the turbulent pulsation in the jet achieves high amplitude, then the velocity field splits into something like vortex worms. This is vortex lines. Does this vaticity disintegration influence on the sound generation condition? Here in this work, we restrict with 2D model. So the standard approach, what is standard approach, is spoken above. It is averaging of background flow on the first step and calculation of share noise of the linear disturbances of this mean flow on the second step. Let's go in inverse order. At first, we calculate the share noise but this system of vortices and then average the result over the vortex locations. We would like to see is there any difference between these two approaches. Again, we restrict with 2D model of mixing layer. We neglect the non-uniformity along the x-axis. We consider the uniformly distributed point vortices in the infinite strip. If the system of vortex is rather dense, then we can consider this system in equilibrium for sufficient time for our purpose. Then we should consider the forcing of the system of point vortices by some external source. If dynamics of the vortices is determined by interaction between them and the effect of external source. If we consider the small disturbances, so the vortex displacement due to external source is much less than the distance between the vortices, then we can obtain linear equation for the small vortex displacement. After that, we can calculate the share noise quadruple moment that is quadruple moment corresponding to the effect of forcing of this system. Then we should average this expression for the share noise quadruple. Let's divide the share noise quadruple in two parts, this first and second. The second part can be average over vortex location directly, but as for the first part, it is not so easy because this part is a function of vortex displacement depending on the history of the whole system. To overcome this problem, we can consider the forcing of system by impulse source and just after the impulse data function of time. Just after this impulse, the displacement of vortices is a function of their own location. In addition, we use the Taylor series expansion for the quadruple moment at times after impulse. So we should average the Taylor series coefficients instead averaging of the quadruple itself. Then we can organize recurrent procedure and fortunately all the derivatives are equal to zero. So what does it mean? It means that as a result, we have following expression for the for the component of share noise component. So what does it mean? It means that average quadruple moment values are constant of motion for the linear disturbances of this system. Using this, we can obtain the solution for the point quadruple source inserted in the system of point vortices. That and source is harmonic in time and this is for two possible quadruple moment of the source itself. We have two solutions for the share noise component. If we compare the results for the standard approach mentioned above and the standard model proposed in this work, we see the difference. Of course, this is only simplified 2D model and to solve what model is better we need to compare with the experiment and of course we can develop the model to 3D case. Nevertheless, we can see that more accurate considering of the reaction of the mixing layer to the quadruple source show that that primary average of the flow like in standard approach leads to incorrect result. So we can conclude. First, the standard description of share noise is incorrect due to primary averaging of the background flow. Correct calculation of share noise radiated by turbulent mixing flow should include averaging at the final step. Then obtained results show possible cause of disagreement between experiment and theory for the net jet noise azimuthal harmonics and as for perspective studies of 3D model for the 3D stochastic model ongoing. Thank you for attention. You mean methods of noise control. In our group in Sagiya we do with that topics of course with experiment with the jet noise with plasma method as well. As for plasma, I should say that the result was achieved when plasma actuators force the jet on the some high frequency, then in the low frequency range the most important for practice. It is attenuation of low frequency spectra due to that. So it is, of course, it is far from practice application, but nevertheless it is something. Maybe it's not used another kind of plasma, maybe it's possible, usual spark, something, not dbd, not dbd, electric barrier is charged, but maybe usual. I know your simple sparks, you mean. Yeah, yeah, yeah. Because it's not destroyed some work, it's very simple idea. Yeah, there are many the direction from corrugated shape of the nozzle itself to forcing of the jet by... As for sparkles, I didn't know these works. We have, deal with plasma. I tried to do it. Yeah? Okay.