[MUSIC] Hello, the turbine wake is normally invisible. But for some specific atmospheric conditions, the wake turbulence becomes visible in the glow clouds formation. On this image, we can visualize the downstream extent of a single turbine wake. How retrieving back the anti-pollution of the single turbine located in the wake. We will present in this short session a very simple, semi-empirical model used to quantify the velocity deficit in the downstream wake. Due to the extraction of kinetic energy by the turbine, the downstream velocity V3, in the near wake, will be reduced in comparison with the upstream velocity, V0. However, the downstream velocity evolves when the distance to the turbine increases. We introduce here the downstream distance x, and we expect that in the far wake, when extent to infinity, the velocity share will disappear, and the the downstream velocity should recover a uniform velocity. The main mechanism responsible for the reduction of the velocity deficit in the far wake is the lateral mixing of momentum. The instability of the shear layer just behind the turbine will induce turbulent motion that will mix the outer unperturbed velocity with the downstream velocity. Hence, in the far wake, the lateral extent of the wake will increase, while the amplitude of the velocity deficit will decay. The semi-empirical model of Jensen assumes that the diameter of the wake increases linearly with the downstream distance x. And if now we apply the mass conservation between the upstream and the downstream sections, we should consider the flow rate of the fluid through the cylindrical section of diameter D3, having the velocity V3, and the flow rate of the outer unperturbed fluid through the section between the diameter D3 + 2kx and D3. The sum of these two flow rates should be equal to the outer flow height which is proportional to the weight velocity V(x). Then, we divide this expression by the diameter D3 and we get the relation which depends on the dimensionless downstream distance x over D3. According to some simple algebra, we obtain the downstream evolution of the velocity deficit, which corresponds to the difference between the unperturbed velocity V0 minus the far wake velocity V(x). And we found that the velocity deficit returns to zero when the downstream distance increases with a typical inverse square parabola. However, this semi-empirical relation depends on the downstream velocity V3 and the diameter D3 of the near wake. How these two values depends on the turbine diameter and the upstream velocity? For the optimal Betz limit, the downstream velocity D3 is equal to one third of the upstream velocity V0, while the near wake diameter D3 is equal to the square root of two third of the turbine diameter. And we get a specific equation which depends only on the coefficient k. However, for realistic flows, the near wake velocity V3 depends on the power coefficient of the turbine. And we can wider generalize the relation that depends on the two parameters Cp, the power coefficient, and k, the lateral extension. The evolution of velocity deficit in the far wake could be easily measured in laboratory. And this plot shows the evolution of the relative velocity deficit as a function of the dimensionless downstream distance for two cases. The black dots correspond to the velocity deficit, while the upstream flow have a turbulence intensity of 25%, while the open dots correspond to a weaker turbulence intensity of 5%. The wake extension parameter k is here equal to 0.03 for the weak turbulence case, while it is one order of magnitude higher up to 0.9 for an higher turbulence intensity. Hence the wake extension parameter strongly depends on the turbulence intensity of downstream flow. It makes sense, because the intensity of the turbulence fluctuation will impact on the lateral mixing. When the turbulence intensity is weak, the velocity deficit will extend on a long distance, as it is shown on this map, where the relative downstream velocity is plotted in the x-y plane. This case was obtained for a wind turbine tested in a laboratory channel. And the velocity deficit is still of 30% at the distance of ten diameters behind the turbine. We usually define the length of the wake as the downstream distance needed to recover 90% of the upstream flow. For this case, where the turbulence density is 5%, we get the typical length of 12 to 13 turbine diameters. If now we measure the turbulence intensity behind the turbine, we notice that its local value could be multiplied by four or even five inside the wake, why? The surrounding flow keeps its low level of turbulence. On the other hand, when the turbulence intensity of the upstream flow is larger, around 25%, we will get a much shorter wake with a characteristic downstream length of 5-6 D. We could also notice that the lateral extension of the wake is significantly larger on this shorter distance, and that the turbulence intensity could get very large values, up to 40% in the near wake. But it will quickly recover the surrounding values at the downstream distance of 5 to 6 turbine diameters. We can now use this simple model to give a first estimate of the wake impact on the power output of a row of three turbines directly aligned with the upstream flow. We consider a separation distance of 8 or 9 diameters with a low level of turbulence intensity, around 5% for the upstream wind. And for this case, the wake of the first turbine will extend downstream with a relatively low decay of velocity deficit. And for instance, the second turbine will get only 85% of the upstream wind velocity. Moreover, the turbulence filtration will increase inside the first wake and the second turbine will feel a turbulence intensity of 25%. Hence, the downstream extension of the second wake will be shorter. And the relative velocity deficit of the first turbine will be smaller than the second one. Why? The turbulence intensity stays the same. If now we quantify the impact on the kinetic power, we found that only 60% of the upstream power will be available for the second turbine, while the third one will have only reduction of 53%. If the upstream flow had a higher level of turbulence, the results would have been totally different. This simple example shows that the wake impacts are quite sensitive to the variability of the upstream flow and that both the velocity deficit and the turbulence intensity should be taken into account for complex turbine wake interactions. Thank you.