 Hello everybody and welcome to video number 30 of the online version of the fusion research lecture The last video we finished with chapter 5 collision and transport and thus in this video We will start with chapter 6 turbulent transport So this is a 6 for Turbulent transport more or less so actually Although we talked a lot about Classical transport and neoclassical transport when you look in the experiment You will see that neoclassical effects alone are not sufficient to explain the observed transport and talk about fusion plasmas so neoclassical effects are not sufficient to Explain the Observed transport in Tokamak fusion plasmas The transport is actually one to two orders of magnitude too small In classical Stellarators, however, this was an agreement However, modern Stellarators are so good that the neoclassical transport losses have been reduced like W7X for example And also turbulent transport is an issue there because What is going on is turbulent transport which is used as an explanation for the increased additional losses So turbulent Sometimes also called anomalous Anomalous this is a bit of an unfortunate expression because it sounds it might sound weird or strange And it was just used because it was not a normal transport something which could not be explained in the beginning so This is why the expression anomalous was used, but in principle is just turbulent transport and this is Due to small scale fluctuations, so small Scale Fluctuations Those are the source of the origin for the observed Transport and those are small scale fluctuations in density in temperature and Also in the plasma potential If we observe these then we call this electrostatic Turbulence which is created by the Fluctuating electric field fluctuating density fluctuating temperature fluctuating plasma potential creates a fluctuating electric field And the resulting e cross B drift then is Leads to electrostatic turbulence As we will see if we have also Magnetic fluctuations just to be clear if they are not zero then we talk about electromagnetic turbulence Then we talk about electromagnetic turbulence and The electromagnetic turbulence is then caused by micro islands. You remember when we talked about magnetic islands by micro magnetic islands and Just for definitions. So since I've used these expressions with the tilde on top So for the density for example, the full density is the background density and not plus the perturbed density and tilde Where the average value of the density denoted by these brackets is Simply and not which of course implies that the average of the fluctuating part is zero Okay, as for the outline of this chapter the outline we will first talk about turbulence in neutral fluids turbulence in neutral fluids and We do so just to be sure that we are all on the same page here I know some of you might have heard a hydrodynamic lecture But if not, then we just ensure that we all talk about the same things Then we talk about turbulence in magnetized plasmas turbulence in magnetized Plasmas Then we will talk about turbulence observed in the experiment And then finally we will talk about methods to suppress or reduce the turbulence methods to suppress or Reduce the Turbulence Okay, when I start with this chapter, I always oops. I'm sorry. Yes restart not now When I start with this chapter, I usually like to start with a quote of these two people so on the very on the left hand side you can see a photography of Richard Feynman and His quote he said once that turbulence is one of the most unsolved problems of classical physics He did not said that literally but figuratively and on the right hand side You can see a photography of Werner Heisenberg who was also the founder of IPP in 1960 and He set the following when I meet God. I will ask him two questions. Why relativity and why turbulence? I really believe he will have an answer for the first So this is just as a motivation to show you that really great minds and physics and physics really great people considered the Problem of turbulence to be one of the most important ones So let's talk about turbulence in neutral fluids. So let's talk about turbulence in Nutri Fluids Turbulence is observed everywhere in nature. This is probably a good way to start using these pictures here Turbulence is Observed everywhere in nature When I say everywhere I mean for example in fluids This is the picture on the left hand side So this one here what you can see there These are the ocean surface currents deduced from satellite measurements from NASA and These data was then fed into a computational model And then you can see in the ocean these kind of currents here these these turbulent structures So I think this is a very nice Graphic there then of course not only fluids, but it's also in gazes So this photography here. This just shows a bit of smoke Coming from a candle. You can see how this is a very nice and turbulent structure and then on the bottom Of course, you can see this one here. This is a simulation of a plasma of a magnetized plasma Actually of a d3d plasma And you can clearly see the turbulence going on here in the colloidal cross section So it is you Turbulence is a ubiquitous phenomena in nature Now what is turbulence so turbulence can be defined in multi ways and a very simple definition might be the following So turbulence is Or can be understood as flow vortices of different size moving with random motion So it can be understood as flow Vortices These are also sometimes called eddies of different size and With random motion This is a very short and simple Definition of turbulence, but it captures. I think the most important or For us relevant properties here. Okay Turbulence has been a hot Topic for centuries a hot topic for centuries and these hot topics include for example the transition Studying the transition from laminar to turbulent flows from laminar to turbulent flows Then to study the lifetime of these eddies to study the lifetime of eddies To study the distribution of the size of these eddies to study the distribution of the size of these eddies to study the size distribution of the energy and To study the energy input and the energy transfer and also the energy dissipation so energy input the energy transfer between the scales and And also how the energy is dissipated and especially these three topics are also topics of modern physics and One very important role in turbulence plays the and in hydrodynamics in general the Navier Stokes equation the Navier Stokes equation because this can be used to describe turbulence in Incompressible fluids in in whoops in in Compressible Meaning that the Gradient of the velocity is zero other divergence An incompressible fluids and it reads as follows. So we have rho m and Then delta t. So this partial derivative with respect to time and then the velocity times nabla times The velocities with the hydrodynamic derivative Being equal to minus grad p plus row m times g the gravitational force plus eta and Then Laplace times the the velocity So this Is the famous Navier Stokes equation and Here as I said, we have the pressure. This is pressure Then this is the gravitation and Then here. This is the friction Laplace times the velocity. What else? We have row m This is the fluid density Oh, I'm as a fluid density then of course you which is the fluid velocity and Finally eta eta The viscosity of the medium viscosity now The Navier Stokes equation is Corresponds to him or is a basically an equation of motion This is an equation of motion and it is similar to the Corresponding Equation in a plasma to the corresponding equation In in a plasma Which reads just as a reminder also the fluid the plasma well density row m and then d t plus you times nabla times oops, sorry Times you Being equal to grad p Plus row m times E plus U cross B for the Lorentz term And this is quite similar now An important simplification is if we talk about ideal fluids for ideal fluids Where eta is equal to zero We get to the Euler equation the Euler equation and often made simplification Because you can already start study important phenomena using this equation the Euler equation and This then obviously reads row M times data t plus you times nabla times you being equal to the gradient of the pressure Okay, that's it for this video which was an introduction into chapter 6 turbulent transport And the major points were that the neoclassical effects are not sufficient to explain the observed transfer in the experiments and the transport being responsible for most of the Losses in the experiment in a trochamark is turbulent transport and In this video we started to talk about turbulence in neutral fluids I gave a few examples and a very simple definition of turbulence which came in and stood as flow vortices Eddies of different size with random motion and on this slide It was probably mostly a reminder for you the Navier-Stokes equation which can be used to describe Turbulence and an incompressible fluids and the Euler equation, which is just setting the viscosity to zero Okay, that's it for this video. See you the next video