Turbulence
357. Vortex line representation. Coulomb interaction of vortex lines
After brief introduction into vortex line representation we are probably ready to discuss the interaction of vortex lines between each other. But before I proceed to the actual derivation, let me focus for a bit on not so terribly popular (but powerful) formulation of ideal hydrodynamics – Hamiltonian formulation.
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354. Vortex line representation. Clebsch variables
Let us continue our brief discussion of behavior of the vorticity field in the Eulerian flow.
(and that’s how vortex lines look like in reality… as if you wouldn’t know 
)
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353. Vortex line representation. Cauchy invariant
Several days ago I’ve promised in comments to discuss dynamics of vortex lines in turbulent flows, today is probably a good day to start. And the natural starting point of course is the Kelvin theorem and Cauchy invariant.
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347. Numerical simulation of vortices: video of the day
A video by New Scientist magazine featuring some really nice simulations of developed turbulence in the presence of vorticity field.
345. Lagrangian turbulence: video of the day
A simulation by Guido Bofetta, U. of Torino. Recall that Lagrangian description of hydrodynamics is when you pick a liquid particle and keep track of its motion. Here it is shown how particles are transported by a turbulent flow in the presence of a vortex.
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330. Some properties of the Burgers dynamics with Brownian or white-noise initial velocity
Patrick Valageas is a permanent researcher at the IPhT (Theoretical Physics department) of CEA, Saclay. His interests include turbulence, observational cosmology (LSS formation in particular) and astrophysics. Dmitry.
I would like to thank Dmitry for giving me the opportunity to present two recent papers of mine (arXiv:0810.4332 and arXiv:0903.0956), on the Burgers equation, from the point of view of a cosmologist. They consider the one-dimensional Burgers dynamics for Brownian and white-noise initial velocity, and expand some previous results on the probability distributions of velocity and Lagrangian increments, as well as on the distribution of the density and the shock mass function.
319. Turbulence. Dynamical approach
When we study a turbulent flow, whether turbulence is realized in fluid, plasma, etc., one of the most interesting and complicated questions is the one about transition to turbulence: how exactly the smooth motion of the field becomes turbulent, chaotic, independent of external noise?
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315. Turbulence: order and disorder in turbulent flow
Let us continue our short excursion into physics of developed turbulence (I hope that you don’t mind, if you do – please let me know ) Last time we have discussed technicalities related to averaging and statistics of the turbulent flow, today I would like to get back to foundations and discuss a bit various structures typically seen in the turbulent flow. This way we will understand better which features our future complete theory of turbulence will have to explain
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312. Turbulence. Statistical approach 2
Let us continue our brief discussion of stochastic approach to description of developed turbulence.
3. Kolmogorov scaling
One of the most important and beautiful results of stochastic approach is Kolmogorov scaling. Earlier, I have already discussed Kolmogorov’s turbulence on the blog in details, let me ramble about it today a little bit more.
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310. Turbulence. Statistical approach 1
Let me get back again to one of my most favourite topics in physics, that is, to developed turbulence. Last time (oh my, mid February) I have tried to explain what I consider the most important (and probably hard-to-solve) open problems in physics of turbulence. Now let me list quickly several (not too promising ) approaches to those problems we were able to develop during last hundred years or so.
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247. Physics of turbulence: four puzzles
Before starting to discuss theories and models describing phenomena of weak and developed turbulence in fluids, plasmas etc., etc., let us first recall why exactly theoretical physicists were so unsuccessful so far in understanding turbulence at the quantitative level. In order not to make this post too long , I am going to list only four main puzzles which, I hope, will show what is the heart of the problem.
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243. Turbulence: brief introduction into phenomenon
About a week ago I have listed top ten open problems in physics. If you say A, you are naturally supposed to say B (especially, if readers ask you ), so, I guess, I will have to discuss each problem from the list in more details. I would like to start with the problem N3 most compelling to me at the present time – the physics of developed turbulence. In order not to make the post too long, I am not going to discuss various models and theories of turbulence today – and will focus instead just on nature of the phenomenon.
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230. Video of the day: viscosity or the arrow of time is reversible
A lot of fun to watch 
CP is clearly conserved in this experiment LOL
LM explanation of the effect: The reason why it looks counterintuitive is the people normally confuse chaotic motion and organized motion.
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226. Top ten open problems in physics
What is the ultimate purpose of my work as theoretical physicist and, if you want, my existence itself? Is it serving the community of other physicists like organizing and participating in conferences? Nop. Then, maybe teaching future physicists in the University, encourage young people to enter the exciting field of physics? Not quite. Writing good papers? Ei. Maybe blogging? Sorry but nein. I think… the ultimate purpose of my work is solving unsolved mysteries in physics. I am afraid, this and only this makes my work enjoyable for me, makes it fun. For the sake of future reference, let me enlist here the most important (from my point of view), hard and interesting unsolved problems in physics.
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221. Turbulence: Kolmogorov law derived in one line
As you surely understood from the previous post, today is hydrodynamics and turbulence Sunday on NEQNET. If so, let me still 5 minutes of your precious time discussing the physics of developed turbulence.
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