3 ms·

Visualizing turbulence with a home demo [video]

11 points by espeed 8y ago

btrettel 8y ago
Fluid dynamicist here. This is a fairly nice video, though there are a few flaws. I was waiting for a derivation of the 5/3rds law, but it's not in the video. This is a shame as it can be derived very simply: http://micromath.wordpress.com/2008/04/04/kolmogorovs-53-law/ http://micromath.wordpress.com/2008/04/04/kolmogorovs-53-law... I don't buy the estimate of the limits of the inertial subrange given. That might be true for a particular velocity, but I imagine the limits of the inertial subrange vary greatly. Unfortunately 3blue1brown falls into a common trap when defining turbulence. Turbulent flows are chaotic... but laminar flows can be chaotic too. They are both solutions to the same non-linear equations. I think it would be better to describe turbulence as seemingly random or more precisely, probabilistic. The governing equations are not stochastic, but practically speaking you can treat the velocity field as a random variable. The uncertainty for laminar flows is much smaller. This is the basis for a lot of turbulence theory. This is not to say that there is not order in turbulence; there is both order and disorder. The Navier-Stokes millennium prize problem is also not as valuable as it seems to outsiders. The solutions most likely exist and are unique, etc. Your prior on the solutions existing should be high as Newtonian physics problems typically have solutions. If the solutions are not unique, add an extra condition to obtain unique solutions. That's already often needed for the compressible Navier-Stokes equations. I'd be much more interested in proofs of various forms of the ergodic hypothesis for turbulence.
- btrettel 8y ago
  Another pet peeve of mine is the absence of a discussion of why turbulence is a hard problem to solve. The reason is actually quite simple: the computational cost for directly solving the Navier-Stokes equations is far too high. They could have shown this in the video; the estimate is actually rather straightforward. (Estimate the "Kolmogorov scale", the scale of the smallest eddies that need to be resolved, and combine that with the CFL condition to get an upper bound on the stable time step, etc., as I recall.) So in practice people typically solve lower cost (but less accurate) equations derived from the Navier-Stokes equations. They could have briefly described the "closure problem" for this, and maybe some basic turbulence models. Well, they could hypothetically do all this in a future video...

11 points by espeed 8y ago

Fluid dynamicist here. This is a fairly nice video, though there are a few flaws. I was waiting for a derivation of the 5/3rds law, but it's not in the video. This is a shame as it can be derived very simply: http://micromath.wordpress.com/2008/04/04/kolmogorovs-53-law/ http://micromath.wordpress.com/2008/04/04/kolmogorovs-53-law... I don't buy the estimate of the limits of the inertial subrange given. That might be true for a particular velocity, but I imagine the limits of the inertial subrange vary greatly. Unfortunately 3blue1brown falls into a common trap when defining turbulence. Turbulent flows are chaotic... but laminar flows can be chaotic too. They are both solutions to the same non-linear equations. I think it would be better to describe turbulence as seemingly random or more precisely, probabilistic. The governing equations are not stochastic, but practically speaking you can treat the velocity field as a random variable. The uncertainty for laminar flows is much smaller. This is the basis for a lot of turbulence theory. This is not to say that there is not order in turbulence; there is both order and disorder. The Navier-Stokes millennium prize problem is also not as valuable as it seems to outsiders. The solutions most likely exist and are unique, etc. Your prior on the solutions existing should be high as Newtonian physics problems typically have solutions. If the solutions are not unique, add an extra condition to obtain unique solutions. That's already often needed for the compressible Navier-Stokes equations. I'd be much more interested in proofs of various forms of the ergodic hypothesis for turbulence.

btrettel 8y ago
Another pet peeve of mine is the absence of a discussion of why turbulence is a hard problem to solve. The reason is actually quite simple: the computational cost for directly solving the Navier-Stokes equations is far too high. They could have shown this in the video; the estimate is actually rather straightforward. (Estimate the "Kolmogorov scale", the scale of the smallest eddies that need to be resolved, and combine that with the CFL condition to get an upper bound on the stable time step, etc., as I recall.) So in practice people typically solve lower cost (but less accurate) equations derived from the Navier-Stokes equations. They could have briefly described the "closure problem" for this, and maybe some basic turbulence models. Well, they could hypothetically do all this in a future video...