
Visualizing turbulence with a home demo [video] - espeed
https://www.youtube.com/watch?v=_UoTTq651dE
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btrettel
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.

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btrettel
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...

