> measure the resulting turbulence

Just a quick solution of a million-dollar math problem (https://en.wikipedia.org/wiki/Millennium_Prize_Problems#Navi...) and you're on your way!

You don't have to solve the Navier Stokes equations analytical for this. You don't even have to solve them explicitly at all: I can see a grad student just getting a lot of experimental data and throwing it all at a neural net with good results.

> You don't have to solve the Navier Stokes equations analytical for this.

Yes, to be sure you are right. It was just a silly (and, as you point out, mathematically inaccurate) joke.

It doesn't solve the hidden cavity problem very well, though.

Indeed. At least not in a way I can think of within thirty seconds.

If you're going to allow infinite engineering effort then I propose going all thermodynamic and having a VERY large piston connected to a small volume, change the volume and therefore pressure of a large quantity of room temperature gas, perhaps a short hydrocarbon like butane or propane or chlorine or ammonia or any one of numerous refrigerants, then the piston can vary the pressure setting the fluid level without moving anything but the piston. It may not be fast but computers can be very patient. Given some pumps and mixing vanes it could generate a ton of thermodynamic data. So toss in a piston, hit start, come back a couple days later to a 3-d model AND chemical composition data.

A somewhat similar, much simpler process is in wide use in the manufacturing industry for form measurement:

https://www.google.de/search?q=air+gaging

Seems like the turbulence would present difficulties. How about lasers? Oh wait that's a known method.. :)

How about shining a normal light though and just inverting the shadow calculations.. hmm.. has that been done?

I think I might have done what you are talking about a while ago. See my write up on my website:

http://jack.minardi.org/software/whats-in-a-shadow/

Fascinating. I'd wondered a while back how feasible it is to reconstruct an object from a 3-view orthographic projection, e.g. https://s-media-cache-ak0.pinimg.com/originals/b2/92/a9/b292.... Your work seems related.

Cool!

I feel like this would only work in limited cases of laminar flow and even then the scattering of the air would be complicated af I think

If you can solve the math (even just numerically), you can in principle do it for non-laminar flow.

I think that's already a thing, right? They use that for corneal deformation at a minimum.