> So the terminology you are using is what confuses me. You first said "there is no equation describing the system", but now you're expanding this to mean "the equation describing the system has no closed form solution".

There is no equation that describes that system. Which part of this is confusing you? A numerical algorithm is not an equation. My other example, easier to grasp, was the three-body problem -- the existence of a numerical solution doesn't mean there's an equation that describes a three- (or more) body orbit, quite the contrary (it has been proven that no such equation can exist) -- such orbits must be solved numerically, and there is no overarching equation, only an algorithm.

The presence of an algorithm doesn't suggest that there's an equation behind it. Here's another example -- the integral of the error function used in statistics. It's central to statistical calculations, there is no closed form (i.e. no equation), consequently it must be, and is, solved numerically everywhere. This is just one of hundreds of practical problems in many disciplines for which there is no equation, only an algorithm. Reference:

https://en.wikipedia.org/wiki/Error_function

We can locate/identify prime numbers with reasonable efficiency. Does this mean there's an equation to locate prime numbers? Well, no, there isn't -- there's an algorithm (several, actually).

We can compute square roots with reasonable efficiency. Does this mean there's an equation that produces a square root for a given argument? As Isaac Newton (and many others) discovered, no, there isn't -- there's an algorithm, a sequential process that ends when a suitable level of accuracy has been attained.

I could give hundreds of examples, but perhaps you will think a bit harder and arrive at this fact for yourself.

> To even think about approaching a description of that precision would require measurements of wind, temperature etc. at a grid resolution of much less than 1 mm.

Your argument is that, because we can't measure the atmosphere to the degree necessary to associate changes with the quantum realm, we therefore can rule it out as a cause. Science doesn't work that way. Remember that I didn't say it was so, I said it was a matter of active discussion among professionals, as it certainly is.

> At scales much smaller than this, such as in QM, the flow is locally uniform everywhere.

What an argument. It says that, even though at larger length scales, there is turbulence that prevents closed-form solutions (and in this connection everyone is waiting for a solution to the Navier-Stokes equations, which may ultimately be a pipe dream), but as the length scale decreases, things smooth out and become uniform (I would have added "predictable" but you had the good sense not to make that claim). This contradicts everything we know about nature in modern times, and contradicts the single most important property of QM.

> Can you show me a strong scaling plot for any PDE solver that shows good scaling significantly beyond 10k DOFs per processor?

Would you like to make the argument that, as time passes and as processors become less expensive, faster and more numerous, any such argument isn't undermined by changing circumstances?

This paper (PDF warning):

http://www.shodor.org/media/content/petascale/materials/UPMo...

Makes the unsurprising argument that, as time passes and as processor costs fall, matrices are broken into more and more, smaller, parallel subsets in the name of rapid throughput (with appropriate graphics to demonstrate the point). The end result of that process should be obvious, and at the present time, 10,000 serial computations per processor is absurd -- this is not a realistic exploitation of a modern supercomputer. In reality, more processors would each be assigned fewer cells, because that produces a faster result. This is not a difficult concept to grasp.