[rusk]

How are Navier Stokes the other way, on the macro scale? e.g. in the context of meteorology. Asking because I had a discussion with somebody recently where they claimed the fundamental flaw to the science underlying Climate Change science is over-reliance on NS at macro scale as a way of predicting climate behaviour, or something. I took it to be Baloney, but I'm wondering if there is some strands of truth to it ...

[neutronicus]

Fluid equations assume that there's a single characteristic velocity for the atoms at each point in space. So, for physical systems where local velocity distributions are wide or even multi-modal, fluid equations won't capture the physics.

In plasma physics, Laser Wakefield dynamics is an example of a system that can't be modeled as a fluid.

I sort of doubt these considerations apply to the atmosphere, but this is one of the main heuristics for when you can't use a fluid equation.

[qubex]

As you intuit, there is no reason to presume that Navier-Stokes would be unreliable at macro scales relevant to meteorology, simply because it is so thoroughly tested in experimental settings and to such sensitivities that it is known that all relevant factors are accounted for.

(Of course, why would one presume that if it is inaccurate at planetary scales, it biases observations towards the climate change narrative? It's just the typical “God of the gaps” kind argument.)

[rusk]

“God of the gaps” yeah that’s pretty much what I thought!

[btrettel]

Who you were talking to doesn't seem to know what they were talking about.

alephnil mentioned a real problem, but the solution in that case is to not use NS. From a practical standpoint NS is a good model of fluids in many instances because there is a certain minimum scale of motion due to viscosity (the Kolmogorov scale) and this usually is much larger than the size of the atoms or molecules. If this is true then a continuous approximation is fine. No present climate simulation can afford to compute everything down to that scale, so a low pass filter is applied to filter out the small scales and turn their effect on the large scales into a single term that can be modelled. This turbulence modeling approach is called large eddy simulation (LES), and it relies on the fact that outside of certain special cases (e.g., major chemical reactions) the small scales have a universal behavior. (Kolmogorov was the first to propose that the small scales are universal back in 1941.) This approach works pretty well usually. If the person you were talking to said the small scale model was wrong, I'd give them more credit, but this approach is generally the most accurate moderate cost turbulence modeling approach.