Wow, thanks for your well-written response. I didn't quite follow all the details; in any case, I have a slightly better idea of what is going on. Next, I look forward to learning a bit more about laminar versus turbulent flow.
I can relate to your comment: "Some people lately have proposed that machine learning could construct a particularly accurate turbulence model, but that seems unlikely to me". A healthy skepticism is important. Different inductive biases in various machine learning algorithms will have a significant effect here, I'd expect.
Here's some additional comments you or some other reader might find useful:
Dimensional homogeneity is the most important constraint I think most machine learning folks would miss. It's not really an "inductive bias", rather something which everyone agrees models need to satisfy, so it should be baked in from the start. This is trivial to meet, actually; just make sure all of the variables are dimensionless and it's automatically satisfied. (Depending on the larger model, you might have to convert back to physical variables.)
In terms of "inductive biases", I'm not certain what that would entail in terms of turbulence, but I'll think about it. Might be something to figure out empirically.
Turbulence models which satisfy certain physical constraints are called "realizable". Some of these constraints are seemingly trivial, but not necessarily satisfied, like requiring that a standard deviation be greater than zero. (Yes, some turbulence models might get that wrong!) The "Lumley triangle" is a more advanced example of a physical constraint that a (RANS) model needs to satisfy that often is not satisfied.
I'd be interested in applying machine learning type methods (combined with the model order reduction approaches to include information from the Navier-Stokes equations), but I'm not knowledgeable about them. My impression is that most people applying machine learning to turbulence are novices at machine learning. And I imagine most machine learning people applying machine learning to turbulence are novices in turbulence and wouldn't know much anything about the realizability constraints I mentioned.
Another issue worth mentioning is experimental design. I think the volume of data needed to make a truly good turbulence model is probably several orders of magnitude higher than anything done today for turbulence. Experimental design could make this more efficient. I don't think most machine learning people worry much about this. They seem to focus on problems which can be run many times without much trouble. Acquiring data for turbulence is slow and hard, so it's outside their typical experience.
I can relate to your comment: "Some people lately have proposed that machine learning could construct a particularly accurate turbulence model, but that seems unlikely to me". A healthy skepticism is important. Different inductive biases in various machine learning algorithms will have a significant effect here, I'd expect.