Turbulence Equations Discovered After Century-Long Quest

As far as I can tell, this paper has nothing to do the generalized solution to the Navier-Stokes equations. It deals with flows near surfaces (boundary layers) and not flows in general. After skimming the paper I could only find one mention of the Navier-Stokes equations, and that was just for a channel flow identity derived from the Navier-Stokes equations under very particular boundary conditions (so not general at all).

This paper provides an interesting connection between the spectral properties of turbulence and the second-order moments of velocity in boundary layers (the "spectral link" as the title says). That is interesting to experts but it is a bit too abstract for the general public to understand easily, unfortunately.

No. This is a better approximation for boundary layer turbulence, it's not a golden equation. Better approximations for annoying problems in fluid dynamics are published quite often. I think has plenty of practical use though, I'll probably be trying to integrate it into some cfd work to see how it behaves compared to our current approach at work. Disclaimer that I am not a physics phd, but I do work with a hydraulic research group so I've picked up bits and pieces.

If you want to see a fun example of fluid dynamics approximations, look at the Wikipedia pages for the Darcy friction factor and Colebrook white equation.

I would also like to know that.

They are popular journals, not scientific ones and fluid dynamics is apparently not sexy (though planes are — go figure!)

I’m pretty stoked by these results.

(Sorry about the pun)

It isn’t that important.

It is an incremental, but perhaps significant improvement for describing flow in a certain situation. It is nothing like a general purpose “solution” to turbulence.

Scientific American kind of sucks.

It isn't that important, the website just tries to make it seem that way. It's useful, but there were already models to estimate boundary layer turbulence. This is just a better approximation.

Amd why are there still only 7 comments on this? Wasn't this one of the major unsolved problems of physics? If they had used a recurrent learning model to figure it out people would care...

Sciam is dealing with a lot of race and gender issues right now, so topics like this are on hold.

I don't think discover implies anything about the effort put in on its own. If anything I'd say it leans towards deliberate effort, even if not always an expected result.

If it's just a fluke then more often and not I'd expect to see that spelled out as either context, or with the words you used: "stumbled upon".

At any rate, I think the reason it's used in this context in particular is because it represents that the 'equation' is not just a mathematical construct someone came up with, but that it represents observable reality in a way that is novel and perhaps unexpected. It wasn't something someone made up, it's something that usefully describes phenomena that are outside human control. Thus, they did not invent, instead they discovered.

Whether equations are invented or discovered is actually a matter of philosophy... somewhere in the areas ontology and epistemology. And the debate is not really settled, I believe.

https://www.pbs.org/wgbh/nova/article/great-math-mystery/

As a native speaker discover sounds fine to me but you are likely looking for a word like derived or calculated.