I have a PhD in physics, primarily working on fluids and now I work in industry on fluid dynamics. Having just read the abstract, I can already tell that this paper is one of those that borders philosophical about the author’s view of their field. Nothing wrong with that though as we physicists tend to wax poetic from time to time.

The question about when we can consider turbulence solved is an interesting one. I still work in the field and for most useful applications of fluid dynamics, I would consider it a solved problem. Not to say that the NS equation is solved analytically, but rather that the field has built up a toolbox of phenomenological models and CFD systems that are more than good enough for the range of scales that we typically work with. The bigger problem for CFD in this space is optimization, an issue where GPUs have proven to be invaluable. Only in the past couple years have the major CFD software packages started supporting GPU computation, speeding things up 2-10x depending on the specifics.

I think that turbulence is an issue really at the extremes of scales at this point (very tiny, very large, small dt, hypersonic, etc.). Also, I think that it would be difficult in a system with complex forces acting on your fluid, like in a plasma where E&M forces are so significant. So, good luck all you folks working on fusion reactors!