We have a mathematical model, Navier-Stokes (NS), that seems to describe motion of fluids well. In practice NS and related approximation models with simpler numerical solutions can be used to derive useful results. In that sense we can simulate turbulence for some sets of conditions and get useful approximations out. In general it’s still an open problem if NS has, given an initial velocity field, a solution that is globally defined and smooth. Practically this means we don’t know one way or the other if NS has initial conditions under which the velocity or pressure fields of the solution tend to infinity in finite time. This is the unsolved Navier-Stokes problem.
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Imo turbulence is “unsolved” in the same way the 3-Body problem is unsolved. It’s chaotic.
https://en.m.wikipedia.org/wiki/Chaos_theory
We have a mathematical model, Navier-Stokes (NS), that seems to describe motion of fluids well. In practice NS and related approximation models with simpler numerical solutions can be used to derive useful results. In that sense we can simulate turbulence for some sets of conditions and get useful approximations out. In general it’s still an open problem if NS has, given an initial velocity field, a solution that is globally defined and smooth. Practically this means we don’t know one way or the other if NS has initial conditions under which the velocity or pressure fields of the solution tend to infinity in finite time. This is the unsolved Navier-Stokes problem.
https://en.m.wikipedia.org/wiki/Navier–Stokes_existence_and_smoothness
Maybe the turbulence was inside us all along / the friends we made along the way.