[btrettel]

Turbulence can be accurately solved by simulating the Navier-Stokes equations on powerful enough computers. [0] The problem is that the computational complexity is enormous. Even relatively simple turbulent flows may exceed the capabilities of a supercomputer 50 years from now. This is pretty easy to show mathematically using the Kolmogorov scales [1] combined with the CFL condition [2] to estimate the computational complexity of unbounded turbulence. (But it's an incomplete estimate. Adding boundaries or other complexities will increase the computational cost.)

The real turbulence problem is figuring out ways to get around the computational complexity with cheaper models. Accurately modeling turbulence without using the full Navier-Stokes equations is really hard.

Also, contrary to what the science media says, the Navier-Stokes existence and uniqueness problem doesn't have anything to do with turbulence being hard aside from that both involve the Navier-Stokes equations. [3, 4] 2D Navier-Stokes, where existence and uniqueness has been proved, still has turbulence.

[0] Given accurate initial and boundary conditions.

[1] https://en.wikipedia.org/wiki/Kolmogorov_microscales

[2] https://en.wikipedia.org/wiki/Courant%E2%80%93Friedrichs%E2%...

[3] https://news.ycombinator.com/item?id=31227133

[4] https://news.ycombinator.com/item?id=31049535