I think the statement has different meanings to different people, but one "unsolved" problem is the ability to model the dynamics of small scales (the "turbulence") in terms of the large-scale "observed" flow.
The question has very strong analogies to thermodynamics. For example, one can average over microscopic motion to yield something like a diffusion equation, where transport of the (microscopically averaged) density is pushed from high to low concentrations, and all of the microscopic details get wrapped into a single number, the diffusion coefficient.
In fact, averaging over molecular dynamics works in so many contexts that the details end up not being terribly important. You will always end up with something like a diffusion equation.
It's very reasonable to think this ought to work more generally, averaging over the turbulence to produce a similar expression for the dynamics of the large-scale. But if you try to apply similar averaging techniques to the Navier-Stokes equations, the averages never end, no clear solution emerges, and the only hope to terminate the exercise is to insert some kind of "closure approximation".
Some consider a robust theory for such a closure approximation, or any method to resolve the impact of the turbulent flow on large-scale flow, to be an unsolved problem of turbulence.
These questions have been researched for many decades, and a great deal has certainly been learned, but a rigorous closure theory has been elusive. Meanwhile, the computers keep getting bigger and faster, to the point where the turbulence can in many cases be modeled reasonably well. And as the questions around turbulence become relegated to smaller and smaller scales, one starts to wonder if this is a problem that will even need to be solved in the future.
The question has very strong analogies to thermodynamics. For example, one can average over microscopic motion to yield something like a diffusion equation, where transport of the (microscopically averaged) density is pushed from high to low concentrations, and all of the microscopic details get wrapped into a single number, the diffusion coefficient.
In fact, averaging over molecular dynamics works in so many contexts that the details end up not being terribly important. You will always end up with something like a diffusion equation.
It's very reasonable to think this ought to work more generally, averaging over the turbulence to produce a similar expression for the dynamics of the large-scale. But if you try to apply similar averaging techniques to the Navier-Stokes equations, the averages never end, no clear solution emerges, and the only hope to terminate the exercise is to insert some kind of "closure approximation".
Some consider a robust theory for such a closure approximation, or any method to resolve the impact of the turbulent flow on large-scale flow, to be an unsolved problem of turbulence.
These questions have been researched for many decades, and a great deal has certainly been learned, but a rigorous closure theory has been elusive. Meanwhile, the computers keep getting bigger and faster, to the point where the turbulence can in many cases be modeled reasonably well. And as the questions around turbulence become relegated to smaller and smaller scales, one starts to wonder if this is a problem that will even need to be solved in the future.