Why is turbulence the most important unsolved problem of classical physics?

[JesseC]

I've heard it said that 'we don't really understand turbulence', and that it is one of the biggest outstanding problems in classical physics right now. (Or at least Feynman thought so back in his day) But what is there to understand about turbulence and why don't we understand it?

I thought we had some very good mathematical descriptions of chaotic and stochastic processes, do these not apply fluid flows? Do we know why a transition to turbulence occurs? Is turbulence not built into the Navier-Stokes equations?

Cheers
JesseC

 

[boneh3ad]

We have good models of relatively low-dimensional chaos and stochastic processes. The problem is that turbulence is neither of these. While it is built into the Navier-Stokes equations, these along with continuity and energy are effectively infinite-dimensional. Turbulence is often modeled as stochastic, but it is really a deterministic process. We just can't directly solve the equations due to their many-dimensional, chaotic nature. Even doing direct numerical simulation on supercomputers is of no use currently because it is simply too complicated a process to be solved in finite time as we understand it now.

 

[olivermsun]

Even doing direct numerical simulation on supercomputers is of no use currently because it is simply too complicated a process to be solved in finite time as we understand it now.

This is not strictly true. DNS of turbulent processes can be and is done for useful purposes. The problem is that, despite one's best efforts numerically and otherwise, it never stays useful for long...

 

[boneh3ad]

This is not strictly true. DNS of turbulent processes can be and is done for useful purposes. The problem is that, despite one's best efforts numerically and otherwise, it never stays useful for long...

I disagree. Simulating a small part of a turbulent boundary layer can be done at low Reynolds number, sure. The problem is there are very few problems that occur at low Reynolds number. On top of that, we still cannot simulate a boundary layer starting from a laminar state and carry the DNS out from the leading edge through the transition phase and on into turbulence. There is no way to accurately predict the onset of turbulence based on the physics. The best we can currently do is empirical relations that only work on certain problems or the much-celebrated \textrm{e}^N methods.

Sure we can run a DNS of certain turbulent processes, but the computational power required to simulate the entirety of a real, useful problem such as the flow over an airplane wing is simply out of our reach currently.

 

[olivermsun]

I guess I consider DNS at moderate Reynolds number in a box to be "useful." You seem to require something on the level of a realistic flow before it qualifies. Okay.

 

[boneh3ad]

Low to moderate Reynolds number in a box is mostly useful to validate various turbulence modeling techniques so that they can later be used on more realistic problems. In that regard, then sure, I guess it is useful. Still, we can't in general solve full fluid-flow problems all the way from laminar to turbulent and you can't simulate a high-Reynolds-number turbulent flow without a turbulence model like k\textrm{-}\epsilon.

DNS is a wonderful tool, but with modern computing power, it still can't really answer that many turbulence questions. Perhaps some day it can.

 

[chrisbaird]

While you probably all realize this, I would not consider turbulence "unsolved" from a fundamental physics standpoint. We have great theories for the structure of the atoms that comprise the turbulent fluid and motion of particles. To me, it's more of a computational problem.

 

[boneh3ad]

Fully developed turbulence is understood reasonably well, but we still have a fairly sparse grasp on all the physics behind a boundary layer's evolution from receptivity all the way to turbulence. That is the real problem to which Feynman referred.