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

Click For Summary

Discussion Overview

The discussion centers on the complexities and challenges associated with understanding turbulence in fluid dynamics, particularly in the context of classical physics. Participants explore the mathematical and computational difficulties of modeling turbulence, the limitations of current theories, and the implications for practical applications.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • Some participants note that turbulence is considered one of the biggest outstanding problems in classical physics, with a lack of understanding about its fundamental nature.
  • It is mentioned that while turbulence is built into the Navier-Stokes equations, these equations are effectively infinite-dimensional, complicating direct solutions.
  • One participant argues that turbulence is often modeled as stochastic, but it is fundamentally deterministic, leading to challenges in solving the equations.
  • Another participant challenges the assertion that direct numerical simulation (DNS) is not useful, stating that DNS can be performed for certain turbulent processes, though it may not remain useful for long.
  • There is a discussion about the limitations of simulating turbulent flows, particularly at high Reynolds numbers, and the reliance on empirical relations and turbulence models like k-ε.
  • Some participants express differing views on what constitutes "useful" simulations, with one emphasizing the need for realistic flow conditions.
  • A participant suggests that turbulence may not be "unsolved" from a fundamental physics perspective, framing it more as a computational issue.
  • Another participant acknowledges that while fully developed turbulence is understood, the transition from laminar flow to turbulence, particularly in boundary layers, remains poorly grasped.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the nature of turbulence, the effectiveness of DNS, and the distinction between fundamental understanding and computational challenges. The discussion remains unresolved with no consensus on the characterization of turbulence as an unsolved problem.

Contextual Notes

Limitations include the dependence on specific Reynolds numbers for simulations, the challenges in predicting the onset of turbulence, and the varying definitions of what constitutes a "useful" simulation in the context of turbulence modeling.

JesseC
Messages
247
Reaction score
2
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
 
Physics news on Phys.org
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.
 
boneh3ad said:
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...
 
olivermsun said:
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 [itex]\textrm{e}^N[/itex] 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.
 
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.
 
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 [itex]k\textrm{-}\epsilon[/itex].

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.
 
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.
 
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.
 

Similar threads

  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 7 ·
Replies
7
Views
5K
  • · Replies 11 ·
Replies
11
Views
4K
  • · Replies 6 ·
Replies
6
Views
6K
  • · Replies 22 ·
Replies
22
Views
2K
  • · Replies 30 ·
2
Replies
30
Views
8K
  • · Replies 1 ·
Replies
1
Views
5K
  • · Replies 135 ·
5
Replies
135
Views
12K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 43 ·
2
Replies
43
Views
10K