# Limit of Turbulence

1. Jun 4, 2012

### Aero51

Just out of curiosity, is there a limit to how turbulent a flow can become? In otherwords, turbulence develop that is so chaotic that no discernible pattern/path can be found in the flow? Thanks.

2. Jun 4, 2012

### Bobbywhy

Why should there be a limit to "how turbulent a flow can become"? It is nearly impossible now to model simple turbulence even with powerful supercomputers, so how would we even measure extreme chaos?

3. Jun 4, 2012

In theory, no. In fact, at extremely higher Reynolds numbers, a flow can re-laminarize (e.g. the Princeton Superpipe).

Otherwise, in a normal situation, turbulence will always involve energy cascades from large flow-scale eddies all the way down to those of the Kolmogorov scale.

Therein lies the problem in performing a DNS of a full-scale turbulent flow. To accurately resolve the Kolmogorov scale in a given flow field, the mesh must be so fine that the problems often cannot be solved in an economically feasible length of time, even on supercomputers.

4. Jun 4, 2012

### Andy Resnick

Turbulence is like pornography- you know it when you see it. Often, laminar/turbulent flow can be parametrized by the Reynolds number, with turbulent flow indicated around a Reynolds number Re ~ 10000. At the low end, the onset of turbulence, there appears to be a fairly well-defined transition region. However, AFAIK, there does not appear to be anything fundamentally new regardless of how large the Reynolds number is: Russel Donnelly's group has done a lot of work generating flow regimes as high as Re ~ 10^7- 10^9, and IIRC stellar interiors can reach Re ~ 10^12.

5. Jun 4, 2012

FWIW, turbulence onset as a function of Reynolds number is only well-defined for pipe flow and perhaps a tiny handful of others. I don't know where 10000 was found, but for things such as airplane wings or automobiles (in the absence of separation), the transition Reynolds number is often much, much higher; well over $10^6$. The problem is that the onset o turbulence is dependent on more than just the Reynolds number, notably the free-stream disturbances (sound, turbulence, temperature), surface temperature and surface roughness.