Is There a Limit to Turbulence in Fluid Dynamics?

[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.

 

[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?

 

[boneh3ad]

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.

 

[Andy Resnick]

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.

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.

 

[boneh3ad]

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.