Suppose we have a isotropic homogeneous turbulent channel flow. We know that this flow is associated with many swirling eddies of different length and time scales. I need to know the direction of rotation of eddies. More specifically, I need to know if most of the eddies are co-rotating, counter-rotating or there is no definite answer (randomly rotating)?

Also, does your answer change if I remove the constraint of isotropy and homogeneity?

Thanks in advance

  • $\begingroup$ This question is not precise enough. Needing to know a direction of flow is too vague a question. From the nebulous gist I'm getting from this question I think this question will be closed because people will not understand it fully or it will be closed for being too broad. $\endgroup$
    – Fred
    Dec 13 '16 at 8:13
  • $\begingroup$ @Fred I am simply not enough good in hydrodynamics to understand or answer this question, but it seems to me okay. If they question seems too broad for the first spot, it doesn't mean it can't have a clear answer. I think it can be determined, on what it hangs on. It is also a possible answer that it will be (or can be) determined by a chaotic process and there is no general answer for the question. I think, it should be also estimated, that the OP, and the googlers of the future, will be able to understand the answer(s) and vote it accordingly. $\endgroup$
    – peterh
    Dec 13 '16 at 9:24

Non-laminar flow is often hard to characterize with much mathematical rigor (though in certain special cases and geometries may be done with a little limitation). The phenomena depends heavily on channel geometry. For example, A backflow eddy can develop from a sudden stepwise increase in channel height/width. The Reynolds number of the fluid flow under examination will determine the strength and formation of the eddy. The formation of the eddy results from the water lamina closest to the wall being deformed by the sudden channel widening due to friction. Viscous interactions between adjacent lamina propagate away from the wall and result in the curling of local flow lines into an eddy. The Reynold's number will determine if an eddy forms, or if there is a smooth lamellar flow into the new channel width.

Ultimately, the Reynolds number is a very useful quantity for characterizing different types of fluid flow.

In the bulk of the fluid, most eddies will be locally co-rotating over a length scale that depends nontrivially on the fluid viscosity, as local lamina will tend to drag each other rather than slip. Of course, on some larger scale, this will appear as turbulent motion. Again, the Reynolds number is useful in this characterization.


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