Can I identify a coherent structure in a turbulent flow field using proper orthogonal decomposition? If yes, what is the theoretical basis for doing so?
Yes, tons of work done with tranisitonal & turbulent shear flows (boundary layers, wakes, mixing layers, jets etc). Your best bet is to start with the follg. papers & references therein:
1. AUBRY, N., HOLMES, P., LUMLEY, J. L. & STONE, E. 1988 The dynamics of coherent structures in the wall region of a turbulent boundary layer. J. Fluid Mech. 192, 115–173.
2. SIROVICH, L. 1987a Turbulence and the dynamics of coherent structures, part I: coherent structures. Q. Appl. Math. 45, 561–571.
3. SIROVICH, L. 1987b Turbulence and the dynamics of coherent structures, part II: symmetries and transformations. Q. Appl. Math. 45, 573–582.
Agree with Satish. However, philosophically speaking, what is a coherent structure is still a question. In my opinion, all the coherent structures identified by different methods, including POD, lambda-2, or VVCS, are all 'true' structures in turbulence and no ultimate truth for them. The identified structures reflect some of the features of CS, and all of them are equally important. In this sense, POD may identify the CS in turbulence with no doubt.
For reference, you could find some senses in our recent publication,
Qingshan Zhang, Yinzheng LIU,Shaofei Wang, The identification of coherent structures using proper orthogonal decomposition and dynamic mode decomposition. Journal of fluids and structures, 2014, http://dx.doi.org/10.1016/j. jfluidstructs.2014.04.002i
I agree that the task is phylosophycally without a unique response.
First the identification of a structure is to be clearly stated then the choerence meaning should be defined and applied..
Open questions in mt opinion
I agree with the previous responses. One more thing to consider... POD is effective at identifying very dominant structures (e.g. Karman vortices) whose energy content comprises a large percent of the overall fluctuations. POD may not be the best tool for weaker structures or those which do not appear frequently.
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