I'm doing a problem on turbulent oscillatory Couette flow. For the lower wall fixed and the upper wall oscillating at a high enough angular velocity such that the flow in between is turbulent. Do you know any on this topic? Or could you suggest some online or book readings for me? Thanks!

I am not sure of the specific Couette flow you are interested in.

Are you interested in the rotating Couette flow, i.e. flow between two rotating cylinders? (you mentioned angular velocity, this is the case only for rotating COuette flow).

Or are you interested in the Couette Flow between two planes?

What do you mean by 'upper' wall and 'lower' wall and 'oscillating'?

If you be more specific I can try to help with references.

Cheers, Patrick Godon

I'm sorry not making the question clear. I'd like to know about Couette flow between two planes. With the lower plane fixed, and the upper plane moving left and right at a high frequency so that the flow in between is turbulent. In fact, I'd like to know the velocity profile and the shear stress distribution of the flow.

I am sorry, but I do not have any reference for that particular kind of Couette flow. THe references I have are on the Couette flow between rotating cylinders and for Plane Couette flow, when the velocity of the 'upper' plane is constant (not oscillating). Even in this case there is a transition to turbulence due to a finite disturbance (subcritical transition to turublence). The plane Couette flow (above) is linearly stable and non-linearly unstable, which just means that for that flow to make a transition to turbulence, one needs a finite-amplitude perturbation.

I don't have any reference on 'oscillatory' Plane Couette flow, and I am sorry to say that I never heard of that one. However, if you think the other references I have could help, then let me know and I will write them down.

Cheers,

Patrick Godon

Thanks very much for your response. I'd like to have the references on any Couette flow. Thx!

OK, Eddie, here is what I have, and of course there are references in these papers themselves that you can look at:

Experimental papers:

Daviaud, Hegseth and Berge, 1992, Physical Review Letters, vol. 69, n.17, page 2511, Subcritical Transition to Turbulence in Plane Couette Flow.

Hegseth, 1996, Physical Review E, Vol.54, n.5, p.4915. Turbulent Spot in Plane Couette flow.

Dauchot and Daviaud, 1995, PHysics of Fluids, vol.7, n.2, p.335. Finite amplitude perturbation and spots growth mechanism in plane COuette flow.

Same as above, but n.5, page 901. Streamwise vortices in plane Couette flow.

Dauchot, Daviaud, 1994, Europhysics Letters, vol.28, n. 4, page 225. Finite amplitude perturbation in Plane Couette Flow.

Barbro, Klingmann, 1992, Journal of FLuid Mechanics, vol. 240, p.167. On the transition due to 3D disturbances in plane Poiseuille flow.

Theoretical papers:

Dubrulle, Zahn, Journal of FLuid Mechanics, 1991, vol.231, p.561. Nonlinear instability of viscous plane Couette flow.

Glatzel, 1989, J. Fluid Mech., 202, 515. The linear stability of viscous compressible plane Couette flow.

Nagata, 1990, J. Fluid Mech., 217, 519. 3D finite amplitude solutions in plane Couette flow: bifurcation from infinity.

Review papers, related to the subject:

Bayly and Orszag, 1988, Annual Review of Fluid Mech., 20, 359. Instability mechanisms in shear-flow transition.

Orszag and Kells, J. Fluid MEch., 1980, vol. 96, p.159. Transition to turbulence in plane Poiseuille and plane COuette flow.

see also :

Saric, 1994, Annual Review of Fluid MEch., vol. 26, page 379. Goertler vortices.

and for example a book like:

Fluid Dynamics of Landau and Lifshitz (gydrodynamika, translated from the Russian), Pergamon Press.

THere are many other books, but I dont remember the exact title (you can check in the cfd-online, there is a list of books), like

Drazin and Reid

Chandrasekhar (very theoretical...)

etc...

And if you have any question, you can post that here, I can try to answer.

Suggestion: start with the book of landau Lifshitz, just read the stuff on Couette flow there, that will be a good introduction. Then read the paper (or part of it) of Saric. Then read the experimental papers. And by the end read the other theoretical and review papers.

Cheers,

Patrick Godon

Thank you very much for your help!