Talk:Couette flow
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I don't think it's right to mention a value for the critical Taylor number. The critical Taylor number depends upon eta and mu, the two variables usually chosen to characterize the flow. Mu is the ratio of outer cylinder angular velocity to inner cylinder angular velocity, and eta is the ratio of inner cylinder radius to outer cylinder radius (see, e.g, Drazin &Reid, Chapter 3, eq. 15.49). The number "1708" actually refers specifically to the thin-gap approximation, eta -> 1, and even then only to a particular value of mu, namely the limit mu -> 1, I believe, see D&R page 99 (in my edition) or eq. 1750, which comes from Chandrasekhar). This only makes sense as a limit, b/c mu = 1 is solid-body rotation and thus stable. And if you aren't talking about some limiting or special case, then it's not so easy to write down a critical Taylor number, even if you can decide upon a consistent definition for what the Taylor number is! (Note, eg., that Chandrasekhar in his book defines Taylor number differently from how Drazin & Reid define it!). Petwil 19:02, 22 December 2005 (UTC)
Regarding nomenclature: It is true that both of my main references on instabilities, Chandrasekhar and Drazin & Reid, refer to flow between two rotating cylinders as Couette flow. However, if I am not mistaken I have always heard of it as Taylor-Couette flow in astrophysics (where this problem has application to things like accretion disks and stellar interiors). I called it Taylor-Couette flow in my dissertation and in various seminars, and nobody has ever corrected me. I understand on the other hand that some people use the term Taylor-Couette flow to refer not to the geometry, but to a particular flow pattern, namely when Taylor cells (or vortices) are present. Perhaps this is the more common usage. Tritton calls Couette flow between two rotating cylinders, "rotating Couette flow", which refers not to the overall flow pattern (laminar, uniform or patterened, turbulent, etc) but to the basic geometric setup. This might be best in terms of clarity, but I'm not sure how broadly this terminology has been adopted in the literature. There may also be some differences depending upon field, not to mention within a given subfield itself. For example, Tritton notes that in the work of Andereck, Liu & Swinney (1986), J. Fluid Mech. 164, 155 that "Couette flow" refers specifically not to the experimental setup but to the purely azimuthal motion of the basic background laminar viscous flow without instabilities, whereas Tritton himself uses "Couette flow" to refer to any flow between parallel surfaces shearing relative to one another, such as the basic cylindrical Couette flow setup. At some point arguing over this nomenclature is really pedantic. If somebody out there working on this problem (14th floor of RLM?) can clarify the nomenclature that'd be great. Petwil 19:23, 22 December 2005 (UTC)
