9. The Couette–Taylor Experiment
Society for Industrial and Applied Mathematics eBooks · 1995
We recall what the Couette flow between rotating cylinders is: the fluid fills a domain Ω of which is limited by two vertical axisymmetric cylinders with the same axis (radii , , ) and by two horizontal planes separated by a distance h. The outer cylinder is at rest and the inner one is rotating with an angular velocity . This corresponds to the flow in a fixed bounded Lipschitz domain Ω of with vanishing forces per unit volume and nonzero boundary conditions on in (1.9) (but ). This case was not studied in Part I to avoid purely technical difficulties, but its mathematical treatment is very similar to that considered in Part I (cf., e.g., C. Foias#x;R. Temam [3], [4], [5]; J. C. Saut#x;R. Temam [2]). When is constant, , a Reynolds number can be defined for this flow (cf. (1.6)), , which corresponds for instance to the choice of as a characteristic length for the flow, and to .