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A statistical study of spots in torsional Couette flow. (English) Zbl 1192.76064
Summary: This article presents some results on the statistical behavior of localized structures-called “spots”–that propagate in the flow between a rotating and a stationary disk when those are very close one to the other. Under these conditions the rotating-disk flow belongs to the Couette-flow family and is called the torsional Couette flow. Some visualizations of its transition to turbulence have already revealed the propagation of these spots [L. Schouveiler, P. Le Gal, M. P. Chauve, J. Fluid Mech. 443, 329–350 (2001; Zbl 0978.76507)] from the rim of the disk towards its center. Using flow visualizations and an original image analysis, the present study aims to better describe the characteristics of the spots whose number continuously increases with the Reynolds number until they invade the whole flow. Moreover, we propose a statistical model that predicts an error-function shape for the probability to observe a spot at a given radial position. This prediction is confirmed by an image analysis of the flow and the stability curve of torsional Couette flow is deduced from these observations.

MSC:
76U05 General theory of rotating fluids
76M35 Stochastic analysis applied to problems in fluid mechanics
76-05 Experimental work for problems pertaining to fluid mechanics
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