A statistical study of spots in torsional Couette flow

Patrice Le Gal (1) , Yuji Tasaka (2) , Jotaro Nagao (2) , Anne Cros (1) , Kohei Yamaguchi (2)

1 IRPHE - Institut de Recherche sur les Phénomènes Hors Equilibre
2 LFC - Laboratory for Flow Control

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 disc when those are very close one to the other. Under these conditions the rotating disc 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 [Schouveiler et al., J. Fluid Mech. 443, pp. 329-350, 2001] from the rim of the disc 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.

Mots clés: rotating disc flow; subcritical transition

Domaines: Dynamique des Fluides [physics.flu-dyn]

Patrice Le Gal, Yuji Tasaka, Jotaro Nagao, Anne Cros, Kohei Yamaguchi. A statistical study of spots in torsional Couette flow. Journal of Engineering Mathematics, 2007, 57 (3), pp.289-302. ⟨hal-00084127⟩