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Shear instabilities and vortex double row in a confined geometry.
Paul Boniface, Luc Lebon, Laurent Limat, ChiTuong Pham and Mathieu Receveur MSC)
We have investigated the appearance of shear instabilities evolving into the formation of a quasistationary vortex double rows in a closed tank, at the free surface of which a belt or a rope is running at high speed. Depending on the aspect ratios governing the different confinements involved, different flow structures are observed, with large stationnary vortices or, on the contrary of a large number of small unstationary ones. We propose three different attempts of modeling, that allow us to recover a part of the observed spatial structure selection mechanisms. In particular, the stability condition found long ago by Von Karman is replaced with a continuous band of allowed solutions, whose shape is in agreement with calculations peformed by several authors in the 20's (Rosenhead, Tomotika, Vila etc.). To our knowlegde, this experiment is perhaps the first experimental proof of these ancient theories based on point vortex dynamics in the complex plane.

