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Super free fall

Published online by Cambridge University Press:  15 December 2009

E. VILLERMAUX  and
Y. POMEAU
E. VILLERMAUX*
Affiliation:
Aix-Marseille Université, IRPHE, 13384 Marseille Cedex 13, France
Y. POMEAU
Affiliation:
Department of Mathematics, The University of Arizona, 617 N. Santa Rita Avenue, PO Box 210089 Tucson, AZ 85721-0089, USA
*
†Also at: Institut Universitaire de France. Email address for correspondence: villerma@irphe.univ-mrs.fr
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Abstract

The free fall of a liquid mass through vertical tubes with a weakly increasing cross-section induces an acceleration of the upper liquid interface larger than gravity. The phenomenon is well described by a one-dimensional inviscid model. The super acceleration of the upper interface comes from the additional positive pressure gradient caused by the expanding geometry, which adds to the gravity body force. A perturbative expansion of this base solution further accounts for the interface shape and stability. In particular, the positive pressure gradient at the interface makes it unstable, forming a concentrated ‘nipple’ on top of the essentially flat base solution. We discuss the possible connexion of these findings with the problem of wave breaking in free surface flows.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 642 , 10 January 2010 , pp. 147 - 157
Copyright
Copyright © Cambridge University Press 2010

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