Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-27T13:06:22.787Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Bernoulli, D. 1738 Hydrodynamica. Strasbourg.Google Scholar
Calkin, M. G. & March, R. H. 1989 The dynamics of a free falling chain: I. Am. J. Phys. 57 (2), 154–157.CrossRefGoogle Scholar
Clavin, P. & Williams, F. 2005 Asymptotic spike evolution in Rayleigh–Taylor instability. J. Fluid Mech. 525, 105–113.CrossRefGoogle Scholar
Duchemin, L. 2008 Self-focusing of thin liquid jets. Proc. R. Soc. A 464, 197–206.CrossRefGoogle Scholar
Hirata, K. & Craik, A. D. D. 2003 Nonlinear oscillations in three-armed tubes. Eur. J. Mech. B – Fluids 22, 3–26.CrossRefGoogle Scholar
Newton, I. 1687 Principia Mathematica. London.Google Scholar
Paterson, A. R. 1983 A First Course in Fluid Dynamics. Cambridge University Press.CrossRefGoogle Scholar
Penney, W. G. & Price, A. T. 1952 Finite periodic stationary gravity waves in a perfect liquid. Phil. Trans. R. Soc. A 244, 254–284.Google Scholar
Phillips, O. M. 1958 The equilibrium range in the spectrum of wind-generated waves. J. Fluid Mech. 4 (4), 426–434.CrossRefGoogle Scholar
Schager, M., Steindl, A. & Troger, H. 1997 On the paradox of the free falling folded chain. Acta Mech. 125, 155–168.CrossRefGoogle Scholar
Taylor, G. I. 1953 An experimental study of standing waves. Proc. R. Soc. A CCXVIII, 44–59.Google Scholar