Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-29T13:15:50.126Z Has data issue: false hasContentIssue false
  • English
  • Français

All bent out of shape: buckling of sheared fluid layers

Published online by Cambridge University Press:  23 February 2012

Neil M. Ribe
Neil M. Ribe*
Affiliation:
Laboratoire FAST, UPMC/Univ Paris-Sud/CNRS, Bât. 502, Campus Universitaire, 91405 Orsay, France
*
†Email address for correspondence: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Buckling instabilities of thin sheets or plates of viscous fluid occur in situations ranging from food and polymer processing to geology. Slim, Teichman & Mahadevan (J. Fluid Mech., this issue, vol. 694, 2012, pp. 5–28) study numerically the buckling of a sheared viscous plate floating on a denser fluid using three approaches: a classical ‘thin viscous plate’ model; full numerical solution of the three-dimensional Stokes equations; and a novel ‘advection-augmented’ thin-plate model that accounts (in an asymptotically inconsistent way) for the advection of perturbations by the background shear flow. The advection-augmented thin-plate model is markedly superior to the classical one in its ability to reproduce the predictions of the Stokes solution, illustrating the utility of judicious violations of asymptotic consistency in fluid-mechanical models.

Type
Focus on Fluids
Information
Journal of Fluid Mechanics , Volume 694 , 10 March 2012 , pp. 1 - 4
Copyright
Copyright © Cambridge University Press 2012

References

1. Benjamin, T. B. & Mullin, T. 1988 Buckling instabilities in layers of viscous liquid subjected to shearing. J. Fluid Mech. 195, 523–540.CrossRefGoogle Scholar
2. Buckmaster, J. D., Nachman, A. & Ting, L. 1975 The buckling and stretching of a viscida. J. Fluid Mech. 69, 1–20.CrossRefGoogle Scholar
3. Eggers, J. & Dupont, T. F. 1994 Drop formation in a one-dimensional approximation of the Navier–Stokes equations. J. Fluid Mech. 262, 205–221.Google Scholar
4. Howell, P. J. 1996 Models for thin viscous sheets. Eur. J. Appl. Math. 7, 321–343.CrossRefGoogle Scholar
5. Johnson, A. M. & Fletcher, R. C. 1994 Folding of Viscous Layers. Columbia University Press.Google Scholar
6. LaBarbera, C. H. & MacAyeal, D. R. 2012 Traveling supraglacial lakes on George VI Ice Shelf. Geophys. Res. Lett., doi:10.1029/2011GL049970, in press.Google Scholar
7. Niordson, F. I. 1985 Shell Theory. North-Holland.Google Scholar
8. Ribe, N. M. 2002 A general theory for the dynamics of thin viscous sheets. J. Fluid Mech. 457, 255–283.CrossRefGoogle Scholar
9. Ribe, N. M. 2003 Periodic folding of viscous sheets. Phys. Rev. E 68, 036305.Google Scholar
10. Skorobogatiy, M. & Mahadevan, L. 2000 Folding of viscous sheets and filaments. Europhys. Lett. 52, 532–538.Google Scholar
11. Slim, A. C., Teichman, J. & Mahadevan, L. 2012 Buckling of a thin-layer Couette flow. J. Fluid Mech. 694, 5–28.CrossRefGoogle Scholar
12. Suleiman, S. M. & Munson, B. R. 1981 Viscous buckling of thin fluid layers. Phys. Fluids 24 (1), 1–5.Google Scholar
13. Taylor, G. I. 1969 Instability of jets, threads and sheets of viscous fluid. In 12th International Congress of Applied Mechanics (ed. Hétenyi, M. & Vincenti, W. G. ). pp. 382–388. Berlin, Springer-Verlag.Google Scholar