Hostname: page-component-848d4c4894-sjtt6 Total loading time: 0 Render date: 2024-06-22T04:38:18.293Z Has data issue: false hasContentIssue false
  • English
  • Français

Hydroelastic waves on fluid sheets

Published online by Cambridge University Press:  09 November 2011

M. G. Blyth ,
E. I. Părău  and
J.-M. Vanden-Broeck
M. G. Blyth*
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK
E. I. Părău
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK
J.-M. Vanden-Broeck
Affiliation:
Department of Mathematics, University College London, London WC1E 6BT, UK
*
†Email address for correspondence: m.blyth@uea.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

Nonlinear travelling waves on a two-dimensional inviscid fluid sheet are investigated when the sheet is bounded above and below by two thin elastic plates. Symmetric and antisymmetric solution branches are identified, together with a pair of bifurcation branches. It is shown that far along the branches the solutions approach limiting configurations that correspond to static solutions valid in the absence of fluid forcing.

JFM classification

Waves/Free-surface Flows: Elastic waves Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 689 , 25 December 2011 , pp. 541 - 551
Copyright
Copyright © Cambridge University Press 2011

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

1. Blyth, M. G. & Vanden-Broeck, J. M. 2004 New solutions for capillary waves on fluid sheets. J. Fluid Mech. 507, 255–264.CrossRefGoogle Scholar
2. Crowdy, D. G. 1999 Exact solutions for steady capillary waves on a fluid annulus. J. Nonlinear Sci. 9, 615–640.CrossRefGoogle Scholar
3. De Langre, E. 2002 Absolutely unstable waves in inviscid hydroelastic systems. J. Sound Vib. 256 (2), 299–317.CrossRefGoogle Scholar
4. Flaherty, J. E., Keller, J. B. & Rubinow, S. I. 1972 Post buckling behaviour of elastic tubes and rings with opposite sides in contact. SIAM J. Appl. Math. 23 (4), 446–455.CrossRefGoogle Scholar
5. Fung, Y. 1965 Foundations of Solid Mechanics. Prentice-Hall.Google Scholar
6. Grotberg, JB 1994 Pulmonary flow and transport phenomena. Annu. Rev. Fluid Mech. 26 (1), 529–571.CrossRefGoogle Scholar
7. Jia, L. B., Li, F., Yin, X. Z. & Yin, X. Y. 2007 Coupling modes between two flapping filaments. J. Fluid Mech. 581 (1), 199–220.CrossRefGoogle Scholar
8. Kim, G. & Davis, D. C. 1995 Hydrodynamic instabilities in flat-plate-type fuel assemblies. Nucl. Engng Des. 158 (1), 1–17.CrossRefGoogle Scholar
9. Kinnersley, W. 1976 Exact large amplitude waves on sheets of fluid. J. Fluid Mech. 77, 229–241.CrossRefGoogle Scholar
10. Korobkin, A., Părău, E. I. & Vanden-Broeck, J. M. 2011 The mathematical challenges and modelling of hydroelasticity. Phil. Trans. R. Soc. Lond. A 369, 2803–2812.Google ScholarPubMed
11. Plotnikov, P. I. & Toland, J. F. 2011 Modelling nonlinear hydroelastic waves. Phil. Trans. R. Soc. Lond. A 369, 2942–2956.Google ScholarPubMed
12. Pozrikidis, C. 2002 Buckling and collapse of open and closed cylindrical shells. J. Engng Maths 42 (2), 157–180.CrossRefGoogle Scholar
13. Shelley, M., Vandenberghe, N. & Zhang, J. 2005 Heavy flags undergo spontaneous oscillations in flowing water. Phys. Rev. Lett. 94 (9), 94302.CrossRefGoogle ScholarPubMed
14. Taylor, G. I. 1959 The dynamics of thin sheets of fluid. II. Waves on fluid sheets. Proc. R. Soc. Lond. A. 253, 296–312.Google Scholar
15. Vanden-Broeck, J. M. & Miloh, T. 1995 Computations of steep gravity waves by a refinement of Davies–Tulin’s approximation. SIAM J. Appl. Maths. 55 (4), 892–903.CrossRefGoogle Scholar
16. Vassilev, V. M., Djondjorov, P. A. & Mladenov, I. M. 2008 Cylindrical equilibrium shapes of fluid membranes. J. Phys. A 41, 435201.CrossRefGoogle Scholar