Hostname: page-component-76fb5796d-skm99 Total loading time: 0 Render date: 2024-04-26T09:13:30.015Z Has data issue: false hasContentIssue false
  • English
  • Français

Inviscid Faraday waves in a brimful circular cylinder

Published online by Cambridge University Press:  08 May 2013

R. Kidambi
R. Kidambi*
Affiliation:
Computational and Theoretical Fluid Dynamics Division, Council of Scientific and Industrial Research, National Aerospace Laboratories, Bangalore 560017, India
*
†Email address for correspondence: kidambi@ctfd.cmmacs.ernet.in
Get access Rights & Permissions [Opens in a new window]

Abstract

We study inviscid Faraday waves in a brimful circular cylinder with pinned contact line. The pinning leads to a coupling of the Bessel modes and leads to an infinite system of coupled Mathieu equations. For large Bond numbers, even though the stability diagrams and the subharmonic and harmonic resonances for the free and pinned contact lines are similar, the free surface shapes can be quite different. With decreasing Bond number, not only are the harmonic and subharmonic resonances very different from the free contact line case but also interesting changes in the stability diagram occur with the appearance of combination resonance tongues. Points on these tongue boundaries correspond to almost-periodic states. These do not seem to have been reported in the literature.

JFM classification

Waves/Free-surface Flows: Faraday waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 724 , 10 June 2013 , pp. 671 - 694
Copyright
©2013 Cambridge University Press 

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

Bechhoefer, J., Ego, V., Manneville, S. & Johnson, B. 1995 An experimental study of the onset of parametrically pumped surface waves in viscous fluids. J. Fluid Mech. 288, 325–350.CrossRefGoogle Scholar
Benjamin, T. B. & Ursell, F. 1954 The stability of the plane free surface of a liquid in vertical periodic motion. Proc. R. Soc. Lond. A 225 (1163), 505–515.Google Scholar
Beyer, J. & Friedrich, R. 1995 Faraday instability: linear analysis for viscous fluids. Phys. Rev. E 51 (2), 1162–1168.Google Scholar
Bhattacherjee, A. B. 2008 Faraday instability in a two-component Bose–Einstein condensate. Phys. Scr. 78 (4), 045009.CrossRefGoogle Scholar
Cerda, E. A. & Tirapegui, E. L. 1998 Faraday’s instability in viscous fluid. J. Fluid Mech. 368, 195–228.CrossRefGoogle Scholar
Christiansen, B., Alstrom, P. & Levinsen, M. T. 1995 Dissipation and ordering in capillary waves at high aspect ratios. J. Fluid Mech. 291, 323–341.Google Scholar
Ciliberto, S. & Gollub, J. P. 1984 Pattern competition leads to chaos. Phys. Rev. Lett. 52 (11), 922–925.CrossRefGoogle Scholar
Douady, S. 1990 Experimental study of the Faraday instability. J. Fluid Mech. 221, 383–409.Google Scholar
Edwards, W. S. & Fauve, S. 1993 Parametrically excited quasicrystalline waves. Phys. Rev. E 47 (2), R778–R791.CrossRefGoogle ScholarPubMed
Edwards, W. S. & Fauve, S. 1994 Patterns and quasi-patterns in the Faraday experiment. J. Fluid Mech. 278, 123–148.CrossRefGoogle Scholar
Hansen, J. 1985 Stability diagrams of coupled Mathieu equations. Ingenieur-Archiv 55, 463–473.Google Scholar
Hill, G. W. 1886 On the part of the motion of lunar perigee which is function of the mean motions of the sun and moon. Acta Math. 8, 1–36.Google Scholar
Hocking, L. M. 1987 The damping of capillary–gravity waves at a rigid boundary. J. Fluid Mech. 179, 253–266.Google Scholar
Kidambi, R. 2009a Capillary damping of inviscid surface waves in a circular cylinder. J. Fluid Mech. 627, 323–340.Google Scholar
Kidambi, R. 2009b Meniscus effects on the frequency and damping of capillary–gravity waves in a brimful circular cylinder. Wave Motion 46, 144–154.CrossRefGoogle Scholar
Kidambi, R. & Shankar, P. N. 2004 The effects of the contact angle on sloshing in containers. Proc. R. Soc. Lond. A 460, 2251–2267.CrossRefGoogle Scholar
Kumar, K. & Tuckerman, L. S. 1994 Parametric instability of the interface between two fluids. J. Fluid Mech. 279, 49–68.CrossRefGoogle Scholar
Kumar, K. 1996 Linear theory of Faraday instability in viscous liquids. Proc. R. Soc. Lond. A 452, 1113–1126.Google Scholar
Lam, K. D. N. T. & Caps, H. 2011 Effect of a capillary meniscus on the Faraday instability threshold. Eur. Phys. J. E 34, 112.Google Scholar
Lindh, K. G. & Likins, P. W. 1970 Infinite determinant methods for stability analysis of periodic-coefficient differential equations. AIAA J. 8 (4).Google Scholar
Mathieu, E. 1868 Le mouvement vibratoire d’une membrane de forme elliptique. J. Math. Pures Appl. 13, 137–203.Google Scholar
McLachlan, G. 1947 Theory and Application of Mathieu Functions. Oxford University Press.Google Scholar
Miles, J. W. 1967 Surface-wave damping in closed basins. Proc. R. Soc. Lond. A 297, 459–475.Google Scholar
Milner, S. T. 1991 Square patterns and secondary instabilities in driven capillary waves. J. Fluid Mech. 225, 81–100.CrossRefGoogle Scholar
Muller, H. W., Wittmer, H., Wagner, C., Albers, J. & Knorr, K. 1997 Analytic stability theory for Faraday waves and the observation of the harmonic surface response. Phys. Rev. Lett. 78 (12), 2357–2360.CrossRefGoogle Scholar
Nayfeh, A. H. & Mook, D. T. 1995 Nonlinear Oscillations. John Wiley & Sons.Google Scholar
Ozakin, A. & Shaikh, F. 2011 Stability analysis of surface ion traps. arXiv:1109.2160v.Google Scholar
Rayleigh, Lord 1883 On the crispation of fluid resting upon a vibrating support. Phil. Mag. 15 (5), 50–58.Google Scholar