Experiments in Fluids

, 61:25 | Cite as

Instability of a horizontal water half-cylinder under vertical vibration

  • Dilip Kumar Maity
  • Krishna KumarEmail author
  • Sugata Pratik Khastgir
Research Article


We present the results of an experimental investigation on parametrically driven waves in a water half-cylinder on a rigid horizontal plate, which is sinusoidally vibrated in the vertical direction. As the forcing amplitude is raised above a critical value, stationary waves are excited in the water half-cylinder. Parametrically excited subharmonic waves are non-axisymmetric and qualitatively different from the axisymmetric Savart–Plateau–Rayleigh waves in a vertical liquid cylinder or jet. Depending on the driving frequency, stationary waves of different azimuthal wave numbers are excited. A linear theory is also supplemented, which captures the observed dispersion relations quantitatively.

Graphic abstract



Partial support from SERB, India through Project Grant No. EMR/2016/000185 is acknowledged. The authors acknowledge fruitful suggestions from anonymous referees, which improved the manuscript.

Supplementary material

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Supplementary material 1 (MP4 4,478 kb)

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Supplementary material 1 (CLO 4 kb)


  1. Adou AE, Tuckerman LS (2016) Faraday instability on a sphere: floquet analysis. J Fluid Mech 805:591. MathSciNetCrossRefzbMATHGoogle Scholar
  2. Binks D, Van de Water W (1997) Nonlinear pattern formation of Faraday waves. Phys Rev Lett 78:4043. CrossRefGoogle Scholar
  3. Chandrasekhar SC (1961) Hydrodynamic and hydromagnetic stability, 3rd edn. Clarendon Press, Oxford (reprinted by Dover Publications, New York, 1981)zbMATHGoogle Scholar
  4. Ciliberto S, Douady S, Fauve S (1991) Investigating space-time chaos in Faraday instability by means of the fluctuations of the driving acceleration. Europhys. Lett. 15:23 CrossRefGoogle Scholar
  5. de Jesus VLB (2017) Experiments and video analysis in classical mechanics. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  6. Donnelly RJ, Glaberson W (1966) Experiments on the capillary instability of a liquid jet. Proc R Soc Lond A 290:547. CrossRefGoogle Scholar
  7. Douady S (1990) Experimental study of the Faraday instability. J Fluid Mech 221:383. CrossRefGoogle Scholar
  8. Douglas B (2016) More details are avialable on the webpage of the free software Tracker at the link:
  9. Edwards WS, Fauve S (1994) Patterns and quasi-patterns in the Faraday experiment. J Fluid Mech 278:123. MathSciNetCrossRefGoogle Scholar
  10. Faraday M (1831) On a peculiar class of acoustical figures; and on certain forms assumed by groups of particles upon vibrating elastic surfaces. Phil Trans R Soc Lond 121:299. CrossRefGoogle Scholar
  11. Fauve S, Kumar K, Laroche C, Beysens D, Garrabos Y (1992) Parametric instability of a liquid–vapour interface close to the critical point. Phys Rev Lett 68:3160. CrossRefGoogle Scholar
  12. Kudrolli A, Gollub JP (1996) Patterns and spatiotemporal chaos in parametrically forced surface waves: a systematic survey at large aspect ratio. Physica D 97:133. CrossRefGoogle Scholar
  13. Kumar K (1996) Linear theory of Faraday instability in viscous fluids. Proc R Soc Lond A 452:1113. CrossRefzbMATHGoogle Scholar
  14. Kumar K, Bajaj KMS (1995) Competing patterns in the Faraday experiment. Phys Rev E 52:R4606. CrossRefGoogle Scholar
  15. Lamb H (1932) Hydrodynamics. Cambridge University Press, CambridgezbMATHGoogle Scholar
  16. McHale G, Elliott SJ, Newton MI, Herbertson DL, Esmer K (2009) Levitation-free vibrated droplets: resonant oscillations of liquid marbles. Langmuir 25:529. CrossRefGoogle Scholar
  17. Moseler M, Landman U (2000) Formation, stability, breakup of nanojets. Science 289:1165. CrossRefGoogle Scholar
  18. Müller HW (1993) Periodic triangular patterns in the Faraday experiment. Phys Rev Lett 71:3287. CrossRefGoogle Scholar
  19. Müller HW, 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 78:2357. CrossRefGoogle Scholar
  20. Noblin X, Buguin A, Brochard-Wyart F (2005) Triplon modes of puddles. Phys Rev Lett 94:166102. CrossRefGoogle Scholar
  21. Plateau JAF (1843) Acad Sci Brux Mem 16:3Google Scholar
  22. Plateau JAF (1849) Acad Sci Brux Mem 23:5Google Scholar
  23. Plateau JAF (1873) Statique experimentale et théorique des Liquides soumis aux seules forces moléculaires, vol 2. Gauthier Villars, PariszbMATHGoogle Scholar
  24. Rayleigh L (1879) Proc R Soc Lond 10:4Google Scholar
  25. Rayleigh Lord (1892) On the instability of a cylinder of viscous liquid under capillary force. Phil Mag 34:145. CrossRefzbMATHGoogle Scholar
  26. Rayleigh L (1896) The theory of sound. Macmillan, London (reprinted by Dover Publications, New York, 1945)Google Scholar
  27. Savart F (1833) Wemoire sur la constitution des veines liquids lancees par des orifices circulaires en mince paroi. Ann de Chimie 53:337Google Scholar
  28. Tarasov N, Perego AM, Churkin DV, Staliunas K, Turitsyn SK (2016) Mode-locking via dissipative Faraday instability. Nat Commun 7:12441. CrossRefGoogle Scholar
  29. Xu J, Attinger D (2007) Acoustic excitation of superharmonic capillary waves on a meniscus in a planar microgeometry. Phys Fluids 19:108107. CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of PhysicsIndian Institute of Technology KharagpurKharagpurIndia

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