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Instability of a horizontal water half-cylinder under vertical vibration

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Abstract

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.

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References

  1. Adou AE, Tuckerman LS (2016) Faraday instability on a sphere: floquet analysis. J Fluid Mech 805:591. https://doi.org/10.1017/jfm.2016.542

  2. Binks D, Van de Water W (1997) Nonlinear pattern formation of Faraday waves. Phys Rev Lett 78:4043. https://doi.org/10.1103/PhysRevLett.78.4043

  3. Chandrasekhar SC (1961) Hydrodynamic and hydromagnetic stability, 3rd edn. Clarendon Press, Oxford (reprinted by Dover Publications, New York, 1981)

  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 http://stacks.iop.org/0295-5075/15/i=1/a=005

  5. de Jesus VLB (2017) Experiments and video analysis in classical mechanics. Cambridge University Press, Cambridge

  6. Donnelly RJ, Glaberson W (1966) Experiments on the capillary instability of a liquid jet. Proc R Soc Lond A 290:547. https://doi.org/10.1098/rspa.1966.0069

  7. Douady S (1990) Experimental study of the Faraday instability. J Fluid Mech 221:383. https://doi.org/10.1017/S0022112090003603

  8. Douglas B (2016) More details are avialable on the webpage of the free software Tracker at the link: https://physlets.org/tracker/

  9. Edwards WS, Fauve S (1994) Patterns and quasi-patterns in the Faraday experiment. J Fluid Mech 278:123. https://doi.org/10.1017/S0022112094003642

  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. https://doi.org/10.1098/rstl.1831.0018

  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. https://doi.org/10.1103/PhysRevLett.68.3160

  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. https://doi.org/10.1016/0167-2789(96)00099-1

  13. Kumar K (1996) Linear theory of Faraday instability in viscous fluids. Proc R Soc Lond A 452:1113. https://doi.org/10.1098/rspa.1996.0056

  14. Kumar K, Bajaj KMS (1995) Competing patterns in the Faraday experiment. Phys Rev E 52:R4606. https://doi.org/10.1103/PhysRevE.52.R4606

  15. Lamb H (1932) Hydrodynamics. Cambridge University Press, Cambridge

  16. McHale G, Elliott SJ, Newton MI, Herbertson DL, Esmer K (2009) Levitation-free vibrated droplets: resonant oscillations of liquid marbles. Langmuir 25:529. https://doi.org/10.1021/la803016f

  17. Moseler M, Landman U (2000) Formation, stability, breakup of nanojets. Science 289:1165. https://doi.org/10.1126/science.289.5482.1165

  18. Müller HW (1993) Periodic triangular patterns in the Faraday experiment. Phys Rev Lett 71:3287. https://doi.org/10.1103/PhysRevLett.71.3287

  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. https://doi.org/10.1103/PhysRevLett.78.2357

  20. Noblin X, Buguin A, Brochard-Wyart F (2005) Triplon modes of puddles. Phys Rev Lett 94:166102. https://doi.org/10.1103/PhysRevLett.94.166102

  21. Plateau JAF (1843) Acad Sci Brux Mem 16:3

  22. Plateau JAF (1849) Acad Sci Brux Mem 23:5

  23. Plateau JAF (1873) Statique experimentale et théorique des Liquides soumis aux seules forces moléculaires, vol 2. Gauthier Villars, Paris

  24. Rayleigh L (1879) Proc R Soc Lond 10:4

  25. Rayleigh Lord (1892) On the instability of a cylinder of viscous liquid under capillary force. Phil Mag 34:145. https://doi.org/10.1080/14786449208620301

  26. Rayleigh L (1896) The theory of sound. Macmillan, London (reprinted by Dover Publications, New York, 1945)

  27. Savart F (1833) Wemoire sur la constitution des veines liquids lancees par des orifices circulaires en mince paroi. Ann de Chimie 53:337

  28. Tarasov N, Perego AM, Churkin DV, Staliunas K, Turitsyn SK (2016) Mode-locking via dissipative Faraday instability. Nat Commun 7:12441. https://doi.org/10.1038/ncomms12441

  29. Xu J, Attinger D (2007) Acoustic excitation of superharmonic capillary waves on a meniscus in a planar microgeometry. Phys Fluids 19:108107. https://doi.org/10.1063/1.2790968

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Acknowledgements

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.

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Correspondence to Krishna Kumar.

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Maity, D.K., Kumar, K. & Khastgir, S.P. Instability of a horizontal water half-cylinder under vertical vibration. Exp Fluids 61, 25 (2020) doi:10.1007/s00348-019-2860-9

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