Instability of a horizontal water half-cylinder under vertical vibration
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.
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.
- Douglas B (2016) More details are avialable on the webpage of the free software Tracker at the link: https://physlets.org/tracker/
- Plateau JAF (1843) Acad Sci Brux Mem 16:3Google Scholar
- Plateau JAF (1849) Acad Sci Brux Mem 23:5Google Scholar
- Rayleigh L (1879) Proc R Soc Lond 10:4Google Scholar
- Rayleigh L (1896) The theory of sound. Macmillan, London (reprinted by Dover Publications, New York, 1945)Google Scholar
- Savart F (1833) Wemoire sur la constitution des veines liquids lancees par des orifices circulaires en mince paroi. Ann de Chimie 53:337Google Scholar