The effect of the Coriolis force on Faraday waves

Abstract

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Mondal Gour Chandra and Kumar Krishna 2004The effect of the Coriolis force on Faraday wavesProc. R. Soc. Lond. A.460897–908http://doi.org/10.1098/rspa.2003.1259SectionRestricted accessResearch articleThe effect of the Coriolis force on Faraday waves Gour Chandra Mondal Gour Chandra Mondal Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 Barrackpore Trunk Road, Kolkata 700108, India Google Scholar Find this author on PubMed Search for more papers by this author and Krishna Kumar Krishna Kumar Department of Physics and Meteorology, Indian Institute of Technology, Kharagpur 721302, India () Google Scholar Find this author on PubMed Search for more papers by this author Gour Chandra Mondal Gour Chandra Mondal Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 Barrackpore Trunk Road, Kolkata 700108, India Google Scholar Find this author on PubMed Search for more papers by this author and Krishna Kumar Krishna Kumar Department of Physics and Meteorology, Indian Institute of Technology, Kharagpur 721302, India () Google Scholar Find this author on PubMed Search for more papers by this author Published:08 March 2004https://doi.org/10.1098/rspa.2003.1259AbstractLinear stability of the free surface of a thin sheet of a viscous fluid on a vertically vibrated rigid plate, in the presence of a uniform and slow rigid body rotation about the vertical axis, is presented. The Coriolis force delays the onset of parametrically excited surface waves. The creation of Faraday waves is always possible by raising the acceleration amplitude above a critical value, if the angular frequency ωv of the vertical vibration is much larger than four times the angular velocity ωr of the rotating plate. The surface waves may be harmonic or superharmonic with the imposed vibration in a thin sheet of slowly rotating viscous fluids at small vibration frequencies. This leads to the possibility of a tri–critical point at the onset of the surface instability in thin layers of a viscous fluid. Subharmonic, harmonic and superharmonic waves with different wavenumbers may coexist at the instability onset in the presence of a small Coriolis force, which is a qualitatively new result. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Tessier J, Castro-Folker N, Poulin F and Stastna M (2021) Anisotropy in Faraday instabilities of a shallow conducting fluid, EPL (Europhysics Letters), 10.1209/0295-5075/ac1779, 135:3, (34001), Online publication date: 1-Aug-2021. Guan X, Jia B, Yang L and Fu Q (2021) Linear instability of an annular liquid jet with gas velocity oscillations, Physics of Fluids, 10.1063/5.0049137, 33:5, (054110), Online publication date: 1-May-2021. Jia B, Xie L, Yang L, Fu Q and Cui X (2020) Energy budget of a viscoelastic planar liquid sheet in the presence of gas velocity oscillations, Physics of Fluids, 10.1063/5.0016311, 32:8, (083104), Online publication date: 1-Aug-2020. Jia B, Xie L, Yang L, Fu Q and Cui X (2019) Linear instability of viscoelastic planar liquid sheets in the presence of gas velocity oscillations, Journal of Non-Newtonian Fluid Mechanics, 10.1016/j.jnnfm.2019.104169, 273, (104169), Online publication date: 1-Nov-2019. Yang L, Jia B, Fu Q and Yang Q (2018) Stability of an air-assisted viscous liquid sheet in the presence of acoustic oscillations, European Journal of Mechanics - B/Fluids, 10.1016/j.euromechflu.2017.10.002, 67, (366-376), Online publication date: 1-Jan-2018. Stastna M and Poulin F (2014) The stochastic mode of the Faraday instability of shallow fluid layers, EPL (Europhysics Letters), 10.1209/0295-5075/106/44003, 106:4, (44003), Online publication date: 1-May-2014. Paul S and Kumar K (2006) Effect of magnetic field on parametrically driven surface waves, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 463:2079, (711-722), Online publication date: 8-Mar-2007. Mondal G and Kumar K (2006) Effect of Marangoni and Coriolis forces on multicritical points in a Faraday experiment, Physics of Fluids, 10.1063/1.2167994, 18:3, (032101), Online publication date: 1-Mar-2006. This Issue08 March 2004Volume 460Issue 2043 Article InformationDOI:https://doi.org/10.1098/rspa.2003.1259Published by:Royal SocietyPrint ISSN:1364-5021Online ISSN:1471-2946History: Published online08/03/2004Published in print08/03/2004 License: Citations and impact KeywordsFaraday WavesCoriolis ForceTri–Critical Point