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Floquet analysis on a viscous cylindrical fluid surface subject to a time-periodic radial acceleration

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Abstract

Parametrically excited standing waves are observed on a cylindrical fluid filament. This is the cylindrical analog of the Faraday instability in a flat surface or spherical droplet. Using Floquet theory, a linear stability analysis is carried out on a viscous cylindrical fluid surface, which is subjected to a time-periodic radial acceleration. Viscosity of the fluid has a significant impact on the critical forcing amplitude as well as the dispersion relation of the non-axisymmetric patterns. The effect of viscosity on the threshold of the pattern with azimuthal wavenumber \(m=1\) shows a different dependence from \(m>1\). It is also observed that the effect of viscosity is greater on the threshold with higher m.

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Acknowledgements

The author would like to thank Krishna Kumar and Sonjoy Majumder for fruitful discussions. The author is also thankful to Moupiya Jana for a careful reading of the manuscript. The author acknowledges the fruitful suggestions from the anonymous referees, which improved the manuscript.

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  1. Department of Physics, Indian Institute of Technology Kharagpur, Kharagpur, 721302, India

    Dilip Kumar Maity

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Correspondence to Dilip Kumar Maity.

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Maity, D.K. Floquet analysis on a viscous cylindrical fluid surface subject to a time-periodic radial acceleration. Theor. Comput. Fluid Dyn. 35, 93–107 (2021). https://doi.org/10.1007/s00162-020-00550-y

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