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Theoretical and Computational Fluid Dynamics

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14.09.2020 | Original Article

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

verfasst von: Dilip Kumar Maity

Erschienen in: Theoretical and Computational Fluid Dynamics | Ausgabe 1/2021

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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.

Vorheriger Artikel Numerical simulations of buoyancy-driven flows using adaptive mesh refinement: structure and dynamics of a large-scale helium plume

Nächster Artikel Stability of confined vortex sheets

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Faraday, M.: On a peculiar class of acoustical figures; and on certain forms assumed by groups of particles upon vibrating elastic surfaces. Philos. Trans. R. Soc. Lond. 121, 299 (1831). https://doi.org/10.1098/rstl.1831.0018CrossRef

Miles, J., Henderson, D.: Parametrically forced surface waves. Annu. Rev. Fluid. Mech. 22, 143–165 (1990). https://doi.org/10.1146/annurev.fl.22.010190.001043MathSciNetCrossRefMATH

Matthiessen, L.: Akustische versuche die kleinsten transversalwellen der flüssigkeiten betreffend. Ann. Phys. Chem. 210, 107–117 (1868). https://doi.org/10.1002/andp.18682100506CrossRef

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

Tufillaro, N., Ramshankar, R., Gollub, J.P.: Order-disorder transition in capillary ripples. Phys. Rev. Lett. 62, 422 (1989). https://doi.org/10.1103/PhysRevLett.62.422CrossRef

Ciliberto, S., Douady, S., Fauve, S.: Investigating space-time chaos in faraday instability by means of the fluctuations of the driving acceleration. Europhys. Lett. 15, 23 (1991)CrossRef

Benjamin, B., Ursell, F.: The stability of the plane free surface of a liquid in vertical periodic motion. Proc. R. Soc. A 225, 505–515 (1954). https://doi.org/10.1098/rspa.1954.0218MathSciNetCrossRefMATH

Edwards, W.S., Fauve, S.: Patterns and quasi-patterns in the faraday experiment. J. Fluid Mech. 278, 123 (1994). https://doi.org/10.1017/S0022112094003642MathSciNetCrossRef

Müller, H.W.: Periodic triangular patterns in the faraday experiment. Phys. Rev. Lett. 71, 3287 (1993). https://doi.org/10.1103/PhysRevLett.71.3287CrossRef

10.

Kumar, K., Bajaj, K.M.S.: Competing patterns in the faraday experiment. Phys. Rev. E 52, R4606 (1995). https://doi.org/10.1103/PhysRevE.52.R4606CrossRef

11.

Kumar, K., Tuckerman, L.S.: Parametric instability of the interface. J. Fluid Mech. 279, 49–68 (1994). https://doi.org/10.1017/S0022112094003812MathSciNetCrossRefMATH

12.

Kelvin, S.L.: Elastic spheroidal shells and spheroids of incompressible liquid. Philos. Trans. R. Soc. Lond. 153, 583 (1863)

13.

Rayleigh, L.: The Theory of Sound. Macmillan, London (reprinted by Dover Publications, New York) (1896)

14.

Lamb, H.: Hydrodynamics. Cambridge University Press, Cambridge (1932)MATH

15.

Reid, W.H.: The oscillations of a viscous liquid drop Q. Appl. Math. 18, 86–89 (1960). https://doi.org/10.1090/qam/114449MathSciNetCrossRef

16.

Chandrasekhar, S.C.: (1961) Hydrodynamic and Hydromagnetic Stability. 3rd edn, Clarendon Press. (reprinted by Dover Publications, New York) (1981)

17.

Miller, C.A., Scriven, L.E.: The oscillations of a fluid droplet immersed in another fluid. J. Fluid Mech. 32, 417–435 (1968). https://doi.org/10.1017/S0022112068000832CrossRefMATH

18.

Plateau, J.A.F.: Mémoire sur les phénomènes que présente une masse liquide libre et soustraite à l’action de la pesanteur. Acad. Sci. Brux. Mem. 16, 3 (1843)

19.

Bohr, N.: Determination of the surface-tension of water by the method of jet vibration. Philos. Trans. R. Soc. Lond. A 209, 441–458 (1909). https://doi.org/10.1098/rspa.1909.0014CrossRefMATH

20.

Popinet, S.: An accurate adaptive solver for surface-tension-driven interfacial flows. J. Comput. Phys. 228, 5838–5866 (2009). https://doi.org/10.1016/j.jcp.2009.04.042MathSciNetCrossRefMATH

21.

Cervone, A., Manservist, S., Scardovellt, R.: Simulation of axisymmetric jets with a finite element Navier–Stokes solver and a multilevel VoF approach. J. Comput. Phys. 229, 6853–6873 (2010). https://doi.org/10.1016/j.jcp.2010.05.025MathSciNetCrossRefMATH

22.

Farsoiya, P.K., Mayya, Y.S., Dasgupta, R.: Axisymmetric viscous interfacial oscillations-theory and simulations. J. Fluid Mech. 826, 797–818 (2017). https://doi.org/10.1017/jfm.2017.443MathSciNetCrossRefMATH

23.

Shen, C.L., Xie, W.J., Wei, B.: Parametrically excited sectorial oscillation of liquid drops floating in ultrasound. Phys. Rev. E 4, 046305 (2010). https://doi.org/10.1103/PhysRevE.81.046305CrossRef

24.

Hill, R.J.A., Eaves, L.: Vibrations of a diamagnetically levitated water droplet. Phys. Rev. E 81, 056312 (2010). https://doi.org/10.1103/PhysRevE.81.056312CrossRef

25.

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

26.

Brunet, P., Snoeijer, J.H.: Star-drops formed by periodic excitation and on an air cushion—a short review. Eur. Phys. J. 192, 207–226 (2011). https://doi.org/10.1140/epjst/e2011-01375-5CrossRef

27.

Ebo-Adou, A., Tuckerman, L.S.: Faraday instability on a sphere: floquet analysis. J. Fluid Mech. 805, 591 (2016). https://doi.org/10.1017/jfm.2016.542MathSciNetCrossRefMATH

28.

Li, Y., Zhang, P., Kang, N.: Linear analysis on the interfacial instability of a spherical liquid droplet subject to a radial vibration. Phys. Fluids 30, 102104 (2018). https://doi.org/10.1063/1.5050517CrossRef

29.

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

30.

Patankar, S., Farsoiya1 PK and Dasgupta R, : Faraday waves on a cylindrical fluid filament—generalised equation and simulations. J. Fluid Mech. 857, 80–110 (2018). https://doi.org/10.1017/jfm.2018.657

31.

Wang, T.G., Anilkumar, A.V., Lee, C.P.: Oscillations of liquid drops: results from USML-1 experiments in space. J. Fluid Mech. 308, 1–14 (1996). https://doi.org/10.1017/S002211209600136XCrossRef

32.

Futterer, B., Krebs, A., Plesa, A.C., Zaussinger, F., Hollerbach, R., Breuer, D., Egbers, C.: Sheet-like and plume-like thermal flow in aspherical convection experiment performed under microgravity. J. Fluid Mech. 735, 647–683 (2013). https://doi.org/10.1017/jfm.2013.507CrossRefMATH

33.

Falcon, C., Falcon, E., Bortolozzo, U., Fauve, S.: Capillary wave turbulence on a spherical fluid surface in low gravity. Europhys. Lett. 86, 14002 (2009). https://doi.org/10.1209/0295-5075/86/14002CrossRef

34.

Batson, W., Zoueshtiagh, F., Narayanan, R.: The Faraday threshold in small cylinders and the sidewall non-ideality. J. Fluid Mech. 729, 496–523 (2013). https://doi.org/10.1017/jfm.2013.324MathSciNetCrossRefMATH

Titel: Floquet analysis on a viscous cylindrical fluid surface subject to a time-periodic radial acceleration
verfasst von: Dilip Kumar Maity
Publikationsdatum: 14.09.2020
Verlag: Springer Berlin Heidelberg
Erschienen in: Theoretical and Computational Fluid Dynamics / Ausgabe 1/2021
Print ISSN: 0935-4964
Elektronische ISSN: 1432-2250
DOI: https://doi.org/10.1007/s00162-020-00550-y

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