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Stability of a growing cylindrical blob

Published online by Cambridge University Press:  18 August 2017

R. Krechetnikov Open the ORCID record for R. Krechetnikov [Opens in a new window]
R. Krechetnikov*
Affiliation:
Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada
*
†Email address for correspondence: krechet@ualberta.ca
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Abstract

The stability of an accelerating cylindrical blob of a time-varying radius is considered with the goals of understanding the effects of time dependence of the underlying base state on a Rayleigh–Plateau instability as well as of evaluating a contribution due to a lateral acceleration of the blob, treated as a perturbation here. All of the key processes contributing to instability development are dissected, with analytical analyses of the exact incompressible inviscid potential flow formulation. Herein, without invoking the ‘frozen’ base state assumption, the entire time interval of the evolution of a perturbation is explored, discerning physical mechanisms at each stage of development. It transpires that the stability picture proves to be cardinally different from Rayleigh’s standard analysis.

JFM classification

Instability: Instability Interfacial Flows (free surface): Interfacial Flows (free surface)
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 827 , 25 September 2017 , R3
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Copyright
© 2017 Cambridge University Press 

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References

Abramowitz, M. & Stegun, I. A. 1965 Handbook of Mathematical Functions. Dover.Google Scholar
Agbaglah, G., Josserand, C. & Zaleski, S. 2013 Longitudinal instability of a liquid rim. Phys. Fluids 25, 022103.Google Scholar
Bellman, R.1949 A survey of the theory of the boundedness, stability, and asymptotic behaviour of solutions of linear and nonlinear differential and difference equations. Tech. Rep. NAVEXOS P-596. Office of Naval Research, Washington DC.Google Scholar
Blair, D. E. 2000 Inversion Theory and Conformal Mapping. AMS.CrossRefGoogle Scholar
Blumenhagen, R. & Plauschinn, E. 2009 Introduction to Conformal Field Theory. Springer.Google Scholar
Culick, F. E. C. 1960 Comments on a ruptured soap film. J. Appl. Phys. 31, 1128–1129.Google Scholar
Davis, S. H. 1976 The stability of time-periodic flows. Annu. Rev. Fluid Mech. 8, 57–74.Google Scholar
Donnelly, R. J. & Glaberson, W. 1966 Experiments on the capillary instability of a liquid jet. Proc. R. Soc. Lond. A 290, 547–556.Google Scholar
Drazin, P. G. & Reid, W. H. 2004 Hydrodynamic Stability. Cambridge University Press.Google Scholar
Dziwnik, M., Korzec, M., Münch, A. & Wagner, B. 2014 Stability analysis of unsteady, nonuniform base states in thin film equations. Multiscale Model. Simul. 12, 755–780.Google Scholar
Fullana, J. M. & Zaleski, S. 1999 Stability of a growing end rim in a liquid sheet of uniform thickness. Phys. Fluids 11, 952–954.Google Scholar
Homsy, G. M. 1973 Global stability of time-dependent flows: impulsively heated or cooled fluid layers. J. Fluid Mech. 60, 129–139.Google Scholar
Kamke, E. 1961 Handbook of Ordinary Differential Equations. Fizmatgiz.Google Scholar
Krechetnikov, R. 2010 Stability of liquid sheet edges. Phys. Fluids 22, 092101.Google Scholar
Levich, V. G. 1962 Physicochemical Hydrodynamics. Prentice-Hall.Google Scholar
Plesset, M. S. 1954 On the stability of fluid flows with spherical symmetry. J. Appl. Phys. 25, 96–98.Google Scholar
Rayleigh, Lord 1878 On the instability of jets. Proc. Lond. Math. Soc. 10, 4–13.Google Scholar
Roisman, I. V., Horvat, K. & Tropea, C. 2006 Spray impact: rim transverse instability initiating fingering and splash, and description of a secondary spray. Phys. Fluids 18, 102104.Google Scholar
Taylor, G. I. 1959 The dynamics of thin sheets of fluid. III. Disintegration of fluid sheets. Proc. R. Soc. Lond. A 253, 313–321.Google Scholar