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Capillary and viscous perturbations to Helmholtz flows

Published online by Cambridge University Press:  21 February 2014

Madeleine Rose Moore ,
H. Ockendon ,
J. R. Ockendon  and
J. M. Oliver
Madeleine Rose Moore
Affiliation:
Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, UK
H. Ockendon
Affiliation:
Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, UK
J. R. Ockendon
Affiliation:
Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, UK
J. M. Oliver*
Affiliation:
Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, UK
*
†Email address for correspondence: oliver@maths.ox.ac.uk
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Abstract

Inspired by recent calculations by Thoraval et al. (Phys. Rev. Lett., vol. 108, 2012, p. 264506) relating to droplet impact, this paper presents an analysis of the perturbations to the free surface caused by small surface tension and viscosity in steady Helmholtz flows. In particular, we identify the regimes in which appreciable vorticity can be shed from the boundary layer to the bulk flow.

JFM classification

Boundary Layers: Boundary layer structure Drops and Bubbles: Cavitation Interfacial Flows (free surface): Interfacial Flows (free surface)
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 742 , 10 March 2014 , R1
Copyright
© 2014 Cambridge University Press 

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Footnotes

Article last updated 07 March 2023

References

Armand, J.-L. & Cointe, R. 1987 Hydrodynamic impact analysis of a cylinder. Trans. ASME: J. Offshore Mech. Arctic Engng 111, 109–114.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Castrejón-Pita, A. A., Castrejón-Pita, J. R. & Hutchings, I. M. 2012 Experimental observation of von Kármán vortices during drop impact. Phys. Rev. E 86, 045301.Google Scholar
Howison, S. D., Ockendon, J. R., Oliver, J. M., Purvis, R. & Smith, F. T. 2005 Droplet impact on a thin fluid layer. J. Fluid Mech. 542, 1–23.Google Scholar
Howison, S. D., Ockendon, J. R. & Wilson, S. K. 1991 Incompressible water-entry problems at small deadrise angles. J. Fluid Mech. 222, 215–230.Google Scholar
Josserand, C. & Zaleski, S. 2003 Droplet splashing on a thin liquid film. Phys. Fluids 15, 1650–1657.Google Scholar
Mandre, S. & Brenner, M. P. 2012 The mechanism of a splash on a dry solid surface. J. Fluid Mech. 690, 148–172.Google Scholar
Moore, D. W. 1963 The boundary layer on a spherical gas bubble. J. Fluid Mech. 16, 161–176.Google Scholar
Moore, M. R., Ockendon, J. R. & Oliver, J. M. 2013 Air-cushioning inimpact problems. IMA J. Appl. Maths 78, 818–838.Google Scholar
Purvis, R. & Smith, F. T. 2004 Air–water interactions near droplet impact. Eur. J. Appl. Maths 15 (6), 853–871.Google Scholar
Thoraval, M.-J., Takehara, K., Etoh, T. G., Popinet, S., Ray, P., Josserand, C., Zaleski, S. & Thoroddsen, S. T. 2012 Von Kármán vortex street within an impacting drop. Phys. Rev. Lett. 108, 264506.Google Scholar
Thoraval, M.-J., Takehara, K., Etoh, T. G. & Thoroddsen, S. T. 2013 Drop impact entrapment of bubble rings. J. Fluid Mech. 724, 234–258.Google Scholar
Thoroddsen, S. T., Thoraval, M.-J., Takehara, K. & Etoh, T. G. 2011 Droplet splashing by a slingshot mechanism. Phys. Rev. Lett. 106 (3), 034501.Google Scholar
Wagner, H. 1932 Über Stoss- und Gleitvorgänge an der Oberfläche von Flüssigkeiten. Z. Angew. Math. Mech. 12, 193–215.Google Scholar
Xu, L., Zhang, W. W. & Nagel, S. R. 2005 Drop splashing on a dry smooth surface. Phys. Rev. Lett. 94 (18), 184505.Google Scholar