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Boundary layers in Helmholtz flows
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Moore, M. R., Cimpeanu, Radu, Ockendon, H., Ockendon, J. R. and Oliver, J. M. (2020) Boundary layers in Helmholtz flows. Journal of Fluid Mechanics, 882 . A19. doi:10.1017/jfm.2019.832 ISSN 0022-1120.
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Official URL: https://doi.org/10.1017/jfm.2019.832
Abstract
Recent comparisons between classical Wagner theory for the impact of two liquid droplets and direct numerical simulations in Cimpeanu & Moore (J. Fluid Mech., vol. 856, 2018, pp. 764–796) show that, in some regimes, the inviscid theory over-predicts the thickness of the root of the splash jet that forms in the impact, while also struggling to predict the angle at which the jet is emitted. The effect of capillary and viscous perturbations to Helmholtz flows was investigated in a previous study, see Moore et al. (J. Fluid Mech., vol. 742, 2014, R1). However, the paper in question ignored a term in the second-order perturbation analysis, which needs to be included in order to predict the displacement of the inviscid free boundary to lowest order. In this paper, we derive a singular integro-differential equation for the free-surface perturbations caused by viscosity in Helmholtz flows and discuss its application both in the context of Wagner theory and more generally. In particular, viscosity can induce non-monotonic behaviour in the free boundary profiles near points of maximum curvature.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Library of Congress Subject Headings (LCSH): | Fluid mechanics, Helmholtz equation, Boundary layer | ||||||||
Journal or Publication Title: | Journal of Fluid Mechanics | ||||||||
Publisher: | Cambridge University Press | ||||||||
ISSN: | 0022-1120 | ||||||||
Official Date: | 10 January 2020 | ||||||||
Dates: |
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Volume: | 882 | ||||||||
Article Number: | A19 | ||||||||
DOI: | 10.1017/jfm.2019.832 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Reuse Statement (publisher, data, author rights): | This article has been published in a revised form in Journal of Fluid Mechanics [http://doi.org/10.1017/jfm.2019.832. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © 2019 Cambridge University Press | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Copyright Holders: | © 2019 Cambridge University Press | ||||||||
Date of first compliant deposit: | 17 October 2019 | ||||||||
Date of first compliant Open Access: | 11 May 2020 | ||||||||
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