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On the dynamics of a free surface of an ideal fluid in a bounded domain in the presence of surface tension

Published online by Cambridge University Press:  07 December 2018

Sergey A. Dyachenko Open the ORCID record for Sergey A. Dyachenko [Opens in a new window]
Sergey A. Dyachenko*
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
*
†Email address for correspondence: sdyachen@math.uiuc.edu
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Abstract

We derive a set of equations in conformal variables that describe a potential flow of an ideal two-dimensional inviscid fluid with free surface in a bounded domain. This formulation is free of numerical instabilities present in the equations for the surface elevation and potential derived in Dyachenko et al. (Plasma Phys. Rep. vol. 22 (10), 1996, pp. 829–840) with some restrictions on analyticity relieved, which allows to treat a finite volume of fluid enclosed by a free-moving boundary. We illustrate with a comparison of numerical simulations of the Dirichlet ellipse, an exact solution for a zero surface tension fluid. We demonstrate how the oscillations of the free surface of a unit disc droplet may lead to breaking of one droplet into two when surface tension is present.

JFM classification

Interfacial Flows (free surface): Capillary flows Interfacial Flows (free surface): Interfacial Flows (free surface) Waves/Free-surface Flows: Waves/Free-surface Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 860 , 10 February 2019 , pp. 408 - 418
Copyright
© 2018 Cambridge University Press 

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