Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Lagrangian formulation of bubble dynamics

Author: D. Y. Hsieh
Journal: Quart. Appl. Math. 33 (1975), 115-130
MSC: Primary 76.53
DOI: https://doi.org/10.1090/qam/446078
MathSciNet review: 446078
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Abstract: The dynamical problem of two ideal fluids separated by an interface is formulated in terms of general coordinates in Lagrangian variables. The same problem is shown to be equivalent to a Hamiltonian variational principle which takes into account explicitly the surface energy of the interface between the two fluids. The formulation is applied to the motion of slightly nonspherical bubbles. It is shown that, although we start from an entirely different set of differential equations, the results of the linear stability analysis in Eulerian formulation are recovered.

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DOI: https://doi.org/10.1090/qam/446078
Article copyright: © Copyright 1975 American Mathematical Society

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