On the variational statement of one boundary-value problem with free interface

Authors

  • A. Timokha Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv

DOI:

https://doi.org/10.3842/umzh.v75i8.7650

Keywords:

Bateman-Luke variational principle, Clebsch potentials, droplet

Abstract

UDC 532.595

With the help of Clebsch's potentials, we propose a Bateman–Luke-type variational principle  for a boundary-value problem with a free (unknown) interface between two ideal compressible barotropic fluids (liquid and gas)  admitting rotational flows.

References

I. A. Lukovskii, A. N. Timokha, Variational formulations of nonlinear boundary-value problems with a free boundary in the theory of interaction of surface waves with acoustic fields, Ukr. Math. J., 45, № 12, 1849–1860 (1993); DOI: 10.1007/BF01061355. DOI: https://doi.org/10.1007/BF01061355

M. O. Chernova, I. A. Lukovsky, A. N. Timokha, Differential and variational formalism for acoustically-levitating drops, J. Math. Sci., 220, № 3, 359–375 (2015); DOI: 10.1007/s10958-016-3189-z. DOI: https://doi.org/10.1007/s10958-016-3189-z

K. Pandey, D. Prabhakaran, S. Basu, Review of transport processes and particle self-assembly in acoustically levitated nanofluid droplets, Phys. Fluids, 31, № 11, Article 112102 (2019); DOI: 10.1063/1.5125059. DOI: https://doi.org/10.1063/1.5125059

H. Chen, A. Li, Y. Zhang, Z. Xiaoqiang, Evaporation and liquid-phase separation of ethanol-cyclohexane binary drops under acoustic levitation, Phys. Fluids, 34, № 9, Article 092108 (2022); DOI: 10.1063/5.0109520. DOI: https://doi.org/10.1063/5.0109520

A. N. Timokha, A note on the variational formalism for sloshing with rotational flows in a rigid tank with unprescribed motion, Ukr. Math. J., 73, № 10, 1580–1589 (2022); DOI: 10.1007/s11253-022-02015-3. DOI: https://doi.org/10.1007/s11253-022-02015-3

H. Bateman, Partial differential equations of mathematical physics, Dover Publ., New York (1944).

O. M. Faltinsen, A. N. Timokha, Sloshing, Cambridge Univ. Press (2009).

Published

30.08.2023

Issue

Section

Research articles