The Bateman–Luke variational formalism in a sloshing with rotational flows

Authors

  • A. N. Timokha Institute of Mathematics of the NAS of Ukraine, Kiev

DOI:

https://doi.org/10.15407/dopovidi2016.04.030

Keywords:

Bateman–Luke variational principle, Clebsch potentials, sloshing

Abstract

Based on a presentation of the velocity field in terms of Clebsch potentials, the Bateman–Luke variational formalism is generalized for the sloshing of an ideal incompressible liquid with rotational flows.

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References

Bateman H. Partial differential equations of mathematical physics, New York: Dover, 1944.

Luke J. G. J. Fluid Mech., 1967, 27: 395–397. https://doi.org/10.1017/S0022112067000412

Faltinsen O. M., Timokha A. N. Sloshing, New York: Cambridge Univ. Press, 2009.

Lukovsky I. A. Nonlinear dynamics: Mathematical models for rigid bodies with a liquid, Berlin: de Gruyter, 2015.

Takahara H., Kimura K. J. Sound Vibr., 2012, 331, No 13: 3199–3212. https://doi.org/10.1016/j.jsv.2012.02.023

Prandtl L. ZAMM, 1949, 29, No 1/2: 8–9. https://doi.org/10.1002/zamm.19490290106

Hutton R. E. J. Appl. Mech., Trans. ASME, 1964, 31, No 1: 145–153.

Royon-Lebeaud A., Hopfinger E., Cartellier A. J. Fluid Mech., 2007, 577: 467–494. https://doi.org/10.1017/S0022112007004764

Clebsch A. J. Reine Angew. Math., 1857, 54: 293–313. https://doi.org/10.1515/crll.1857.54.293

Clebsch A. J. Reine Angew. Math., 1869, 56: 1–10.

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Published

19.10.2024

How to Cite

Timokha, A. N. (2024). The Bateman–Luke variational formalism in a sloshing with rotational flows . Reports of the National Academy of Sciences of Ukraine, (4), 30–34. https://doi.org/10.15407/dopovidi2016.04.030