Title | The Bateman–Luke variational formalism in a sloshing with rotational flows |
Publication Type | Journal Article |
Year of Publication | 2016 |
Authors | Timokha, AN |
Abbreviated Key Title | Dopov. Nac. akad. nauk Ukr. |
DOI | 10.15407/dopovidi2016.04.030 |
Issue | 4 |
Section | Mathematics |
Pagination | 30-34 |
Date Published | 4/2016 |
Language | English |
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. |
Keywords | Bateman–Luke variational principle, Clebsch potentials, sloshing |
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.