1Timokha, AN 1Institute of Mathematics of the NAS of Ukraine, Kyiv |
Dopov. Nac. akad. nauk Ukr. 2018, 8:45-51 |
https://doi.org/10.15407/dopovidi2018.08.045 |
Section: Mechanics |
Language: English |
Abstract: The quantifying of the experimentally-known (Prandtl, 1949) steady rotary current during the swirl-type sloshing is first given. The current is treated as the sum of the mean wave (pseudo-) momentum through the meridional cross-section and the mean wave Eulerian flow, which is governed by the Craik—Leibovich equation. The constructed analytical inviscid theory is supported by existing experimental data. |
Keywords: Craik—Leibovich equation, sloshing, Stokes drift, swirling wave |
References:
- Prandtl, L. (1949). Erzuengung von Zirkulation beim Sch ü tteln von Gef ä ssen. ZAMM, 29, No. 1/2, pp. 8-9. doi: https://doi.org/10.1002/zamm.19490290106
- Hutton, R. E. (1964). Fluid-particle motion during rotary sloshing. J. Appl. Mech., Transactions ASME, 31, No. 1, p. 145-153. doi: https://doi.org/10.1115/1.3629532
- Royon-Lebeaud, A., Hopfinger, E.J. & Cartellier, A. (2007). Liquid sloshing and wave breaking in circular and square-base cylindrical containers. J. Fluid Mech., 577, pp. 467-494. doi: https://doi.org/10.1017/S0022112007004764
- Reclari, M. (2013). Hydrodynamics of orbital shaken bioreactors. Ecole Polytechnique Federale de Lausanne, PhD Thesis, No. 5759, 159 pp.
- Bouvard, J., Herreman, W. & Moisy, F. (2017). Mean mass transport in an orbitally shaken cylindrical con- tainer. Phys. Review, Fluids, 2, No. 084801, pp. 1-17.
- Faltisen, O. M., Lukovsky, I. A. & Timokha, A. N. (2016). Resonant sloshing in an upright annular tank. J. Fluid Mech. 804, pp. 608-645. doi: https://doi.org/10.1017/jfm.2016.539
- Faltisen, O. M., Lukovsky, I. A. & Timokha, A. N. (2009). Sloshing. Cambridge Univ. Press.
- Craik, A. D. & Leibovich, S. (1976). A rational model for Langmuir circulations. J. Fluid Mech., 73, No. 3, pp. 401-426. doi: https://doi.org/10.1017/S0022112076001420
- Timokha, A. N. (2018). Nonlinear boundary-layer and laminar vertical stream generated by resonant sloshing in a circular-base tank. Nonlinear Oscillations, 21, No. 1, pp. 131-145.