Prandtl steady rotary current in an upright cylindrical container

1Timokha, AN
1Institute of Mathematics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2018, 8:45-51
Section: Mechanics
Language: English

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
  1. Prandtl, L. (1949). Erzuengung von Zirkulation beim Sch ü tteln von Gef ä ssen. ZAMM, 29, No. 1/2, pp. 8-9. doi:
  2. Hutton, R. E. (1964). Fluid-particle motion during rotary sloshing. J. Appl. Mech., Transactions ASME, 31, No. 1, p. 145-153.
  3. 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:
  4. Reclari, M. (2013). Hydrodynamics of orbital shaken bioreactors. Ecole Polytechnique Federale de Lausanne, PhD Thesis, No. 5759, 159 pp.
  5. 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.
  6. 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:
  7. Faltisen, O. M., Lukovsky, I. A. & Timokha, A. N. (2009). Sloshing. Cambridge Univ. Press.
  8. Craik, A. D. & Leibovich, S. (1976). A rational model for Langmuir circulations. J. Fluid Mech., 73, No. 3, pp. 401-426. doi:
  9. 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.