|1Timokha, AN, 2Raynovskyy, IA |
1Institute of Mathematics of the NAS of Ukraine, Kyiv
2Centre of Excellence "Autonomous Marine Operations and Systems", Norwegian University of Science and Technology, Trondheim, Norway
|Dopov. Nac. akad. nauk Ukr. 2017, 10:48-53|
The nonlinear Narimanov—Moiseev-type modal system with linear damping terms is employed to study the damped steady-state resonant sloshing in an upright circular tank due to a prescribed horizontal orbital (elliptic) tank motion with the forcing frequency close to the lowest natural sloshing frequency. Whereas the undamped sloshing implies coexisting the co-directed (with forcing) and counter-directed angular progressive waves (swirling), the damping makes the counter-directed swirling impossible as the forcing orbit tends to a circle.
|Keywords: damping, sloshing, steady-state waves|
- Reclari, M. (2013). Hydrodynamics of orbital shaken bioreactors (PhD Thesis, No. 5759). Ecole Polytechnique Federale de Lausanne, Suisse.
- Faltisen, O. M., Lukovsky, I. A. & Timokha, A. N. (2016). Resonant sloshing in an upright tank. J. Fluid Mech., 804, pp. 608-645. https://doi.org/10.1017/jfm.2016.539
- Miles, J. W. (1998). A note on interior vs. boundary-layer damping of surface waves in a circular cylinder. J. Fluid Mech., 364, pp. 319-323. https://doi.org/10.1017/S0022112098001189
- Lukovsky, I. A. (2015). Nonlinear dynamics: Mathematical models for rigid bodies with a liquid. Berlin: De Gruyter. https://doi.org/10.1515/9783110316575
- Raynovskyy, I. & Timokha, A. (2016). Resonant liquid sloshing in an upright circular tank performing a periodic motion. J. Numer. Appl. Math., No. 2(122), pp. 71-82.
- Royon-Lebeaud, A., Hopfinger, E. & Cartellier, A. (2007). Liquid sloshing and wave breaking in circular and square- base cylindrical containers. J. Fluid Mech., 577, pp. 467-494. https://doi.org/10.1017/S0022112007004764
- Faltisen, O. M. & Timokha, A. N. (2017). Resonant three-dimensional nonlinear sloshing in a square-base basin. Part 4. Oblique forcing and linear viscous damping. J. Fluid Mech., 822, pp. 139-169. https://doi.org/10.1017/jfm.2017.263