Steady-state sloshing in an orbitally-forced square-base tank


  • O. M. Timokha The Centre of Excellence “Autonomous Marine Operations and Systems”, Norwegian University of Science and Technology, NO-7491, Trondheim, Norway; Institute of Mathematics of the NAS of Ukraine
  • O. E. Lahodzinskyi Institute of Mathematics of the NAS of Ukraine, Tereshchenkivska 3, str., Kiev, 01004



The paper conducts a series of analytical studies on the resonant steady-state sloshing in a rigid square base container, which have been originated by Faltinsen & Timokha who derived and applied the Narimanov-Moiseev—type nonlinear modal equations for investigation in the sloshing problem. The modal equations, which consist on nine-dimensional system of ordinary differential equations, should be applicable for sway/pitch/surge/roll periodic excitations but, due to, basically, mathematical difficulties, the previous papers exclusively concentrated on the reciprocating (longitudinal, oblique and diagonal) motions of the container. This article is showed that the steady-state waves caused by this kind of forcing are asymptotically identical to those occurring when the tank performs horizontal orbital motions. We generalize the previous results by Faltinsen & Timokha to classify the steady-state wave regimes versus the semi-axes ratio of the forcing ellipse in the tank which is filled by a liquid with a finite depth.

Key words: sloshing, damping, steady-state waves.

Pages of the article in the issue: 210-213

Language of the article: English


FALTINSEN, O. M. & ROGNEBAKKE, O. F. & TIMOKHA, A.N. (2003) Resonant threedimensional nonlinear sloshing in a square base basin. Journal of Fluid Mechanics. 387.p. 1-42.

RAYNOVSKYY, I. & TIMOKHA, A. (2018) Damped steady-state resonant sloshing in a circular base container. Fluid Dynamics Research. 50. Article ID 5487178.—p. 1-8.

FALTINSEN, O. M. & TIMOKHA, A.N. (2001) Adaptive multimodal approach to nonlinear sloshing in a rectangular rank. J. Fluid Mech. 432, 167–200.

MOISEYEV, N. N. & RUMYANTSEV, V. V. 1968 Dynamic Stability of Bodies Containing Fluid. Springer


How to Cite

Timokha, O. M., & Lahodzinskyi, O. E. (2019). Steady-state sloshing in an orbitally-forced square-base tank. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics, (1), 210–213.



Differential equations, mathematical physics and mechanics