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ISRN Mathematical Physics
Volume 2012 (2012), Article ID 869070, 19 pages
Research Article

Generalizing the Multimodal Method for the Levitating Drop Dynamics

1Institute of Mathematics, National Academy of Sciences of Ukraine, Tereschenkivska 3 St., 01601 Kiev, Ukraine
2CeSOS, Norwegian University of Science and Technology, 7491 Trondheim, Norway

Received 23 April 2012; Accepted 30 July 2012

Academic Editors: S. Ansoldi, K. Netocny, K.-E. Thylwe, and G. F. Torres del Castillo

Copyright © 2012 M. O. Chernova et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The present paper extends the multimodal method, which is well known for liquid sloshing problems, to the free-surface problem modeling the levitating drop dynamics. The generalized Lukovsky-Miles modal equations are derived. Based on these equations an approximate modal theory is constructed to describe weakly-nonlinear axisymmetric drop motions. Whereas the drop performs almost-periodic oscillations with the frequency close to the lowest natural frequency, the theory takes a finite-dimensional form. Periodic solutions of the corresponding finite-dimensional modal system are compared with experimental and numerical results obtained by other authors. A good agreement is shown.