Resonant steady-state sloshing in upright tanks performing a three-dimensional periodic motion

Authors

  • 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 https://orcid.org/0000-0002-6750-4727
  • E. M. Tkachenko Institute of Mathematics of the NAS of Ukraine, Tereshchenkivska 3, str., Kiev, 01004

DOI:

https://doi.org/10.17721/1812-5409.2019/1.50

Abstract

Analytical approaches to hydrostatic capillary (meniscus) problem in infinite horizontal channel and axisymmetric container are developed. For these geometric cases, finding the capillary menisci reduces to freeboundary problems for special systems of ordinary differential equations. Their solutions describe capillary curves, which appear as intersections of the capillary menisci and (depending on the container type) either crosssection or meridional plane. Further studies on capillary waves require to know analytical approximations of these capillary curves in the Cn, n ? 3 metrics. An objective may consists of constructing analytical approximate solutions of the corresponding systems of ordinary differential equations. The present paper focuses on limits of applicability of the Taylorpolynomial and Pad´e approximations, which were proposed for this class of capillary problems in 1984 by Barnyak&Timokha.

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

Pages of the article in the issue: 214-217

Language of the article: English

References

BARNYAK, M. Ya., TIMOKHA, A. N. (1984) On finding approximate analytical solutions of planar and axisymmetric single-connected capillary surfaces in the form of rational functions. In Book: “Numerical-Analytical Methods for Investigation of Dynamics and Stability of Multidimensional Systems”. Kiev: Institute of Mathematics. Academy of Sciences of the UkrSSR.

CONCUS, P., FINN, R., WEISLOGEL, M. (1999) Capillary surfaces in an exotic container: results from Space experiments. Journal of Fluid Mechanics. 394. pp. 119-135.

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How to Cite

Timokha, O. M., & Tkachenko, E. M. (2019). Resonant steady-state sloshing in upright tanks performing a three-dimensional periodic motion. Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences, (1), 214–217. https://doi.org/10.17721/1812-5409.2019/1.50

Issue

Section

Differential equations, mathematical physics and mechanics