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The shape of the fundamental sloshing mode in axisymmetric containers

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Abstract

We numerically study positions of high spots (extrema) of the fundamental sloshing mode of a liquid in an axisymmetric tank. Our approach is based on a linear model and reduces the problem to an appropriate Steklov eigenvalue problem. We propose a numerical scheme for calculating sloshing modes and a novel method for making images of an oscillating fluid.

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Acknowledgments

Bartłomiej Siudeja was partially supported by the Polish National Science Centre Grant 2012/07/B/ST1/03356. T. Kulczycki and M. Kwaśnicki were supported in part by Project S30011/I-18 of the Institute of Mathematics and Computer Science of Wrocław University of Technology. The authors would like to thank N. Kuznetsov for many useful discussions on the subject of the paper and for sharing his knowledge about the sloshing problem.

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Authors and Affiliations

  1. Department of Pure and Applied Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370, Wrocław, Poland

    Tadeusz Kulczycki & Mateusz Kwaśnicki

  2. Department of Mathematics, University of Oregon, Eugene, OR, 97403, USA

    Bartłomiej Siudeja

Authors
  1. Tadeusz Kulczycki
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  2. Mateusz Kwaśnicki
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  3. Bartłomiej Siudeja
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Correspondence to Bartłomiej Siudeja.

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Kulczycki, T., Kwaśnicki, M. & Siudeja, B. The shape of the fundamental sloshing mode in axisymmetric containers. J Eng Math 99, 157–183 (2016). https://doi.org/10.1007/s10665-015-9826-6

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  • DOI: https://doi.org/10.1007/s10665-015-9826-6

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