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A Note on the Variational Formalism for Sloshing with Rotational Flows in a Rigid Tank with Unprescribed Motion

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Ukrainian Mathematical Journal Aims and scope

The Bateman–Luke-type variational formulation of the free-boundary “sloshing” problem is generalized to the case of irrotational flows and unprescribed tank motions, i.e., to the case where the motions both of the tank and of the liquid should be found simultaneously for a given set of external forces applied to fixed points of the rigid tank body. We prove that the variational equation corresponding to the formulated problem implies both the dynamic (force and moment) equations of the rigid body and the free-boundary problem that describes sloshing in terms of the Clebsch potentials.

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    I. A. Lukovsky

  2. Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine; Norwegian University of Science and Technology, Trondheim, Norway

    A. N. Timokha

Authors
  1. I. A. Lukovsky
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  2. A. N. Timokha
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Corresponding author

Correspondence to A. N. Timokha.

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 10, pp. 1368–1376, October, 2021. Ukrainian DOI: https://doi.org/10.37863/umzh.v73i10.6795.

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Lukovsky, I.A., Timokha, A.N. A Note on the Variational Formalism for Sloshing with Rotational Flows in a Rigid Tank with Unprescribed Motion. Ukr Math J 73, 1580–1589 (2022). https://doi.org/10.1007/s11253-022-02015-3

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  • DOI: https://doi.org/10.1007/s11253-022-02015-3

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