A note on variational formalism for sloshing with rotational flows in a rigid tank with an unprescribed motion

I. A. Lukovsky; A. N. Timokha

doi:10.37863/umzh.v73i10.6795

I. A. Lukovsky Inst. Math. Acad. Sci. Ukraine, Kiev
A. N. Timokha Inst. Math. Nat. Acad. Sci. Ukraine, Kyiv and Norwegian Univ. Sci and Technology, Trondheim

DOI: https://doi.org/10.37863/umzh.v73i10.6795

Keywords: sloshing, rotational flows, variational formalism

Abstract

UDC 517.9

The Bateman – Luke-type variational formulation of the free-boundary ‘sloshing’ problem is generalized to irrotational flows and unprescribed tank motions, i.e., to the case where both the tank and liquid motions 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, which corresponds to the formulated problem, implies both the dynamic (force and moment) equations of the rigid body and the free-boundary problem, which describes sloshing in terms of the Clebsch potentials.

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