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Viscous damping of steady-state resonant sloshing in a clean rectangular tank

Published online by Cambridge University Press:  13 June 2023

Anton Miliaiev  and
Alexander Timokha Open the ORCID record for Alexander Timokha [Opens in a new window]
Anton Miliaiev
Affiliation:
Institute of Mathematics of the National Academy of Sciences of Ukraine, 01024 Kyiv, Ukraine
Alexander Timokha*
Affiliation:
Institute of Mathematics of the National Academy of Sciences of Ukraine, 01024 Kyiv, Ukraine
*
†Email address for correspondence: atimokha@gmail.com
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Abstract

A machine learning of the unknown a priori viscous damping, incorporated into the single-dominant nonlinear ‘inviscid’ modal theory by Faltinsen et al. (J. Fluid Mech., vol. 407, 2000, pp. 201–234) on resonant sloshing (the forcing frequency close to the lowest natural sloshing frequency) in a clean (no internal structures) rigid rectangular tank, is proposed. The learning procedure requires a set of measured phase lags between the harmonic horizontal tank excitation and the steady-state resonant wave response. A good consistency with experiments by Bäuerlein & Avila (J. Fluid Mech., vol. 925, 2021, A22) on the liquid-mass centre motions is shown. The latter confirms that the free-surface nonlinearity (causing an energy flow from the primary-excited to higher natural sloshing modes) and viscous damping of the higher natural sloshing modes matter, as well as that the damping rates can depend on the steady-state wave amplitude.

JFM classification

Interfacial Flows (free surface): Interfacial Flows (free surface)
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 965 , 25 June 2023 , R1
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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