Learning the single-dominant modal system on resonant sloshing in a rectangular tank
Keywords:sloshing, machine learning, damping
A machine learning technique is proposed to derive the damping rate functions in the co-called single-dominant modal system describing the resonant liquid sloshing in a rectangular tank performing harmonic longitudinal motions. Its implementation is demonstrated for the steady-state (periodic) resonance waves when the modal system admits an analytical asymptotic solution depending on the introduced damping rate functions. Recent experiments by Bäuerlein & Avila (2021) are employed to show that the viscous damping of the higher natural sloshing modes matters, and the damping functions depend on the wave amplitude.
Faltinsen, O. M. & Timokha, A. N. (2009). Sloshing. Cambridge University Press.
Keulegan, G. H. (1959). Energy dissipation in standing waves in rectangular basins. J. Fluid Mech., 6, pp. 33-50. https://doi.org/10.1017/S0022112059000489
Bäuerlein, B. & Avila, K. (2021). Phase lag predicts nonlinear response maxima in liquid-sloshing experiments. J. Fluid Mech., 925, A22, pp. 1-29.https://doi.org/10.1017/jfm.2021.576
Hermann, M. & Timokha, A. (2005). Modal modelling of the nonlinear sloshing in a circular tank I: A singledominant model. Math. Models Methods Appl. Sci., 15, No 9, pp. 1431-1458. https://doi.org/10.1142/S0218202505000777
Hermann, M. & Timokha, A. (2008). Modal modelling of the nonlinear sloshing in a circular tank II: Secondary resonance. Math. Models Methods Appl. Sci., 18, No 11, pp. 1845-1867. https://doi.org/10.1142/S0218202508003212
Ahmed, S. E., Pawar, S., San, O., Rasheed, A., Iliescu, T. & Noack, B. R. (2021). On closures for reduced order models — A spectrum of first-principle to machine-learned avenues. Phys. Fluids, 33, Art. 091301, 32 p. https://doi.org/10.1063/5.0061577
Raynovskyy, I. A. & Timokha, A. N. (2018). Damped steady-state resonant sloshing in a circular container. Fluid Dyn. Res., 50, Art. 045502, 20 p. https://doi.org/10.1088/1873-7005/aabe0e
Faltinsen, O. M. & Timokha, A. N. (2001). Adaptive multimodal approach to nonlinear sloshing in a rectangular tank. J. Fluid Mech., 432, pp. 167-200. https://doi.org/10.1017/S0022112000003311
How to Cite
Copyright (c) 2022 Reports of the National Academy of Sciences of Ukraine
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.