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<p>We generalize recent results of the authors [A.&#xa0;Miliaev and A.&#xa0;Timokha, <i>J. Fluid Mech.,</i> <b>965</b>, No.&#xa0;R1, 1–11 (2023); DOI: doi.org/10.1017/jfm.2023.372] on machine learning of multidimensional modal systems derived to describe nonlinear sloshing in rigid tanks exposed to resonant excitations. The multimodal systems neglect viscous damping but the procedure of learning pursues incorporating <i>a priori</i> unknown damping terms into these systems. The main focus is made on steady-state swirling wave mode in an upright circular tank which moves longitudinally according to a harmonic law with an excitation frequency close to the lowest sloshing eigenfrequency. The nonlinear Narimanov–Moiseev-type modal system is used with a set of phenomenological linear and nonlinear damping quantities whose coefficients are a subject of the learning procedure. The procedure requires semianalytic periodic (steady-state) solutions of the Narimanov–Moiseev-type system constructed in the paper. Based on these solutions and the loss (cost) function that describes the “distance” between the measured and theoretical phase lags for the swirling wave mode, the proposed learning procedure is tested by using the experimental data from [A.&#xa0;Royon-Lebeaud, E.&#xa0;J.&#xa0;Hopfinger, and A.&#xa0;Cartellier, <i>J. Fluid Mech.,</i> <b>577</b>, 467–494 (2007); DOI: doi.org/10.1017/S0022112007004764].</p>

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DAMPING OF THE SWIRLING WAVE MODE

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • Anton Miliaiev,
  • Alexander Timokha

摘要

We generalize recent results of the authors [A. Miliaev and A. Timokha, J. Fluid Mech., 965, No. R1, 1–11 (2023); DOI: doi.org/10.1017/jfm.2023.372] on machine learning of multidimensional modal systems derived to describe nonlinear sloshing in rigid tanks exposed to resonant excitations. The multimodal systems neglect viscous damping but the procedure of learning pursues incorporating a priori unknown damping terms into these systems. The main focus is made on steady-state swirling wave mode in an upright circular tank which moves longitudinally according to a harmonic law with an excitation frequency close to the lowest sloshing eigenfrequency. The nonlinear Narimanov–Moiseev-type modal system is used with a set of phenomenological linear and nonlinear damping quantities whose coefficients are a subject of the learning procedure. The procedure requires semianalytic periodic (steady-state) solutions of the Narimanov–Moiseev-type system constructed in the paper. Based on these solutions and the loss (cost) function that describes the “distance” between the measured and theoretical phase lags for the swirling wave mode, the proposed learning procedure is tested by using the experimental data from [A. Royon-Lebeaud, E. J. Hopfinger, and A. Cartellier, J. Fluid Mech., 577, 467–494 (2007); DOI: doi.org/10.1017/S0022112007004764].