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

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.