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

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.