In the present paper, the sloshing flow in a cuboid tank forced to oscillate horizontally is investigated with both experimental and numerical approaches. The filling depth chosen is $h/L=0.35$ (with h the water depth and L the tank height), which is close to the critical depth. According to Tadjbakhsh & Keller (J. Fluid Mech., vol. 8, issue 3, 1960, pp. 442–451), as the depth passes through this critical value the response of the resonant sloshing dynamics changes from ‘hard spring’ to ‘soft spring’. The experimental tank has a thickness of $0.1L$ , reducing three-dimensional effects. High-resolution digital camera and capacitance wave probes are used for time recording of the surface elevation. By varying the oscillation period and the amplitude of the motion imposed on the tank, different scenarios are identified in terms of free-surface evolution. Periodic and quasi-periodic regimes are found in most of the frequencies analysed but, among these, sub-harmonic regimes are also identified. Chaotic energetic regimes are found with motions of greater amplitude. Typical tools of dynamical systems, such as Fourier spectra and phase maps, are used for the regime identification, while the Hilbert–Huang transform is used for further insight into doubling-frequency and tripling-period bifurcations. For the numerical investigation, an advanced and well-established smoothed particle hydrodynamics method is used to aid the understanding of the physical phenomena involved and to extend the range of frequencies investigated experimentally.

We propose a simple, robust and efficient sloshing model that accounts for breaking phenomena evolving in rectangular tanks and in shallow-water conditions. The model has been obtained by applying Fourier analysis to Boussinesq-type equations and using an approximate analytic solution for the vorticity generated by wave breaking. The toe of the breaker and the intensity of the vorticity injected at the free surface are computed on the basis of literature results for coastal-type breakers. A first experimental campaign has been used to calibrate the turbulent viscosity of the sloshing model, while a second campaign has been run as final validation. The overall good agreement between the numerical outputs and the experimental data confirms the reliability and robustness of the proposed model.

This article presents the data-driven equation-free modeling of the dynamics of a hexafloat floating offshore wind turbine based on the application of dynamic mode decomposition (DMD). The DMD has here been used (i) to extract knowledge from the dynamic system through its modal analysis, (ii) for short-term forecasting (nowcasting) from the knowledge of the immediate past of the system state, and (iii) for system identification and reduced-order modeling. All the analyses are performed on experimental data collected from an operating prototype. The nowcasting method for motions, accelerations, and forces acting on the floating system applies Hankel-DMD, a methodological extension that includes time-delayed copies of the states in an augmented state vector. The system identification task is performed by using Hankel-DMD with a control (Hankel-DMDc), which models the system as externally forced. The influence of the main hyperparameters of the methods is investigated with a full factorial analysis using error metrics analyzing complementary aspects of the prediction. A Bayesian extension of the Hankel-DMD and Hankel-DMDc is introduced by considering the hyperparameters as stochastic variables, enriching the predictions with uncertainty quantification. The results show the capability of the approaches for data-lean nowcasting and system identification, with computational costs being compatible with real-time applications. Accurate predictions are obtained up to 4 wave encounters for nowcasting and 20 wave encounters for system identification, suggesting the potential of the methods for real-time continuous-learning digital twinning and surrogate data-driven reduced-order modeling.