A shallow-water sloshing model for wave breaking in rectangular tanks

Abstract

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.

Wetting and drying of two-layer shallow-water flow in a moving vessel via semi-Lagrangian simulation

“…To aid with the stability of the numerical scheme, we adopt a variation on the weakly compressible form of the mass conservation equation used in the works of [39,40,37,41].…”

“…The parameter δ is included to smooth over the dispersive oscillations which occur on the hydraulic jumps during the solution procedure [39,42]. The weakly compressible form of the mass conservation equations has been implemented and validated in the Smoothed Particle Hydrodynamics works of [39,40,37,41]. In these papers δ represents a numerical diffusion with δ = c∆xξ where ∆x is the grid step size in the x direction, c is the flow speed and ξ is a non-dimensional constant.…”

Global force and moment in rectangular tanks through a modal method for wave sloshing

“…The above schemes are both limited to the modelling of non-breaking waves and, consequently, can only describe the evolution of rather weak sloshing phenomena. This issue is overcome in the work of Antuono et al (2014) where a modal scheme based on the depth-averaged equations of Antuono and Brocchini (2013) is implemented along with a semi-analytical solution for the vorticity injected at the free-surface during wave breaking. The above model provides a fairly good match with experimental measurements for moderate wave breaking.…”

“…In this context, the aim of the present contribution is the derivation of proper formulas for global forces and momentum and for the consequent evaluation of the loads on the tank, this being a missing aspect in the work of Antuono et al (2014). This is a requisite for enabling a successful coupling between an efficient sloshing model and an external flow solver for ship seakeeping and stability (Rognebakke and Faltinsen 2003).…”

“…To extend the use of the proposed formulas for global forces and momentum to practical naval problems, we also broaden the applicability of the modal scheme of Antuono et al (2014) to more violent sloshing phenomena. This latter point is achieved by introducing a diffusive term in the continuity equation of the model, following the approach described in Molteni and Colagrossi (2009); Antuono et al (2010Antuono et al ( , 2012b in the framework of the Smoothed Particle Hydrodynamics (SPH).…”