The dynamics of violent-sloshing flows: a numerical study on the genesis and lifespan of turbulent eddies

This study investigates the genesis and temporal evolution of turbulent eddies in violent-sloshing flows using a fully meshless computational framework. A quasi-Lagrangian delta δ $\delta$ -large-eddy simulation–smoothed particle hydrodynamics formulation is employed to solve the weakly compressible Navier–Stokes equations, together with a novel methodology to quantify slosh-induced energy dissipation, where delta δ $\delta$ denotes the density-diffusion operator introduced in the delta δ $\delta$ -SPH formulation. Under violent periodic forcing, the flow exhibits a strongly nonlinear free-surface dynamics, characterised by recurrent wave breaking and energetic impacts against the tank walls. By decomposing the total viscous dissipation into enstrophy-related and deformation-related contributions, we find that the enstrophy fraction remains nearly constant, at around 30 percent sign 30 % $30\,\%$ , across the investigated regimes. Moreover, in the absence of surface tension, the enstrophy-related dissipation does not converge under grid refinement; the inclusion of surface tension regularises this behaviour and promotes a shift of the vortex population towards larger coherent structures. High-resolution two-dimensional simulations, spanning a wide range of spatial resolutions, are complemented by fully three-dimensional simulations and by reduced-width three-dimensional configurations, in which the spanwise direction is fully resolved over a limited extent. This combined analysis shows that, for this class of bounded violent free-surface flows, global loads and energy dissipation are primarily governed by free-surface fragmentation and reconnection, rather than by fully three-dimensional turbulent cascade mechanisms. As a result, two-dimensional simulations provide an accurate description of the dynamics controlling the integral quantities of interest. These findings offer new physical insight into the coupling between free-surface fragmentation, vortex dynamics and dissipation mechanisms in violent sloshing, and establish a reference framework for future studies of turbulence generation in confined free-surface flows.