Numerical analysis of nonlinear shoaling characteristics over surf zone using SPH and Lagrangian Dynamic Smagorinsky model

Nonlinear shoaling characteristics over surf zone are numerically investigated based on spatially averaged Navier-Stokes equation. We also test the validity of gradient model for turbulent stresses due to wave breaking using the data acquainted during SUPERTANK LABORATORY DATA COLLECTION PROJECT (Krauss et al., 1992). It turns out that the characteristics length scale of breaking induced current is not negligible, which firmly stands against ever popular gradient model - k - ε model , but favors Large Eddy Simulation (LES) with finer grid. Based on these observations, we model the residual stress of spatially averaged Navier-Stokes equation after Lagrangian Dynamic Smagorinsky (Meneveau et al.,1996). We numerically integrate newly proposed wave equations using SPH with Gaussian kernel function. Severely deformed water surface profile, free falling water particle, queuing splash after landing of water particle on the free surface and wave finger due to structured vortex on rear side of wave crest (Narayanaswamy and Dalrymple, 2002) are successfully duplicated in the numerical simulation of wave propagation over uniform slope beach, which have been, regarded very difficult features to mimic in the computational fluid mechanics so far.