Wave-Height Dissipation and Undertow of Spilling Breakers over Beaches of Varying Slopes

Abstract

Spilling breaking over beach profiles of varying slopes was studied numerically using an immersed-boundary/level-set method where both the bed profile and the free surface were immersed in a Cartesian grid. The combined water/air flow was governed by the incompressible Navier-Stokes equations and a Smagorinsky model for the subgrid scale stresses. The numerical model was validated by comparison to experimental data of waves breaking over a constant-slope beach. The examined beach profiles consisted of an outer region where the slope was constant and an inner region, which included the breaking point and the surf zone, where the slope was varying and the bed shape was concave. Eight cases were examined, and the main results are: (a) the decay coefficient of the wave-energy flux in the surf zone is correlated to the beach slope in the outer region; (b) the vorticity generation at the free surface and its distribution in the surf zone, as well as the intrawave velocity, the streaming boundary layer, and the undertow in the surf zone, are affected significantly by the varying slope in the inner region only for the cases of milder beach slope in the outer region; and (c) the effect of the normalized eddy-viscosity of the mean flow in the surf zone on the undertow profile is of the same order to the effect of the normalized net momentum gradient.