In the present study, the two-dimensional, incompressible, viscous, free-surface flow, developing by the propagation of nonlinear breaking waves over a constant slope, rigid bed is numerically simulated. The main objective is to investigate in depth, the process of spilling wave breaking and the characteristics of the developing undertow current. The comparison of present numerical results to corresponding experimental results of other researchers, indicate that the numerical model predicts adequately the wave breaking parameters - breaking height and depth - and the wave dissipation in the surf zone.
The continuous interaction between water waves propagating in the coastal zone and the sea bed is responsible for the generation of significant coastal processes, such as wave breaking, wave induced currents, sediment transport, etc. Wave breaking takes place when the wave height and steepness become very large as the water depth becomes shallower. It can be divided in three important categories depending on the slope of the sea bed, i.e., spilling, plunging and surging breaking, appearing at mild, steep and very steep bed slopes, respectively. For the case of spilling breaking, a vortex structure, usually called "surface roller", is formed under the collapsing wavefront just after breaking. Coupled with wave breaking is the development of an induced cross-shore current in the surf zone, known as the undertow current. The undertow current is associated to the mean shear stress field developing due to breaking in order to balance the pressure gradient induced by wave set-up and momentum fluxes due to wave dissipation in the surf zone. The direction of this current is offshore and opposite to the shoreward water discharge taking place close to the free surface, due to the surface roller developing within the breaking wave crest, and ensures that the total cross-shore water flux is zero.