Euler–Lagrange model for scour in front of vertical breakwater

► We develop an Euler–Lagrange two-phase model to study scour in front of a vertical breakwater. ► We model the frequent interparticle collision of sediments with a spring and dashpot system. ► During scour, transport rate decrease till the bed reaches to a semi-equilibrium shape. ► Bed sediments are transported in the hyper-concentrated, saltation and suspension mode. ► Vertical momentum transfers from steady streaming cells induce sediment motion in lower layer. A two-dimensional Euler–Lagrange model was developed to study the scour in front of a vertical breakwater. The fluid phase was described via the Reynolds Averaged Navier–Stokes equations in conjunction with the k– ɛ turbulence closure model. The sediment phase was treated as an assembly of discrete sand grains and the scour was introduced as the motion of a granular media from the Lagrangian point of view. Motion of the sand grains was traced with a numerical code based on the so-called MBS model, in which the frequent interparticle collision described with a spring and dashpot system. Comparison between the numerical result and experimental measurement confirms that the numerical model successfully predicts the scour profile and steady streaming field. The results reveal that during the scour process sediment transport rate decrease and the scour/deposition pattern reaches to a semi-equilibrium shape. The sand grains were transported in three different modes; namely the hyper-concentrated flow, saltation and suspension mode. The concept of vertical momentum transfer is exploited to describe features of concurrently present of these different modes. It is evident that the vertical momentum transfers between upper recirculating cells of steady streaming moves the bed sediment into the upper layer; whereas the vertical motion of particles is not significantly active in the hyper-concentrated layer and the sediment grains momentum is preserved.