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The results of Direct Numerical Simulations of the oscillatory flow over a cohesionless bed of spherical particles, mimicking sediment grains, are described. The flow around the sediment particles is explicitly computed by using the immersed boundary method, which allows the force and torque acting on the particles to be evaluated along with their dynamics. Different values of the Reynolds number and different values of the ratio between the grain size and the thickness of the boundary layer are considered such that the results are useful to quantify the sand transport generated by sea waves in the region offshore of the breaker line. Therefore, the results are used to test the capability of empirical sediment transport formulae to predict the sediment transport rate during the oscillatory cycle., Comment: 25 pages, 19 figures, Accepted for publication in "International Journal of Multiphase Flow"

The flow within an oscillatory boundary layer, which approximates the flow generated by propagating sea waves of small amplitude close to the bottom, is simulated numerically by integrating Navier-Stokes and continuity equations. The bottom is made up of spherical particles, free to move, which mimic sediment grains. The approach allows to fully-resolve the flow around the particles and to evaluate the forces and torques that the fluid exerts on their surface. Then, the dynamics of sediments is explicitly computed by means of Newton-Euler equations. For the smallest value of the flow Reynolds number presently simulated, the flow regime turns out to fall in the intermittently turbulent regime such that turbulence appears when the free stream velocity is close to its largest values but the flow recovers a laminar like behaviour during the remaining phases of the cycle. For the largest value of the Reynolds number turbulence is significant almost during the whole flow cycle. The evaluation of the sediment transport rate allows to estimate the reliability of the empirical predictors commonly used to estimate the amount of sediments transported by the sea waves. For large values of the Shields parameter, the sediment flow rate during the accelerating phases does not differ from that observed during the decelerating phases. However, for relatively small values of the Shields parameter, the amount of moving particles depends not only on the bottom shear stress but also on flow acceleration. Moreover, the numerical results provide information on the role that turbulent eddies have on sediment dynamics., Comment: 33 pages, 24 figures, Pre-print of manuscript accepted by Journal of Fluid Mechanics