Detailed knowledge of the dynamics of vortex structures in an oscillatory boundary layer is essential for the correct modelling of transport processes in many engineering problems and, in particular, of the pick-up and transport of sediments at the bottom of sea waves. In the present contribution, the formation of turbulent spots in an oscillatory boundary layer is investigated by means of direct numerical simulations. Two of the laboratory experiments of Carstensen, Sumer and Fredsøe are reproduced and, after a comparison of the numerical results with laboratory measurements, a detailed and quantitative characterization of the turbulent spots is also given on the basis of further simulations. The speeds of the head (u 1H ) and tail (u 1T ) of the spots are found to scale with the instantaneous free stream velocity U e and to be similar to those observed in steady boundary layers. The ratios u 1H /U e and u 1T /U e seem to increase with the Reynolds number (R δ ) while the streamwise expansion rate of the spots appears to be independent of R δ .

The dynamics of spherical particles resting on a horizontal wall and set into motion by an oscillatory flow is investigated by means of a fully coupled model. Both a smooth wall and a rough wall, the latter being composed of resting particles with a random arrangement and with the same diameter as the moving particles, are considered. The fluid and particle motions are determined by means of direct numerical simulations of Navier-Stokes equations and Newton's laws, respectively. The immersed boundary approach is used to force the no-slip condition on the surface of the particles. In particular, the process of formation of transverse sediment chains, within the boundary layer but orthogonal to the direction of fluid oscillations, is simulated in parameter ranges matching those of laboratory experiments investigating rolling-grain ripple formation. The numerical results agree with the experimental observations and show that the transverse sediment chains are generated by steady recirculating cells, generated by the interaction of the fluid and particle oscillations

Direct numerical simulation of open-channel flow over a bed of spheres arranged in a regular pattern has been carried out at bulk Reynolds number and roughness Reynolds number (based on sphere diameter) of approximately 6900 and 120, respectively, for which the flow regime is fully-rough. The open-channel height was approximately 5.5 times the diameter of the spheres. Extending the results obtained by Chan-Braun et al. (J. Fluid Mech., vol. 684, 2011, 441) for an open-channel flow in the transitionally-rough regime, the present purpose is to show how the flow structure changes as the fully-rough regime is attained and, for the first time, to enable a direct comparison with experimental observations. Different statistical tools were used to investigate the flow field in the roughness sublayer and in the logarithmic region.The results indicate that, in the vicinity of the roughness elements, the average flow field is affected both by Reynolds number effects and by the geometrical features of the roughness, while at larger wall-distances this is not the case, and roughness concepts can be applied. Thus, the roughness function is computed which in the present set-up can be expected to depend on the relative submergence.The flow-roughness interaction occurs mostly in the region above the virtual origin of the velocity profile, and the effect of form-induced velocity fluctuations is maximum at the level of sphere crests. In particular, the root mean square of fluctuations about the streamwise component of the average velocity field reflects the geometry of the spheres in the roughness sublayer and attains a maximum value just above the roughness elements. The latter is significantly weakened and shifted towards larger wall-distances as compared to the transitionally-rough regime or the case of a smooth wall. The spanwise length scale of turbulent velocity fluctuations in the vicinity of the sphere crests shows the same dependence on the distance from the wall as that observed over a smooth wall, and both vary with Reynolds number in a similar fashion. Moreover, the hydrodynamic force and torque experienced by the roughness elements are investigated and the footprint left by vortex structures on the stress acting on the sphere surface is observed. Finally, the possibility either to adopt an analogy between the hydrodynamic forces associated with the interaction of turbulent structures with a flat smooth wall or with the surface of the spheres is also discussed, distinguishing the skin-friction from the form-drag contributions both in the transitionally-rough and in the fully-rough regimes.

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. *