Numerical simulations of the two-dimensional, incompressible, viscous, free-surface flow, developing by the propagation of water waves over a rippled bed, and the corresponding bed morphology evolution are performed. The simulations are based on the numerical solution of the unsteady Navier-Stokes equations subject to the fully-nonlinear, free-surface boundary conditions and the appropriate bottom, inflow and outflow boundary conditions, and the morphology evolution equations driven by bed load transport. Results indicate that, close to the bottom, flow separation occurs at the ripple crests, which leads to the generation of alternating circulation regions. The amplitude of the wall shear stress distribution over the ripples increases substantially in the rippled region, exceeding the critical magnitude of incipient sediment motion and resulting into the initiation of bed load sediment transport. For given sand grain size, a unique dynamic friction angle value exists, which achieves equilibrium of the bed profile independently of the initial ripple steepness.