The objective of this study is to simulate the transition to turbulence of the oscillatory flow over three-dimensional (3-D) vortex ripples by means of an advanced Navier-Stokes solver and compare the behavior of the results with respect to the corresponding ones for twodimensional (2-D) ripples. Two cases of sinusoidal ripples were examined: a 2-D case of constant ripple length Lr, and a 3-D case of ripple length varying smoothly between Lr and 0.6Lr in the spanwise direction. The ripple height was the same for both cases. Results are presented for the behavior of the vorticity field and the bed shear stress.
Oscillatory flows over 3-D ripples are of practical as well as scientific interest because of their relevance to beach processes (Hara & Mei, 1990). Surface waves in the coastal zone induce oscillatory flow motions in the vicinity of the seabed. These motions interact with the bottom sediment and modify the bed shape by generating coherent structures, which are generally known as sand ripples. Sand ripples have usually a symmetric shape with respect to the crest due to the oscillatory nature of the boundary layer flow induced by the propagation of waves. A typical 2-D ripple formation is shown in Fig. 1
Ripple dimensions are associated with the parameters of the oscillatory flow that generated them. According to field and experimental data (Nielsen, 1981; Wiberg and Harris, 1994), it has been reported that for the relevant ripple length and ripple steepness, the following expressions are valid
Lr/ao ≤ 2.2 (1)
hr/Lr ≤ 0.2 (2)
where Lr is the ripple length, ao is the oscillatory flow amplitude and hr is the ripple height. The presence of a rippled bed in oscillatory flows modifies the development of the wave boundary layer and the propagation of water waves in comparison to a flat bed because of flow separation and vortex shedding at the ripple crest. In coastal engineering applications, the influence of these flow phenomena on parameters associated with sediment transport close to the bed, i.e., wall stress, bed resistance, and time-averaged velocity, is of particular interest (Dimas and Kolokythas, 2011).