The objectives of this study are to obtain the turbulence characteristics produced by an oscillatory flow over three-dimensional (3-D) vortex ripples and the comparison of the corresponding results to the ones over two-dimensional (2-D) ripples. Four cases of sinusoidal ripples were examined: a 2-D case of constant ripple length Lr, and three 3-D cases where the length of the two middle ripples varies sinusoidally in the spanwise direction in the ranges of ±10%Lr, ±20%Lr and ±30%Lr. The ripple height was the same for all cases. The behavior of the turbulent kinetic energy and the phase-averaged streamlines are presented.


Sand ripples arise in subaqueous environments as the result of the complex interaction between turbulent flows and mobile sand beds. They occur across a wide range of spatial scales and evolve at temporal scales much slower than the integral scale of the transporting turbulent flow (Sotiropoulos and Khosronejad, 2016). 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 3-D rippled bed is shown in Fig. 1.

The streamwise velocity, uo, of a purely oscillatory external flow induced close to the rippled sand bed by the propagation of water waves is


where Uo = maximum velocity; ω = 2Φ/T = radial frequency; T = oscillation period; and t = time. The characteristic velocity scale is Uo and the characteristic length scale is the amplitude of the orbital motion αo = Uo/w; therefore, the corresponding Reynolds number is


where v = water kinematic viscosity.

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



where Lr is the ripple length, ao is the oscillatory flow amplitude and hris 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).

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