On the morphodynamics of wave-generated ripples

Abstract

Wave-generated ripples are subaqueous topographic patterns often present on the seafloor. The presence of these patterns increases the seabed roughness, disturbs the near-bottom velocity distribution and encourages the near-bed sediment suspension. The appearance and dimensions of ripples are also important means in reconstructing the ancient hydrological conditions. Under regular waves, ripples evolve towards an equilibrium configuration characterized by a preferred wavelength and height. In natural environments where the wave forcing is always changing, ripples do not adjust immediately to the equilibrium configuration. As a result, two processes of ripple seabed patterns become relevant. Firstly, hysteresis, the time required for ripples to adjust to changes in wave forcing, as they reach a new equilibrium configuration. Secondly, defects, bedform irregularities in ripple crestlines, the presence and propagation of which also affects equilibrium configuration. Both processes are critical to understand and predict ripple evolution, but only a few studies have addressed their role in detail. We carried out laboratory experiments and high-resolution Direct Numerical Simulations (DNS) to study ripple hysteresis and defect dynamics systematically. The hysteresis is proportional to the change in wave orbital diameter, and the coefficient of proportionality differs between decreasing and increasing wave forcing. When the Shields parameter is lower than a certain threshold, there is no change in ripple geometry (or changes extremely slowly), but sediment transport is still active. Laboratory experiments confirm that defects in pre-existing bedforms affect ripple hysteresis. The dependence of hysteresis on defect density implies that a larger density of defects results in faster ripple adjustment, confirming previous theoretical and numerical model results. Additionally, defects are likely to affect the final equilibrium ripple wavelength. Laboratory observations are compared with a three-dimensional DNS model, that uses the same bedform geometry and forcing conditions as in the laboratory experiments. We find that flow characteristics (e.g., velocity and vortex) in the vertical plane are comparable between laboratory experiments and numerical simulations. Despite the use of regular ripple geometry and monochromatic flow motions, we observe three-dimensional flow structures in the spanwise direction, in both laboratory experiments and numerical simulations. The “rib” pattern, developing perpendicular to the ripple crest, is also observed in the numerical simulations. The three-dimensional vortex dynamics are quantified using the concept of vortex strength. The results, consistent between laboratory experiments and numerical simulations, add to the debate on ripple-generated turbulence and show the presence of four peaks in the vortex strength throughout an oscillatory cycle with each peak occurring every π/2 phase. Finally, numerical simulations on hydrodynamics over bedforms with defects (termination/bifurcation) display a three-dimensional spatial distribution of the velocity field, vortex structures, and shear stress. Defects affect the maximum velocity, vortex strength and vortex center position over the neighboring ripples. The spanwise variation of the vortex dynamics over the neighboring ripples of a defect are related to the geometry of the defect. The spanwise varying vortex structures result in heterogeneous distribution of bed shear stress in the spanwise direction that extends over straight crestlines surrounding the defects, which has evident implications for ripple morphodynamics.