Vortex ripples are very common features when waves 'feel' the frictional influence of a sandy bed. They are important in understanding the processes of sediment transport and entrainment. Vortices form over the lee slopes of ripples each wave half-cycle and subsequently get ejected into the flow completely dominating the hydrodynamics close to the bed. This hydrodynamical modelling study aims to look at the process in detail, but also to produce results over parameter ranges of physical interest to allow a more general interpretation of the results by the wider sediment transport community.
To this end two discrete vortex models, which are suited to modelling vortex-shedding processes, have been developed: These are a simple irrotational model, which contains no diffusion of vorticity, and a cloud-in-cell model with diffusion represented by random walk.
Both models have been shown capable of producing the vortex strengths, positions and bed stresses seen in laboratory experiments. Also the cloud-in-cell model is able to produce the expected breakdown of the vortices into more homogenous turbulence as the orbital excursion of the wave increases. For lower orbital excursions the bed friction shows quite different behaviour from that predicted by flat-bed approaches.
Mean circulation cells develop above each flank of the ripple. These are the time-averaged signatures of the eddy shedding process which drive flow towards the ripple crest close to the bed. These cells have been related to the potential mechanisms governing stable asymmetric ripple shapes and also the direction and strength of horizontally-averaged velocity residuals.
The convective eddy viscosity approach, based on relating the time varying horizontally averaged shear stress and horizontal velocity, has been demonstrated to be a useful means of describing the flow in a one-dimensional sense. The approach has also been extended to include weak wave asymmetry.