Direct numerical simulations of flow over two-dimensional and three-dimensional ripples and implication to sediment transport: Steady flow

A well resolved and highly accurate direct numerical simulation (DNS) solver has been developed to understand the implication of hydrodynamics to sediment transport. In the first part of the study we focus on steady flow over two-dimensional and three-dimensional ripples at two Reynolds numbers Reτ = 180 and 400 (defined by channel half-height and wall-friction velocity) in a channel geometry. The DNS scheme is based on a fourth-order vertical velocity and second-order vertical vorticity formulation, which resolves the difficulties in pressure boundary condition encountered when solving the Navier–Stokes equations. The complex boundary introduced due to the ripples has been imposed in the Cartesian domain using an elegant immersed boundary method. Detailed hydrodynamic analysis has revealed turbulence statistics (in particular, the higher order) and henceforth, the flow structures are sensitive — whether the ripples are two-dimensional or three-dimensional. The importance of fluctuating component of the bottom stress in addition to its mean component; and its significance to sediment transport and ripple migration speed have been investigated.