Turbulent flows over rough surfaces are encountered in many engineering and geophysical applications. Flows of this nature, due to their increasing technological interests, have been a subject of rigorous investigation in recent years. Of the particular interest to the oceanographic community is the study of turbulent oscillatory flow over rough surfaces, representative of sediment-bed in a coastal environment. In order to study sediment transport under coastal conditions, particularly onset of sediment erosion, detailed knowledge of particle-bed turbulence interactions and in turn, their influence on unsteady destabilizing particle forces is necessary.
In this study, direct numerical simulations are performed using fictitious domain approach (Apte & Finn 2013) to investigate the effects of an oscillatory flow field over a rough wall made up of a regular hexagonal pack of fixed spherical particles, in a setup similar to the experimental configuration of (Keiller & Sleath 1976). Transitional and turbulent flows in the range of particle Reynolds numbers ReD = 660 – 4250 are explored. Characterizations of the resulting flow fields are performed in terms of the Reynolds stress variation, turbulent kinetic-energy budget, near-bed flow structures, cross-correlations between forces upon particles and flow variables, along with statistical distributions of near-bed velocities and pressure fluctuations. Turbulent flow analyses reveal the presence of fully developed equilibrium turbulence in the central part of the oscillation cycle, with the near-bed region of two-component turbulence and outer region of cigar-shaped turbulence. The presence of particles was seen to modulate the near-bed turbulence structure by redistribution of the energy from stream-wise fluctuations to wall-normal, leading to overall reduction in near-wall anisotropy.
The unsteady forces on particles and their cross-correlations with flow variables are also studied. Temporal correlations showed drag/lift to be positively correlated with a phase difference, which is approximately equal to the Taylor micro-scale related to drag/lift correlations. Spatio-temporal correlations between the flow field and particle forces showed that the lift is well correlated with the streamwise velocity fluctuations up to distances of the same order as the particle diameter, beyond which the cross correlation decays considerably. Pressure fluctuations are correlated and anti-correlated with the lift force in the front and aft regions of the particle, respectively, as a result of wake effects. Further statistical analyses revealed that the near-bed velocity and pressure fluctuations fit poorly with Gaussian distributions. Instead, a fourth order Gram-Charlier distribution model is proposed.