Spatio-Temporal Correlations of Hydrodynamic Forces on Particles in an Oscillatory Wall-Bounded Flow Environment

Particle-resolved direct numerical simulations are performed using fictitious domain approach [1] to investigate the effect 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 [2]. Turbulent flows at Reynolds numbers, Re_δ = 200 and 400 (based on the Stokes-layer thickness δ) are studied. The unsteady nature of hydrodynamic forces on particles and their cross-correlations with measurable flow variables are investigated. Temporal correlations showed drag and 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-related quantities showed that the lift force 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. On the other hand, the 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 showed that the near-bed velocity and pressure fluctuations fit poorly with Gaussian distributions. Instead, a fourth order Gram-Charlier distribution model is proposed that may have consequences on the Gaussian descriptions of sediment pick-up functions typically used in quantification of turbulent transport of sediment particles.