Particle-resolved direct numerical simulations (DNS) are performed to investigate the behaviour of an oscillatory flow field over a rough bed, corresponding to the experimental set-up of Keiller & Sleath (J. Fluid Mech., vol. 73 (04), 1976, pp. 673-691) for transitional and turbulent flows over a range of Reynolds numbers (95-400) based on the Stokes-layer thickness. It is shown that the roughness modulates the near-bed turbulence, produces streamwise horseshoe structures which then undergo distortion and breaking, and therefore reduces the large-scale anisotropy. A fully developed equilibrium turbulence is observed in the central part of the oscillation cycle, with two-component turbulence in the near-bed region and cigar-shaped turbulence in the outer region. A double averaging of the flow field reveals spatial inhomogeneities at the roughness scale and alternate paths of energy transport in the turbulent kinetic energy (TKE) budget. Contrary to the unidirectional, steady flow over rough beds, bed-induced production terms are important and comparable to the shear production term. It is shown that the near-bed velocity and pressure fluctuations are non-Gaussian, a result of critical importance for the modelling of incipient motion of sediment grains.

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A numerical investigation of unsteady hydrodynamic forces on the particle bed in an oscillatory flow environment is performed by means of direct numerical simulations. Statistical descriptions of drag and lift forces for two particle sizes of diameter 372 and 125 in wall units in a very rough turbulent flow regime are reported. Characterization of unsteady forces in terms of spatial distribution, temporal autocorrelation, force spectrum as well as cross-correlations with measurable flow variables is carried out. Based on the concept of impulse, intermittency in the drag and lift forces is also investigated. Temporal correlations show drag and lift to be positively correlated with a time delay that is approximately equal to the Taylor micro-scale related to the drag/lift fluctuations. The force spectra for drag and lift reveal roughly two scaling regions, $-11/3$ and $-7/3$; the former typically represents turbulence–mean-shear interactions, whereas the latter indicates dominance of turbulence–turbulence interactions. Particle forces are strongly correlated with streamwise velocity and pressure fluctuations in the near-bed region for both flow cases. In comparison to the large-diameter particle case, the spatial extent of these correlations is 2–3 times larger in homogeneous directions for the small sized particle, a feature that is reminiscent of longer near-bed structures. For both large- and small-particle cases, it is shown that the distributions of drag (lift) fluctuations, in particular, peakedness and long tails, match remarkably well with fourth-order Gram–Charlier distributions of velocity (pressure) fluctuations. Furthermore, it is demonstrated that the intermittency is larger in the case of the lift force compared to that for the drag in both flow cases. Distributions of impulse events are heavily and positively skewed and are well described by a generalized extreme value distribution.

Lack of accurate criteria for onset of incipient motion and sediment pickup function remain two of the biggest hurdles in developing better predictive models for sediment transport. To study pickup and transport of sediment, it is necessary to have a detailed knowledge of the small amplitude oscillatory flow over the sediment layer near the sea bed. Fully resolved direct numerical simulations are performed using fictitious domain approach (Apte & Finn, 2012) to investigate the effect of a sinusoidally oscillating flow field over a rough wall made of regular hexagonal pack of spherical particles. The flow arrangement is similar to the experimental data of Keiller & Sleath (1976). Transitional and turbulent flows at Re d = 95, 150, 200 (based on the Stokes layer thickness, d =) are studied. Turbulent flow is characterized in terms of coherent vortex structures, Reynolds stress variation and PDF distributions. The nature of unsteady hydrodynamic lift forces on sediment grains and their correlation to sweep and burst events is also reported. The dynamics of the oscillatory flow over the sediment bed is used to understand the mechanism of sediment pickup .