A review of open channel turbulence, focusing especially on certain features stemming from the presence of the free surface and the bed of a river. Part one presents the statistical theory of turbulence; Part two addresses the coherent structures in open-channel flows and boundary layers.

Turbulence in Open-Channel Flows

A model of sand transport in water is produced by combining a turbulence-resolving large eddy simulation (LES) with a discrete element model (DEM) prescribing the motion of individual grains of medium sand. The momentum effect of each particle on the fluid is calculated at the LES cell containing the particle, and the fluid velocity and pressure, interpolated to each particle center, is used to derive fluid force on each particle in the DEM. Eleven numerical experiments are conducted of an initially flat bed of particles. The experiments span a range of motion, from essentially no motion to vigorous suspension. Hydraulic roughness is found to increase abruptly at the transition from bed load to suspended load transport. Suspended sediment extracts momentum from the flow and decreases the rate of shear. Whereas, slightly higher in the flow, vertical drag by suspended grains damps turbulence and increases the rate of shear. Vertical sediment diffusivity and effective particle settling velocity are much smaller than is commonly assumed in suspended sediment models. The bed load experiments suggest that saltation by itself is a poor model of bed load sand transport. In contrast to expectations from saltation models, the peak bed load flux occurs at essentially the same level as the bed, and grains move slowly in frequent contact with other grains. Higher- and faster-moving bed load grains that can be considered to be in saltation represent a smaller portion of the total flux. Entrainment of bed load grains occurs in response to fluid penetration of the bed by high-vorticity turbulence structures embedded within broader high speed fluid regions referred to as a sweeps or high-speed wedges.

Numerical simulation of turbulence and sediment transport of medium sand

Sand transport and morphological change occur in the wave bottom boundary layer due to sand particle interactions with an oscillatory flow and granular interactions between particles. Although these interactions depend strongly on the characteristics of the particle population, i.e. size and shape, little is known about how natural sand particles behave under oscillatory conditions and how variations in particle size influence transport behaviour. To enable this to be studied numerically, an Euler–Lagrange point-particle model is developed which can capture the individual and collective dynamics of subaqueous natural sand grains. Special treatments for particle collision, friction and hydrodynamic interactions are included to take into account the wide size and shape variations in natural sands. The model is used to simulate sand particle dynamics in two asymmetric oscillatory flow conditions corresponding to the vortex ripple experiments of Van der Werf et al. (J. Geophys. Res., vol. 112, 2007, F02012) and the sheet-flow experiments of O’Donoghue & Wright (Coast. Engng, vol. 50, 2004, pp. 117–138). A comparison of the phase resolved velocity and concentration fields shows overall excellent agreement between simulation and experiments. The particle based datasets are used to investigate the spatio-temporal dynamics of the particle-size distribution and the influence of three-dimensional vortical features on particle entrainment and suspension processes. For the first time, it is demonstrated that even for the relatively well-sorted medium-size sands considered here, the characteristics of the local grain size population exhibit significant space–time variation. Both conditions demonstrate a distinct coarse-over-fine armouring at the bed surface during low-velocity phases, which restricts the vertical mobility of finer fractions in the bed, and also results in strong pickup events involving disproportionately coarse fractions. The near-bed layer composition is seen to be very dynamic in the sheet-flow condition, while it remains coarse through most of the cycle in the vortex ripple condition. Particles in suspension spend more time sampling the upward directed parts of these flows, especially the smaller fractions, which delays particle settling and enhances the vertical size sorting of grains in suspension. For the submillimetre grain sizes considered, most particle–particle collisions occur at low impact Stokes numbers and can be expected to have low rebound velocities. The results are considered to be fundamental to the understanding of particle sorting and transport mechanisms, and can help to improve current transport modelling approaches.

/pdf/particle-based-modelling-and-simulation-of-natural-sand-4557mpssqy.pdf

Particle based modelling and simulation of natural sand dynamics in the wave bottom boundary layer

The local granular rheology is investigated numerically in turbulent bedload transport. Considering spherical particles, steady uniform configurations are simulated using a coupled fluid-discrete-element model. The stress tensor is computed as a function of the depth for a series of simulations varying the Shields number, the specific density and the particle diameter. The results are analyzed in the framework of the $\mu(I)$ rheology and exhibit a collapse of both the shear to normal stress ratio and the solid volume fraction over a wide range of inertial numbers. Contrary to expectations, the effect of the interstitial fluid on the granular rheology is shown to be negligible, supporting recent work suggesting the absence of a clear transition between the free-fall and turbulent regime. In addition, data collapse is observed up to unexpectedly high inertial numbers $I\sim2$, challenging the existing conceptions and parametrization of the $\mu(I)$ rheology. Focusing upon bedload transport modelling, the results are pragmatically analyzed in the $\mu(I)$ framework in order to propose a granular rheology for bedload transport. The proposed rheology is tested using a 1D volume-averaged two-phase continuous model, and is shown to accurately reproduce the dense granular flow profiles and the sediment transport rate over a wide range of Shields numbers. The present contribution represents a step in the upscaling process from particle-scale simulations toward large-scale applications involving complex flow geometry.

Dense granular flow rheology in turbulent bedload transport

This paper numerically investigates particle saltation in a turbulent channel flow having a rough bed consisting of two to three layers of densely packed spheres. The Shields function is 0.065 which is just above the sediment entrainment threshold to give a bed-load regime. The applied methodology is a combination of three technologies, i.e., the direct numerical simulation of turbulent flow; the combined finite-discrete element modeling of the deformation, movement, and collision of the particles; and the immersed boundary method for the fluid-solid interaction. It is shown that the presence of entrained particles significantly modifies the flow profiles of velocity, turbulent intensities, and shear stresses in the vicinity of a rough bed. The quasi-streamwise-aligned streaky structures are not observed in the near-wall region and the particles scatter on the rough bed owing to their large size. However, in the outer flow region, the turbulent coherent structures recover due to the weakening rough-bed effects and particle interferences. First- and second-order statistical features of particle translational and angular velocities, together with sediment concentration and volumetric flux density profiles, are presented. Several key parameters of the particle saltation trajectory are calculated and agree closely with published experimental data. Time histories of the hydrodynamic forces exerted upon a typical saltating particle, together with those of the particle's coordinates and velocities, are presented. A strong correlation is shown between the abruptly decreasing streamwise velocity and increasing vertical velocity at collision which indicates that the continuous saltation of large-grain-size particles is controlled by collision parameters such as particle incident angle, local bed packing arrangement, and particle density, etc.

/pdf/saltation-of-particles-in-turbulent-channel-flow-3vq616avqm.pdf

Saltation of particles in turbulent channel flow.

In this paper, the entrainment and movement of coarse particles on the bed of an open channel is numerically investigated. Rather than model the sediment transport using a concentration concept, this study treats the sediment as individual particles and investigates the interaction between turbulent coherent structures and particle entrainment. The applied methodology is a combination of the direct numerical simulation of turbulent flow, the combined finite-discrete element modeling of particle motion and collision, and the immersed boundary method for the fluid-solid interaction. In this study, flow over a water-worked rough-bed consisting of 2-3 layers of densely packed spheres is adopted and the Shields function is 0.065 which is just above the entrainment threshold to give a bed-load regime. Numerical results for turbulent flow, sediment entrainment statistics, hydrodynamic forces acting on the particles, and the interaction between turbulence coherent structures and particle entrainment are presented. It is shown that the presence of entrained particles significantly modifies the mean velocity and turbulence quantity profiles in the vicinity of a rough-bed and that the instantaneous lift force can be larger than a particle's submerged weight in a narrow region above the effective bed location, although the mean lift force is always smaller than the submerged weight. This, from a hydrodynamic point of view, presents strong evidence for a close cause-and-effect relationship between coherent structures and sediment entrainment. Furthermore, instantaneous numerical results on particle entrainment and the surrounding turbulent flow are reported which show a strong correlation between sediment entrainment and sweep events and the underlying mechanisms are discussed.

/pdf/direct-numerical-simulation-of-sediment-entrainment-in-2j87uz1a6d.pdf

Direct numerical simulation of sediment entrainment in turbulent channel flow

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Direct numerical simulation of sediment entrainment in turbulent channel flow