Fundamental to our understanding of erosional and transport phenomena in earth-surface dynamics and engineering is knowledge of the conditions under which sediment motion will begin when subjected to turbulent flow. The onset criterion currently in use emphasizes the time-averaged boundary shear stress and therefore is incapable of accounting for the fluctuating forces encountered in turbulent flows. We have validated through laboratory experiments and analytical formulation of the problem a criterion based upon the impulse imparted to a sediment grain. We demonstrate that in addition to the magnitude of the instantaneous turbulent forces applied on a sediment grain, the duration of these turbulent forces is also important in determining the sediment grain's threshold of motion, and that their product, or impulse, is better suited for specifying such conditions.

[1] A new criterion for the onset of entrainment of coarse sediment grains is presented here. It is hypothesized that not only the magnitude, but also the duration of energetic near bed turbulent events is relevant in predicting grain removal from the bed surface. It is therefore proposed that the product of force and its duration, or impulse, is a more appropriate and universal criterion for identifying conditions for particle dislodgement. This conjecture is investigated utilizing two theoretical models, representative of two modes of entrainment: saltation and rolling. In these models, instantaneous, highly fluctuating turbulent forces are simulated as short-lived pulses of characteristic magnitude and duration, which transfer adequate fluid momentum to the particle, to trigger its entrainment. The analytical solution of the respective equations of motion is employed in deriving representations of threshold conditions in terms of the impulse characteristics. It is shown that hydrodynamic forces of sufficiently high magnitude are capable of entraining a particle only when they last long enough so that their impulse exceeds a critical value. To illustrate further the validity of the critical impulse concept, as well as extend and generalize its application to different entrainment levels of an individual grain, a novel experimental setup is utilized. This setup facilitates observations of angular displacement of a steel mobile particle in air due to electromagnetic pulses of different magnitude and duration. The experimentally obtained conditions for partial or complete entrainment support the concept of a critical impulse.

In this study, we investigated the role of turbulence fluctuations on the entrainment of a fully exposed grain near threshold flow conditions. Experiments were carried out to measure synchronously the near bed flow velocity and the particle movement for a range of flow conditions and resulting particle entrainment frequencies. We used a simplified bed geometry consisted of spherical particles to reduce the complexities associated with the variations in the bed and flow details in an effort to identify the underlying dominant physical mechanism. An analysis was performed based on common force approximations using near bed flow velocity. Turbulence fluctuations were treated as impulses, which are products of magnitude and duration of applied force. It is demonstrated that besides the magnitude of the instantaneous forces applied on a sediment grain, their duration is important as well in determining whether a particle will be entrained by a turbulent flow event. Frequency of particle entrainment varied remarkably with minute changes in gross flow parameters. Impulse imparted on the sediment grain by turbulent flow was found to be well represented by a log-normal distribution. We obtained a ͑log-normal͒ probability density function ͑pdf͒ dependent on only the coefficient of variation of the impulse ͑impulse intensity͒. Relation of the impulse intensity to the particle Reynolds number, Re ‫ء‬ , was established. The sensitivity of the computed impulse to the critical force level, as well as the influence of the critical impulse level on the dislodgement events, was explored. Particle entrainment probabilities were found using the derived pdf as well as experimental observations and a good agreement between the two is reported. Implications of the presented impulse concept and our experimental findings for sediment mobility at low bed shear stress conditions are also discussed.

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[1] The entrainment of coarse sediment particles under the action of fluctuating hydrodynamic forces is investigated from an energy perspective. It is demonstrated that the entrainment of a grain resting on the channel boundary is possible when the instantaneous flow power transferred to it exceeds a critical level. Its complete removal from the bed matrix occurs only if the impinging flow events supply sufficient mechanical energy. The energy-based criterion is formulated theoretically for entrainment of individual spherical particles in both saltation and rolling modes. Out of the wide range of flow events that can perform mechanical work on a coarse grain, only those with sufficient power and duration or equivalent energy density and characteristic length scale may accomplish its complete dislodgement. The instantaneous velocity upstream of a mobile particle is synchronously recorded with its position, enabling the identification of the flow events responsible for grain entrainment by rolling at near incipient motion flow conditions. For each of the entrainment events, the energy transfer coefficient defined as the ratio of the mechanical work performed on the particle to the mean energy of the flow event responsible for its dislodgement obtains values ranging from 0.04 to 0.10. At the examined low-mobility flow conditions, the majority (about 80%) of the energetic structures leading to complete particle entrainment have a characteristic length of about two to four particle diameters.

[1] The occurrence of sufficiently energetic flow events characterized by impulses of varying magnitude is treated as a point process. It is hypothesized that the rare but extreme magnitude impulses are responsible for the removal of coarse grains from the bed matrix. This conjecture is investigated utilizing distributions from extreme value theory and a series of incipient motion experiments. The application of extreme value distributions is demonstrated for both the entire sets of impulses and the maxima above a sufficiently high impulse quantile. In particular, the Frechet distribution is associated with a power law relationship between the frequency of occurrence and magnitude of impulses. It provides a good fit to the flow impulses, having comparable performance to other distributions. Next, a more accurate modeling of the tail of the distribution of impulses is pursued, consistent with the observation that the majority of impulses above a critical value are directly linked to grain entrainments. The peaks over threshold method is implemented to extract conditional impulses in excess of a sufficiently high impulse level. The generalized Pareto distribution is fitted to the excess impulses, and parameters are estimated for various impulse thresholds and methods of estimation for all the experimental runs. Finally, the episodic character of individual grain mobilization is viewed as a survival process, interlinked to the extremal character of occurrence of impulses. The interarrival time of particle entrainment events is successfully modeled by the Weibull and exponential distributions, which belong to the family of extreme value distributions.

This study investigated the physics of separated turbulent flows near the vertical intersection of a flat wall with a cylindrical obstacle. The geometry imposes an adverse pressure gradient on the incoming boundary layer. As a result, flow separates from the wall and reorganizes to a system of characteristic flow patterns known as the horseshoe vortex. We studied the time-averaged and instantaneous behaviour of the turbulent horseshoe vortex using planar time-resolved particle image velocimetry (TRPIV). In particular, we focused on the effect of Reynolds number based on the diameter of the obstacle and the bulk approach velocity, Re D . Experiments were carried out at Re D : 2.9 × 10 4 , 4.7 × 10 4 and 12.3 × 10 4 . Data analysis emphasized time-averaged and turbulence quantities, time-resolved flow dynamics and the statistics of coherent flow patterns. It is demonstrated that two large-scale vortical structures dominate the junction flow topology in a time-averaged sense. The number of additional vortices with intermittent presence does not vary substantially with Re D . In addition, the increase of turbulence kinetic energy (TKE), momentum and vorticity content of the flow at higher Re D is documented. The distinctive behaviour of the primary horseshoe vortex for the Re D = 12.3 × 10 4 case is manifested by episodes of rapid advection of the vortex to the upstream, higher spatio-temporal variability of its trajectory, and violent eruptions of near-wall fluid. Differences between this experimental run and those at lower Reynolds numbers were also identified with respect to the spatial extents of the bimodal behaviour of the horseshoe vortex, which is a well-known characteristic of turbulent junction flows. Our findings suggest a modified mechanism for the aperiodic switching between the dominant flow modes. Without disregarding the limitations of this work, we argue that Reynolds number effects need to be considered in any effort to control the dynamics of junction flows characterized by the same (or reasonably similar) configurations.

[1] The overall objective of this study is to identify the physical mechanisms responsible for the entrainment of an exposed particle subject to rapidly fluctuating hydrodynamic forces in the case of channel flow with a fully rough boundary. This is pursued here by examining particle dislodgment under uniform and cylinder wake-flow experiments. The critical impulse concept is investigated more rigorously by measuring directly the pressures at four points on the surface of a fixed test grain. The number of impulse events determined from these experiments increases by more than an order of magnitude, over a modest change of roughness Reynolds number. Furthermore, they are well described by a lognormal probability density function. Both results are consistent with those obtained from similar experiments via indirect (velocity-based) impulse calculations and reported in a prior contribution. This comparison supports the use of the velocity record for determining instantaneous hydrodynamic forces and impulses instead of the more difficult approach of measuring the pressure fluctuations directly. The present results demonstrate the dominant role the local, streamwise velocity component plays on particle dislodgment. This is attributed to the large impulse content and occasionally strong positive lift force associated with flow events, exhibiting pronounced positive streamwise velocity fluctuations. The majority ($70%) of these events occur in the fourth quadrant, while a significant number ($22%) appear as first-quadrant episodes. It was also determined that wake flows can increase substantially particle entrainment via enhanced lift and increased turbulence intensity.Citation: Celik, A. O., P. Diplas, and C. L. Dancey (2013), Instantaneous turbulent forces and impulse on a rough bed: Implications for initiation of bed material movement, Water Resour.