Stochastic Incipient Motion Criterion for Spheres under Various Bed Packing Conditions

Papanicolaou, A. N.; Diplas, Panayiotis; Evaggelopoulos, N.; Fotopoulos, S.

doi:10.1061/(asce)0733-9429(2002)128:4(369)

Cited by 188 publications

(148 citation statements)

References 42 publications

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“…A number of pdfs has been proposed for u 2 in studies concerning the sediment entrainment. 18,19,21 Based on the assumption that the drag force is proportional to u 2 , in combination with a Gaussian distribution for u, Papanicolaou 18 proposed a chisquared distribution to describe instantaneous drag force, which was later modified by Hofland and Battjes 30 to account for the relative turbulence intensity. But the distribution of the impulse, impulse duration or force magnitude associated with impulse events, to the writers' knowledge, has never been examined in sediment transport research.…”

Section: Results and Analysismentioning

confidence: 99%

“…F͑t͒ Ն F cr between t 1 and t 2 , where T = t 2 − t 1 is the total duration of the applied force, ͗F͘ is the time average force over duration T, and F cr is the minimum ͑critical͒ force required to initiate bed material motion ͑obtained from the resting equilibrium conditions 18 FIG. 1.…”

Section: ͑1͒mentioning

confidence: 99%

“…where the hydrodynamic mass coefficient, 18 f V = ͓1 + 0.5͑ / S − ͔͒, S is the density of the particle, is the density of water, X and Z are the lever arms, aligned with and normal to the bed, respectively, and ␤ is the angle between the channel bed and the horizontal plane. For steady flows, the relationship between F D and local flow velocity in the streamwise direction, u, upstream of the submerged body is given by…”

Section: ͑2͒mentioning

confidence: 99%

“…18, 23 Balakrishnan, 24 using a video camera together with local flow velocity measurements, provided evidence contrary to the general consensus, and demonstrated that not all local flow velocity fluctuations well above the mean value result in particle dislodgement under incipient flow conditions. A recent study examined this phenomenon further under well controlled laboratory conditions and demonstrated that it is not the magnitude of the applied force alone that serves as the necessary and sufficient condition for particle entrainment but rather the combination of force and duration, or impulse.…”

Section: Introductionmentioning

confidence: 98%

“…[17][18][19][20][21][22] Common in these approaches is the importance of the magnitude of peaks in the local flow velocity, the streamwise component in particular, and resulting instantaneous forces acting on individual grains in mobilizing these particles. Despite these efforts and partially due to the experimental difficulties in observing the threshold of sediment movement with synchronized flow measurements, which also lead to subjectivity in defining the bed mobility, 2,17,18 the precise determination of the incipient condition remains elusive. Moreover, the nature of the processes that are causing the phenomenon observed by Paintal 10 has not been explained by the recent methods so far.…”

Section: Introductionmentioning

confidence: 99%

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Impulse and particle dislodgement under turbulent flow conditions

et al. 2010

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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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Section: Results and Analysismentioning

confidence: 99%

Section: ͑1͒mentioning

confidence: 99%

Section: ͑2͒mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Impulse and particle dislodgement under turbulent flow conditions

et al. 2010

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A mechanistic-stochastic formulation of bed load particle motions: From individual particle forces to the Fokker-Planck equation under low transport rates

Fan

Zhong

Wang

et al. 2014

J. Geophys. Res. Earth Surf.

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Bed load transport is a highly complex process. The probability density function (PDF) of particle velocities results from the local particle momentum variability in response to fluid drag and interactions with the bed. Starting from the forces exerted on a single particle under low transport rates (i.e., rolling and sliding regimes), we derive here the nonlinear stochastic Langevin equation (LE) to describe the dynamics of a single particle, accounting for both the deterministic and the stochastic components of such forces. Then, the Fokker-Planck equation (FPE), which describes the evolution of the PDF of the ensemble particle velocities, is derived from the LE. We show that the theoretical PDFs of both streamwise and cross-stream velocities obtained by solving the FPE under equilibrium conditions have exponential form (PDFs of both positive and negative velocities decay exponentially), consistent with the experimental data by Roseberry et al. (2012). Moreover, we theoretically show how the exponential-like PDF of an ensemble of particle velocities results from the forces exerted on a single particle. We also show that the simulated particle motions using the proposed Langevin model exhibit an emergent nonlinear relationship between hop distances and travel times (power law with exponent 5/3), in agreement with the experimental data, providing a statistical description of the particles' random motion in the context of a stochastic transport process. Finally, our study emphasizes that the motion of individual particles, described by the LE, and the behavior of the ensemble, described by the FPE, are connected within a statistical mechanics framework.

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Spatial correlations in bed load transport: Evidence, importance, and modeling

Heyman

Mettra

et al. 2014

JGR Earth Surface

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This article examines the spatial dynamics of bed load particles in water. We focus particularly on the fluctuations of particle activity, which is defined as the number of moving particles per unit bed length. Based on a stochastic model recently proposed by Ancey and Heyman (2014), we derive the second moment of particle activity analytically, that is, the spatial correlation functions of particle activity. From these expressions, we show that large moving particle clusters can develop spatially. Also, we provide evidence that fluctuations of particle activity are scale dependent. Two characteristic lengths emerge from the model: a saturation length sat describing the length needed for a perturbation in particle activity to relax to the homogeneous solution and a correlation length c describing the typical size of moving particle clusters. A dimensionless Péclet number can also be defined according to the transport model. Three different experimental data sets are used to test the theoretical results. We show that the stochastic model describes spatial patterns of particle activity well at all scales. In particular, we show that c and sat may be relatively large compared to typical scales encountered in bed load experiments (grain diameter, water depth, bed form wavelength, flume length, etc.) suggesting that the spatial fluctuations of particle activity have a nonnegligible impact on the average transport process.

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Stochastic Incipient Motion Criterion for Spheres under Various Bed Packing Conditions

Cited by 188 publications

References 42 publications

Impulse and particle dislodgement under turbulent flow conditions

Impulse and particle dislodgement under turbulent flow conditions

A mechanistic-stochastic formulation of bed load particle motions: From individual particle forces to the Fokker-Planck equation under low transport rates

Spatial correlations in bed load transport: Evidence, importance, and modeling

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