^{1}, Panayiotis Diplas

^{1}, Clinton L. Dancey

^{2}and Manousos Valyrakis

^{1}

### Abstract

In this study, we investigated the role of turbulencefluctuations on the entrainment of a fully exposed grain near threshold flow conditions. Experiments were carried out to measure synchronously the near bed flowvelocity 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 flowvelocity.Turbulencefluctuations 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-normal) probability density function (pdf) dependent on only the coefficient of variation of the impulse (impulse intensity). Relation of the impulse intensity to the particle Reynolds number, , 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.

The support of the National Science Foundation (Grant Nos. EAR-0439663 and EAR-0738759) and Army Research Office for this study is gratefully acknowledged.

I. INTRODUCTION

II. IMPULSE CONCEPT

A. Impulse detection

III. EXPERIMENTS

A. Incipient particle motion detection

B. Experimental procedure

IV. RESULTS AND ANALYSIS

A. Distribution of impulse

B. Critical and number of impulses

C. Critical impulse and number of grain entrainments

D. Probability of particle entrainment

V. IMPLICATIONS OF THE IMPULSE CONCEPT FOR LOW MOBILITY CONDITIONS

VI. CONCLUSIONS

### Key Topics

- Turbulent flows
- 46.0
- Hydrodynamics
- 9.0
- Velocity measurement
- 8.0
- Particle fluctuations
- 5.0
- Data analysis
- 4.0

## Figures

Definition sketch of the forces acting on a spherical particle resting on identical size densely packed spheres, side view (left) and top view (right) of the bed geometry.

Definition sketch of the forces acting on a spherical particle resting on identical size densely packed spheres, side view (left) and top view (right) of the bed geometry.

Representation of the impulse events in the time series. The event is characterized by and values, representing force magnitude and duration, the product of which is (corresponds to the shaded rectangular area below the line). and were determined by interpolating the adjacent data points in the time series. The vertical line between the and indicates that the particle movement was observed during the event.

Representation of the impulse events in the time series. The event is characterized by and values, representing force magnitude and duration, the product of which is (corresponds to the shaded rectangular area below the line). and were determined by interpolating the adjacent data points in the time series. The vertical line between the and indicates that the particle movement was observed during the event.

Side view (right) and top view (upper left corner) sketches of the mobile test particle and pocket geometry (diameter of the grains, ).

Side view (right) and top view (upper left corner) sketches of the mobile test particle and pocket geometry (diameter of the grains, ).

From top to bottom: representative time series of, , impulse , and photodetector output, from run E1. Dashed vertical lines in the top two plots indicate detected particle movements. Secondary vertical axes in the top two plots: binary 0/1 signal. Explanation of the solid vertical lines in the bottom plot: (a) beginning of a rocking event, (b) beginning of a pivoting event, (c) instant when the test particle reached the retaining pin, (d) instant when the test particle started rolling back to its original pocket, and (e) instant when the particle reached its original pocket.

From top to bottom: representative time series of, , impulse , and photodetector output, from run E1. Dashed vertical lines in the top two plots indicate detected particle movements. Secondary vertical axes in the top two plots: binary 0/1 signal. Explanation of the solid vertical lines in the bottom plot: (a) beginning of a rocking event, (b) beginning of a pivoting event, (c) instant when the test particle reached the retaining pin, (d) instant when the test particle started rolling back to its original pocket, and (e) instant when the particle reached its original pocket.

Histograms of , , , and from left to right for the run E1. Nearly 280 000 data points (counts) for and total of 1978 data points for , , and are represented in each histogram.

Histograms of , , , and from left to right for the run E1. Nearly 280 000 data points (counts) for and total of 1978 data points for , , and are represented in each histogram.

Relationship between impulse intensity, , and particle Reynolds number, .

Relationship between impulse intensity, , and particle Reynolds number, .

Plots of the function given by Eq. (5) for a range of values.

Plots of the function given by Eq. (5) for a range of values.

Comparison of Eq. (5) with measured pdfs for E1–E8. Solid lines are used to show pdfs obtained from Eq. (5).

Comparison of Eq. (5) with measured pdfs for E1–E8. Solid lines are used to show pdfs obtained from Eq. (5).

Semilogarithmic plot of measured pdfs from all eight runs. Equation (5) is also presented with and 1.1 for comparison.

Semilogarithmic plot of measured pdfs from all eight runs. Equation (5) is also presented with and 1.1 for comparison.

vs plots. 1978 data points from run E1 (left), 1101 data points from run E4 (right). Black circles indicate , combinations that are associated with full particle dislodgement (pivoting).

vs plots. 1978 data points from run E1 (left), 1101 data points from run E4 (right). Black circles indicate , combinations that are associated with full particle dislodgement (pivoting).

(a) Illustration of the approach used for varying the critical . (b) Number of detected impulses vs the ratio of critical level used to the original .

(a) Illustration of the approach used for varying the critical . (b) Number of detected impulses vs the ratio of critical level used to the original .

vs plot. The region where movement and no movement areas overlap is shown with a gray band between the impulse values of 0.0034 and . Horizontal arrow indicates the critical impulse level.

vs plot. The region where movement and no movement areas overlap is shown with a gray band between the impulse values of 0.0034 and . Horizontal arrow indicates the critical impulse level.

The plot of number of impulse events above critical impulse per min vs total number of impulse events above critical per min. Data points with black circles are from all eight runs where a constant was used. White and gray circles indicate results from runs E1 and E5, respectively, where various values were used. Data with the plus sign indicate the actual particle movements vs observed in each run.

The plot of number of impulse events above critical impulse per min vs total number of impulse events above critical per min. Data points with black circles are from all eight runs where a constant was used. White and gray circles indicate results from runs E1 and E5, respectively, where various values were used. Data with the plus sign indicate the actual particle movements vs observed in each run.

Illustration of the probability analysis. The probability that a flow event will generate a level of impulse that exceeds a specified critical level, , is indicated by the shaded area and is assumed to be equal to the probability of particle entrainment, .

Illustration of the probability analysis. The probability that a flow event will generate a level of impulse that exceeds a specified critical level, , is indicated by the shaded area and is assumed to be equal to the probability of particle entrainment, .

Probability of particle entrainment vs probability of exceedance of critical impulse.

Probability of particle entrainment vs probability of exceedance of critical impulse.

Dimensionless bed load parameter vs shields stress (left -axis) from Refs. 10 and 12. Note that data only in the range between 0.005 and 0.016 were used. The number of impulse events above critical impulse per min (right -axis) vs shields stress is also plotted.

Dimensionless bed load parameter vs shields stress (left -axis) from Refs. 10 and 12. Note that data only in the range between 0.005 and 0.016 were used. The number of impulse events above critical impulse per min (right -axis) vs shields stress is also plotted.

## Tables

Summary of the test conditions for entrainment experiments.

Summary of the test conditions for entrainment experiments.

Summary of the impulse parameters obtained from 15 min runs.

Summary of the impulse parameters obtained from 15 min runs.

Number of impulse events and particle movements observed for 15 min. Note that .

Number of impulse events and particle movements observed for 15 min. Note that .

Summary of the results from conditions where various critical values were used for run E1.

Summary of the results from conditions where various critical values were used for run E1.

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