## 4 Discussion  
In this work, the frequency of entrainment of the instrumented particle, 7 cm in diameter, that was estimated using its logged readings, is linked to the frequency of flow impulses above the critical impulse at the positions in the middle of the top half of the particle's diameter, which is the position of investigation. Different threshold values were assessed to determine the critical impulse that results in a good agreement between the frequencies of entrainment of the instrumented particle, estimated using its readings, and the flow impulses above the critical impulse as shown in Figure 2. The main aim of this study was to assess whether there was any trend in terms of the type of flow structures that occur in sequence before and after the occurrences of the flow impulses that have resulted in the coarse particle's entrainment. The ADV logging frequency that was used in the experiment of this work for flow velocity measurements was 25 Hz. The ADV was able to detect events with a timescale of 0.04 s and higher. Based on the conclusion of the experimental work of [PERSON] et al. (2013), more than 50% of the turbulent flow events that have resulted in the dislodgement of the particle that was used in their research in the stream-wise direction have length scales of the particle's diameter. Additionally, only a very small fraction of the turbulent flow events that have resulted in the dislodgement of the coarse particle that was used in the stream-wise direction have length scales four times the particle's diameter. [PERSON] et al. (2008) reported a similar observation, specifically that the length scale of the events that have resulted in sediment entrainment are sweeps of two to four grain diameters in the stream-wise direction. In the experiment in this work, the instrumented particle that was used was 7 cm in diameter. The critical velocity used to overcome the resistance and to entrain the instrumented particle that was placed on the micro-topography used in this experiment, based on the moment balance equations ([PERSON], 2010), was 0.623 m/s. Therefore, assuming the length scale of a turbulent flow event of the coarse particle's diameter, the mean time scale of such an event could be estimated using Equation (3):  
\[t_{ffe}=\frac{0.07\ \text{m}}{0.623\ \text{m/s}}=0.1123\text{s} \tag{3}\]  
where \(t_{ffe}\) is the time-scale of the turbulent flow event. The ADV that was used in the experiment of this work for flow velocity measurements has a logging frequency of 25 Hz, therefore it was able to detect turbulent flow events of length scales of 35% of the particle's diameter and longer, assuming their velocities are equal to the critical velocity. Therefore, the logging frequency of the ADV used in this work is sufficient for the study of coherent flow structures that can result in the entrainment of the instrumented particle placed on the micro-topography used in this work based on the conclusions of the experimental work presented in ([PERSON], 2010; 2010). Further investigation was performed by assessing the histogram of the durations of the impulses above the critical impulse (\(I_{cr}\) = 0.0445 m\({}^{2}\)/s), as shown in Figure 23 below. Close investigation of the histogram of the durations of impulses above 0.0445 m\({}^{2}\)/s indicates that about 75% of the impulses have durations of less than 0.2 s. This duration, 0.2 s, is equivalent to five ADV readings. Therefore, it has been decided to investigate the quadrant readings for a window of 1-5 readings in the case of \(I_{cr}\) = 0.0445 m\({}^{2}\)/s. Another investigation that was performed was lowering the critical impulse to a value of 0.0063 m\({}^{2}\)/s. This is similar to the critical impulse used by [PERSON] et al. (2010). This procedure increases the number of impulses above the critical impulse and provides more data for the quadrant analysis.