Wave Dynamics

The variation in the wave dynamics induced by the stereo-videogrammetry is explored ini- tially in the time domain in Figure 2.8. The nominal wave condition is 0.8 Hz frequency and 25 mm amplitude. For these tests there is no model in the experimental area. The top plot is for the incident wave gauge, which is located between the wavemaker and the start of the experimental area, and the bottom plot is for a location in the centre of the experimental area. Both plots have four time series displayed for comparison. These include a clear water condition; two runs with the particle fences in place; and a run where the particles were in the experimental area. This qualitative comparison indicates that there is exceptional agreement between shape and frequency, with a very slight variation in peak values (<0.5 mm). As the wave probes were not moved between runs, this variation can be attributed to either equipment effects or lack of repeatability in the wavemaker.

Figure 2.8: Time comparison between wave gauge measurements to assess effect of stereo-

videogrammetry equipment on wave dynamics for 0.8 Hz 25 mm. (Left) extended time series (Right) restricted time series.

A quantitative study on the discrepancies between experimental set-up conditions is presented in Figure 2.9, this plot shows relative RMSE for the three frequency conditions explored in this study. The data is differentiated by the incident wave gauge, which should be consistent, and the experimental set-up for the other wave gauges. This plot indicates that irrespective of wave gauge location or experimental equipment, the variation between set-ups is in the range of 1-5 %. This testing was restricted to limited conditions, with an expectation that

the effects of the particles become less important at lower wave frequencies. 0.6 0.8 1 Frequency (Hz) 0 2 4 6 Realtive Difference (%)

Incident Wave Gauge Fences

Particles and Fences

Figure 2.9: Relative error study of wave gauge measurements to assess effect of stereo-videogrammetry equipment on wave dynamics.

2.3.2 Measurement Accuracy

The comparison between the wave gauges and the stereo videogrammetry is of importance due to the relative novelty of the stereo videogrammetry approach. All experimental results presented are for a setup with the cylinder present. A time domain comparison for a wave with frequency 0.9 Hz and amplitude 25 mm at WP 10 is given in Figure 2.10, the top plot is an overlay of the two approaches and the bottom presents the relative and absolute errors. For this condition it is clear that there is very good agreement, with only slight discrepancies around the crests and troughs.

A similar comparison is made in Figure 2.11 except the condition has a frequency of 1.0 Hz and amplitude 50 mm and location WP 06. These plots show that for the period of t=0-10 s a similar accuracy is evident to the previous condition. Following this, very large instantaneous error occurs around 12.5 s; these errors are due to entire time steps failing to compute correctly. The accuracy returns until 15 s at which point errors increase until the processing completely fails at 22 s. These increasing errors and eventual failure to compute have been attributed to the particles being dispersed by non-linear wave drift effects, from Figure 2.2 this condition is from Stokes 3rdorder.

Extending the investigation from the two runs given above to all test conditions, the RMSE is compared with wave steepness in Figure 2.12. Wave steepness is used as RMSE varies with both the wave frequency and amplitude. The conditions ranged in frequency from 0.25 Hz to 1.0 Hz and amplitude from 25 mm to 100 mm. The left plot shows a comparison between the RMSE of each run and the wave steepness while the right shows the processing failure rate

0 5 10 15 20 25 30 35 40 45 Time (s) -30 -20 -10 0 10 20 30 η (mm)

Overlay of Wave Gauge and Surface Flow

Wave Gauge Surface Flow 0 5 10 15 20 25 30 35 40 45 Time (s) -2 0 2 Absolute Error (mm)

Difference Between Wave Gauge and Surface Flow Absolute RMSE = 1.4mm Relative RMSE = 2.8% 0 2 4 6 Relative Error (%) Absolute Error Relative Error

Figure 2.10: Comparison between wave gauge and DaVis measurements for a wave with frequency

of 0.9 Hz and amplitude of 25 mm (Top) Overlay (Bottom) Absolute Error on Left Axis and Relative error on Right Axis.

0 5 10 15 20 25 Time (s) -60 -40 -20 0 20 40 60 η (mm)

Overlay of Wave Gauge and Surface Flow

Wave Gauge Surface Flow 0 5 10 15 20 25 Time (s) -40 -20 0 20 40 Absolute Error (mm)

Difference Between Wave Gauge and Surface Flow Absolute RMSE = 8.8mm Relative RMSE = 8.8% 0 10 20 30 40 Relative Error (%) Absolute Error Relative Error

Figure 2.11: Comparison between wave gauge and DaVis measurements for a wave with frequency

of 1.0 Hz and amplitude of 50 mm (Top) Overlay (Bottom) Absolute Error on Left Axis and Relative error on Right Axis.

and the total number of frames captured compared to wave steepness. The wave steepness is that which was measured through phase averaging experimental results. From these plots it is clear that for low steepness waves, stereo-videogrammetry has low error relative to wave gauges and there is a very low risk of processing failure. A caveat to this is WP 04 which routinely exhibits the largest RMSE; this wave gauge is the measurement point closest to the cylinder. This is thought to be a result of higher nonlinearities in this region causing higher drift resulting in fewer particles for the digital image correlation. Errors increase however as wave steepness increases. Furthermore, the processing failure rate increases beyond 40% as steepness increases above 0.2. As highlighted above with Figure 2.11 this is not due to the inability of DaVis to operate in these conditions, rather it is a result of the seeded particles being swept away from the experimental area. An alternate presentation of Figure 2.12 (left) is presented in Appendix A in terms of wave frequency and amplitude.

0 0.05 0.1 0.15 0.2 0.25 0.3

Wave Steepness (ka)

0 5 10 15 20 25 Relative RMSE (%)

Relative RMSE against Wave Steepness WP # WP 04 0 2 4 6 8 10 12 14 16 18 20 22 Frames Captured ('000) Processing Success 0 0.05 0.1 0.15 0.2 0.25 0.3

Wave Steepness (ka)

0 5 10 15 20 25 30 35 40 45 50 Processing Failure(%)

Figure 2.12: (Left) RM SEA between stereo-videogrammetry and resistive wave probes. With WP

# indicating all wave probes except WP 04. (Right) Failure rate of processing data and total frames captured.