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Abstract: Coastal vegetation is capable of decreasing wave run-up. However, because of regrowth, decay or man-made damage, coastal vegetation is always distributed in patches, and its internal distribution is often non-uniform. This study investigates the effects of patchy vegetation on solitary wave run-up by using a numerical simulation. A numerical model based on fully nonlinear Boussinesq equations is established to simulate the wave propagation on a slope with patchy vegetation. By using the model, the process of solitary wave run-up attenuation due to patchy vegetation is numerically analysed. The numerical results reveal that patchy vegetation can considerably attenuate the wave run-up in an effective manner. In addition, high-density patched vegetation can attenuate the solitary wave run-up more effectively than low-density patched vegetation can. For the same density, patchy vegetation with a uniform distribution has a better attenuation effect on wave run-up compared to that of patchy vegetation with a non-uniform distribution.
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Key words:
- solitary wave /
- run-up /
- patchy vegetation /
- Boussinesq equation
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Figure 2. Distribution of the three different cylinders in experiments conducted by Maza et al. (2016). a. C1 consisted of 880 cylinders disposed in a single circular shape with a diameter of 3 m, b. C2 was composed of 8 circular cylindrical patches with a diameter of 1 m each. Each patch was made of 112 cylinders, leading to the total number of cylinders being 896, c. C3 was formed by the four inner patches of the second configuration.
Figure 3. Comparison between the relative surface of numerical results and laboratory data obtained by Maza et al. (2016) for solitary wave propagation with patchy vegetation for C2.
Figure 4. Experimental setup of Yao et al. (2015). a. Model configuration of vegetation stems and b. sectional view of experimental basin.
Figure 5. Free surface simulation for case A. Comparison of free surface at gauge S1 (a), gauge S2 (b) and gauge S3 (c).
Figure 8. Comparison of solitary wave run-up at vegetation area (y=0.3 m) for different cases.
Figure 9. Comparison of solitary wave run-up at channel (y=2.85 m) for different cases.
Table 1. The arrangement of patchy vegetation cases
Case The number of cylinders Density /m2 Volume portion $(\phi) $ A. Non-vegetation 0 0 0 B. Low density 600 300 0.023 6 C. Medium density 1 600 800 0.062 8 D. High density 3 200 1 600 0.126 0 E. High-low density 1 600 800 0.094 0–0.031 4 F. Low-high density 1 600 800 0.031 4–0.094 0 
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Table 2. Wave gauges location
WG1 WG2 WG3 WG4 WG5 WG6 x/m 19.00 19.00 19.60 19.60 19.00 19.00 y/m 1.00 2.50 1.00 2.50 0.30 2.85
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Table 3. The wave run-up locations and heights at y =0.3 m
Case Run-up location (x/m) Run-up height (y/m) A 20.46 0.050 B 19.88 0.036 C 19.60 0.029 D 19.40 0.024 E 19.69 0.031 F 19.79 0.034
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Table 4. The wave run-up locations and heights at y =2.85 m
Case Run-up location (x/m) Run-up height (y/m) A 20.46 0.050 B 20.46 0.050 C 20.46 0.050 D 20.51 0.052 E 20.46 0.050 F 20.46 0.050
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