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Abstract: Coastal wetlands such as salt marshes and mangroves provide important protection against stormy waves. Accurate assessments of wetlands’ capacity in wave attenuation are required to safely utilize their protection services. Recent studies have shown that tidal currents have a significant impact on wetlands’ wave attenuation capacity, but such impact has been rarely considered in numerical models, which may lead to overestimation of wave attenuation in wetlands. This study modified the SWAN (Simulating Waves Nearshore) model to account for the effect of accompanying currents on vegetation-induced wave dissipation. Furthermore, this model was extended to include automatically derived vegetation drag coefficients, spatially varying vegetation height, and Doppler Effect in combined current-wave flows. Model evaluation against an analytical model and flume data shows that the modified model can accurately simulate wave height change in combined current-wave flows. Subsequently, we applied the new model to a mangrove wetland on Hailing Island in China with a special focus on the effect of currents on wave dissipation. It is found that the currents can either increase or decrease wave attenuation depending on the ratio of current velocity to the amplitude of the horizontal wave orbital velocity, which is in good agreement with field observations. Lastly, we used Hailing Island site as an example to simulate wave attenuation by vegetation under hypothetical storm surge conditions. Model results indicate that when currents are 0.08–0.15 m/s and the incident wave height is 0.75–0.90 m, wetlands’ wave attenuation capacity can be reduced by nearly 10% compared with pure wave conditions, which provides implications for critical design conditions for coastal safety. The obtained results and the developed model are valuable for the design and implementation of wetland-based coastal defense. The code of the developed model has been made open source, in the hope to assist further research and coastal management.
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Key words:
- wave attenuation by vegetation /
- wave-current interaction /
- SWAN model /
- storm waves /
- drag coefficient
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Figure 1. Wetland ecosystem in combined current-wave flows (a) and wave flume set up (Hu et al., 2014) (b). ADP, RBR, WG, EMF, FT represent Acoustic Doppler Profiler, pressure sensors (RBR solo3), Wave Gauge, electromagnetic flow meter, and force transducer for measuring parameters of currents and waves.
Figure 2. Comparisons of
$ {H}_{\mathrm{r}\mathrm{m}\mathrm{s}} $ evolution for SWAN-CWV model with the SWAN model, the analytical model proposed in this study on Eqs (26) and (27), and the analytical model from Losada et al. (2016) with different current velocities. a. Pure waves, b. current velocity = 0.05 m/s, c. current velocity = 0.20 m/s; and d. current velocity = 0.30 m/s. All the tested incident wave height$ {H}_{\mathrm{r}\mathrm{m}\mathrm{s}} $ is 0.1 m and the wave period Tp is 1.5 s. The drag coefficients were all calculated according to the empirical Re-$ {C}_{\mathrm{D}} $ relation on Eq. (16) to exclude the influence of$ {C}_{\mathrm{D}} $ to wave attenuation.
Figure 3. Comparisons of the wave height along mimic canopies (green patch) in the current-wave flows (
$ {U}_{\mathrm{c}} $ = 0.20 m/s): SWAN-CWV, SWAN-$ {C}_{\mathrm{D}} $ and the measured data (Hu et al., 2014). All cases are in non-submerged canopies with medium mimic stem densities (139 stems/m2). The case name stands for the combination of incident wave height 0.04 m and wave period 1.2 s, namely wave0412.
Figure 4. Comparisons of wave height attenuation induced by a unit length of canopies (
$ \Delta H $ in Eq. (28)) between numerical models (SWAN-CWV and SWAN-$ {C}_{\mathrm{D}} $ ) and experiment data (Hu et al., 2014).
Figure 5. The study area (enclosed by the red rectangle) on Hailing Island, South of China (a), top view of the study area (b), and ADP (c) and RBR (d) for current and wave measurements, respectively. S1–S4 represent the four stations set up at the field site for measuring wave and current parameters.
Figure 6. Comparisons between measured significant wave height in the mature mangroves and results from SWAN-
$ {C}_{\mathrm{D}} $ and SWAN-CWV models for field observations in Hailing Island (a and b), and variation of depth-averaged current velocity at Station S1 (c). The shaded area in a is enlarged in b to better show the influence of currents to wave vegetation. Three shaded parts in b represent relatively strong current in the observed period.
Figure 7. Statistical results of R2 for numerical models (SWAN-
$ {C}_{\mathrm{D}} $ = 1.2, SWAN-$ {C}_{\mathrm{D}} $ , SWAN-CWV) simulated results according to velocity ratio$ \alpha $ ($ \mathrm{\alpha }={U}_{\mathrm{c}}/{U}_{\mathrm{w}} $ ) in the field observations.
Figure 8. Variation of the significant wave height along with the canopy in different combinations of waves and currents. a. Weak current (
$ {H}_{0} $ = 0.8 m,$ {T}_{\mathrm{p}} $ = 4.0 s,$ {U}_{\mathrm{c}} $ = 0.10 m/s); b. strong current ($ {H}_{0} $ = 0.8 m,$ {T}_{\mathrm{p}} $ = 4.0 s,$ {U}_{\mathrm{c}} $ = 0.45 m/s). The numerical test in pure wave conditions with the same incident waves was carried out as a reference to assess the currents to wave attenuation (blue line). L is the length of the vegetated area.$ \Delta {H}_{\mathrm{p}\mathrm{w}} $ and$ \Delta {H}_{\mathrm{c}\mathrm{w}} $ stand for the wave height attenuation induced by a unit length of canopies for pure wave and combined current-wave flows in Eq. (28).
Figure 9. Variation of
$ {r}_{\mathrm{w}} $ ($ {r}_{\mathrm{w}}=\Delta {H}_{\mathrm{c}\mathrm{w}}/\Delta {H}_{\mathrm{p}\mathrm{w}} $ ) with different hydrodynamic combinations under the storm surge. The white solid line represents contour 1 ($ {r}_{\mathrm{w}}=1 $ ), indicating that the wave attenuation caused by vegetation has neither increased nor decreased in the combined current-wave flows compared to the pure wave conditions. Area I indicates a decrease in the amount of vegetation-induced wave height reduction. Area II indicates an increase in wave attenuation by vegetation when the currents become stronger under the same wave conditions.Table 1. Input parameters of vegetation characters
Region Vegetation character Length (x)/m Height ($ {h}_{\mathrm{v}} $)/m Diameter ($ {b}_{\mathrm{v}} $)/m Density ($ {N}_{\mathrm{v}} $)/(stem·m−2) Drag coefficient ($ {C}_{\mathrm{D}} $) Mudflat 15 0 0 0 0 Seedling zone 35 0.6 0.05 6 Re-$ {C}_{\mathrm{D}} $ Mature mangrove 20 1.8 0.15 2 Re-$ {C}_{\mathrm{D}} $ 
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