Impact of Patchy Vegetation on Wave and Runup Dynamics

Yongqian Yang

Dissertation submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulﬁllment of the requirements for the degree of

Doctor of Philosophy in Civil Engineering

Jennifer L. Irish, Chair Christopher J. Roy Nina Stark Robert Weiss

July 28, 2016 Blacksburg, Virginia

Yongqian Yang

ABSTRACT

Coastal regions are vulnerable to various natural processes, ranging from normal waves to extreme events. Given the flourishing development and large population along coastlines, various measures have been taken to mitigate the water-induced damage. Nature-based coastal protection, especially vegetation, has attracted unprecedented studies over the past two decades. To enhance understanding of this subject, this dissertation evaluates the impact of patchy vegetation on wave and runup dynamics along coastlines. Selecting from a prototype in Dalehite Cove, Galveston Bay, TX, results from a Boussinesq model (COULWAVE) showed patchy vegetation reduced up to 75% mean shoreward current in the mound-channel wetland systems. These vegetation patches also reduced the primary circulation around mounds, with a power-form relation between circulation size and various parameters (i.e., bathymetry, incident wave and vegetated roughness). Substituting spectral waves for regular waves in the similar wetlands, more energy was transferred into the higher frequencies. The impact of patchy vegetation on wave energy was frequency- and space-dependent, with increased energy observed in specific harmonics and locations. Comparison with unvegetated horizontal bathymetry demonstrated that mound-channel bathymetry was the dominant factor in transferring and dissipating wave energy, while vegetation patches added a fair contribution. As for extreme events, such as tsunamis, laboratory experiments and numerical simulations were conducted to assess the effectiveness of patchy vegetation with various roughness levels, spacings and sizes. Overall, vegetation patches reduced the most destructive loads onshore by up to 80%. Within-patch roughness variation only caused uncertainty on the hydrodynamics around the seaward patches, while the mitigation of extreme loads was not undermined. A logarithmic relation was observed between the protected area from extreme loads and the vegetated coverage. These findings will fill the knowledge gap of hydrodynamics in the presence patchy vegetation, and improve the engineering practice of coastal protection using nature-based infrastructure.

This material is base on a work supported by the National Sea Grant College Program of the U.S. Department of Commerce’s National Oceanic and Atmospheric Administration via Grant No. NA14OAR4170102; the National Oceanic and Atmospheric Administration, U.S. Department of Commerce, under Award No. NA14OAR4170093 to Virginia Sea Grant; and the National Science Foundation via Grant No. CMMI-1206271. This work used resources of Advanced Research Computing at Virginia Tech. Impact of Patchy Vegetation on Wave and Runup Dynamics

Yongqian Yang

GENERAL AUDIENCE ABSTRACT

As a transition zone between land and water, coasts are subject to a wide range of natural processes. Normal processes include waves, tides and currents, while disasters like storm surge and tsunami are defined as extreme processes. Both normal and extreme processes can undermine the integrity of coastal communities by causing erosion and flooding. Given the flourishing development and large population along coastlines, various measures, including hard structures and vegetation, have been taken to mitigate water-induced damage. By far, there is not as much research on the protection by vegetation as there is on hard structures. Moreover, in nature, areas of coastal vegetation are often divided into patches separated by unvegetated open spaces. This dissertation aims to enhance understanding of how water flows interact with vegetation patches along coastlines. The results from experiments and computer modeling demonstrated that the impact of patchy vegetation on water flows were dependent on wave condition, bathymetry and patch configuration. Overall, though higher wave energy might occur in specific situations, patchy vegetation helped to reduce most negative water-induced effects. These findings will improve the management and application of nature-based infrastructure to coastal protection. These nature-based methods are more ecologically beneficial and sustainable than hard structures.

I want to express my sincerest gratitude to my advisor, Dr. Jennifer Irish. Throughout my Ph.D. life, she has kept providing professional guidance on my research and encouraging me to overcome all difficulties. With her support, I had the first opportunity in my life to lead a series of large-scale tsunami experiments in Oregon State University, and to develope collaborations across multiple universities and agents. In addition, Dr. Irish has been very supportive to my career choice since she knew my work preference as an engineer. She offered sufficient flexibility on my research schedule, which allowed me an important internship in a consulting company (Taylor Engineering, Inc.) during the summer of 2015. In addition, I want to thank Dr. Patrick Lynett for his instructions on COULWAVE modeling. All suggestions, comments and supports from my committee members, Dr. Christopher Roy, Dr. Nina Stark and Dr. Robert Weiss are also sincerely acknowledged. Your earnest attitude on science and research has deeply inspired me. Last but not the least, I want to thank my dearest parents and wife. Thank you for understanding and supporting my decision to pursue this Ph.D. degree in the U.S. It was a hard decision and a big challenge, but after all the days of hard work and suffering, I finally manage to complete the task. The honor also belongs to all of you.

iv Attribution

As the primary advisor of Yongqian Yang, Jennifer Irish provided scientiﬁc guidance on the methods and analysis throughout this dissertation, and helped to edit all manuscripts submitted to peer-reviewed journals. Patrick Lynett, professor in University of South California, provided the source code of COULWAVE with instructions. All co-authors and aﬃliations of the three journal manuscripts are acknowledged at the beginning of each chapter. Con- tributions from other colleagues are described in the following. Chapter 2: Malanie Truong and Kerri Whilden conducted the experiments in the Haynes Coastal Engineering Laboratory at Texas A&M University and processed the raw experimental data for model validation. Chapter 3: Amir Zainali and Rui Sun provided suggestions on setting the boundary conditions in the model. Karen Duhring shared her expertise in nature-based shoreline protection. Chapter 4: Melora Park, Jason Killian and Timothy Maddux helped to operate the instru- ments in the O.H. Hinsdale Wave Research Laboratory at Oregon State University during the experiments. Amir Zainali, Roberto Marivela-Colmenarejo, Youn Kyung Song and Stephanie Smallegan helped to conduct the experiments. Youn Kyung Song also developed the initial version of the optical technique.

v Contents

1 Introduction 1

2 Numerical investigation of wave-induced flow in mound-channel wetland systems 6 2.1 Abstract ...... 7 2.2 Introduction ...... 7 2.3 Methodology ...... 9 2.3.1 Wetland Layout ...... 9 2.3.2 Numerical Model Theory ...... 10 2.4 Model Calibration and Validation ...... 12 2.5 Numerical Results ...... 15 2.5.1 Wave Reflection Influence ...... 15 2.5.2 Mean Flow Field Characteristics ...... 15 2.5.3 Spatial Circulation Characteristics ...... 20 2.6 Discussion ...... 23 2.7 Summary & Conclusions ...... 25

3 Evolution of wave spectra in mound-channel wetland systems 28 3.1 Abstract ...... 29 3.2 Introduction ...... 29 3.3 Methodology ...... 30 3.3.1 Boussinesq Model ...... 30

vi 3.3.2 Study Domain ...... 31 3.3.3 Data Analysis ...... 33 3.4 Results ...... 33 3.4.1 Signiﬁcant Wave Height ...... 34 3.4.2 Evolution of Wave Spectra ...... 38 3.5 Discussion ...... 39 3.5.1 Non-uniform spatial distribution of wave energy in mound-channel systems ...... 39 3.5.2 Impact of bathymetry on wave dissipation ...... 42 3.5.3 Impact of wave period on wave dissipation ...... 42 3.5.4 Implications of spectral evolution on sediment transport ...... 45 3.6 Conclusions ...... 45

4 Impact of patchy vegetation on tsunami dynamics 47 4.1 Abstract ...... 48 4.2 Introduction ...... 48 4.3 Methodology ...... 50 4.3.1 Experimental Design ...... 50 4.3.2 Numerical Model Description and Setup ...... 52 4.3.3 Momentum Flux ...... 54 4.4 Results ...... 54 4.4.1 Impact of Roughness Patches on Momentum Flux ...... 54 4.4.2 Impact of Roughness Patches on Runup Height ...... 57 4.4.3 Impact of Planform Roughness Size on Momentum Flux ...... 58 4.5 Discussion ...... 61 4.5.1 Conclusions ...... 62

5 Conclusions 65 5.1 Appendix A ...... 78

vii 5.1.1 Optical Technique for Estimating Bore-front Velocity ...... 78 5.1.2 Experimental Bore Front Data ...... 79 5.2 Appendix B ...... 79 5.2.1 Model Calibration and Validation ...... 79

viii List of Figures

1.1 (a) Breakwaters in Norfolk, VA, U.S. (photo by Yongqian Yang); (b) levee in Gretna, LA, U.S. (photo by Infrogmation, CC BY-SA 3.0, https://commons. wikimedia.org/w/index.php?curid=88220); (c) seawall in Ventnor, Isle of Wight, U.K. (photo by Oikos-team at English Wikipedia, https://commons. wikimedia.org/w/index.php?curid=2746549)...... 3 1.2 (a) Wetland vegetation growing in patches (Chesapeake Bay Program, http: //www.chesapeakebay.net/issues/issue/wetlands); (b) patchy vegetation (marked by red circles) in Gearhart, OR (Google Earth 2014)...... 4

2.1 (a) Side view of laboratory setup (in m) (modified from Truong (2011)); (b) measurement locations of wave gauge locations (∗) for 8.66 m mound separation, scaled from (a) to show the domain of interest...... 10 2.2 Offshore free surface elevation (normalized by incident wave height) of two experimental trials (triangle and circle) and numerical data (solid line) with (a) 0.50-m water level and 0.17-m incident wave height; (b) 0.36-m water level and 0.06-m incident wave height. Free surface elevation (normalized by incident wave height) of two experimental trials (triangle and circle) and numerical data (solid line) at x = 22 m (behind the mounds) with (c) 0.50- m water level and 0.17-m incident wave height; (d) 0.36-m water level and 0.06-m incident wave height...... 13 2.3 Time-averaged velocity fields and mean water levels (in m) of 0.50 m (a - c) and 0.36 m (d - f) water levels in non-vegetated setups (incident waves travel from left to right). Symmetry about the centerline of the domain is obtained in each simulation, so only subdomains around the centerline are shown. . . 17 2.4 Cross-shore profile of mean current profiles through the channel (a and d) and over the mound (b and e) with 0.50-m (a and b) and 0.36-m (c and d) water levels. The legend denotes the mound separation distances. Panes (c) and (f) show the side view of basin bed elevation through the mound centerline. Vertical dotted lines correspond to the edges of the mound, while horizontal dashed lines show U =0...... 18

ix 2.5 Cross-shore profiles of mean current and significant wave height over the mound (a - d) and channel (f - i). Panes (a), (b), (f) and (g) are for 0.50-m water level and 0.17-m incident wave height, while (c), (d), (h) and (i) are in 0.36-m water level and 0.06-m incident wave height. The legend denotes the mound separation distances and vegetated versus non-vegetated conditions. Panes (e) and (j) show the side view of basin bed elevation through the mound centerline. Vertical dotted lines correspond to the edges of and mound, while horizontal dashed lines show U = 0...... 19 2.6 Percent difference in mean current between non-vegetated and vegetated setups for different mound separations and water levels...... 20 2.7 Swirling strength (in s−1) for 0.50-m depth (a - f) and 0.36-m depth (g - l) cases. Panes (a) - (c) and (g) - (i) are non-vegetated setups with different mound separations, while (d) - (f) and (j) - (l) are the corresponding vegetated setups. The red rectangles mark the primary circulations on the middle mounds using a swirling strength threshold of 0.01 s−1. Incident waves travel from left to right...... 22 2.8 Dimensionless relationship between mound separation distance and rip current amplitude. Stars denote simulations for validation...... 24 2.9 Dimensionless size of swirling strength versus friction coefficient on the top of mound. Stars denote simulations for validation...... 25

3.1 (a) Bathymetry (in m) for the 7.02-m mound spacing and 0.50-m offshore depth. Cross-shore channels are along y = ±3.51 and ±10.53 m. Vegetation is represented by higher friction on top of the mounds, marked by black dotted circles. Waves propagate from left to right. The mounds are assumed to distribute periodically and infinitely in the alongshore direction. To save computational time, we only model a narrow alongshore-symmetric portion of the domain, and mirror it into infinity in the alongshore direction. (b) Transect of bathymetry along centerline (y = 0 m). Horizontal bathymetry without mounds and channels (constant depth after x = 17.0 m) is simulated for reference...... 32

3.2 Incident TMA spectra with significant wave period Ts = 1.5 s (solid line), 2.0 s (dashed line), 3.0 s (dash-dot line) and 4.0 s (dotted line). Significant wave height Hi = 0.14 m and offshore depth ho = 0.50 m...... 33 3.3 Instantaneous free surface and wave-averaged current in (a, c) non-vegetated scenario and (b, d) vegetated scenario, all at time step t = 160 s. Offshore depth ho = 0.50 m, significant wave period Ts = 2 s, incident wave height Hi = 0.14 m and mound spacing S = 7.02 m. Waves propagate from left to right. Black dotted lines depict the ramp and mounds in Fig. 3.1...... 35

x 3.4 Contours of significant wave height (in m) for non-vegetated scenarios (a, d, g), significant wave height (in m) for vegetated scenarios (b, e, h) and percent difference between non-vegetated and vegetated scenarios (c, f, i). Red and blue colors in (c, f, i) indicate wave height increase and decrease by vegetation. (a, b, c), (d, e, f) and (g, h, i) are for mound spacing of 5.48 m, 7.02 m and 8.66 m, respectively, where offshore depth ho = 0.50 m and significant wave period Ts = 2 s. Panels (j-r) are the same contours with ho = 0.36 m and Ts = 2 s. Waves propagate from left to right. Black dotted lines depict the ramp and mounds in Fig. 3.1...... 36 3.5 Contours of significant wave height (in m) for non-vegetated scenarios (a, d, g, h), significant wave height (in m) for vegetated scenarios (b, e, h, j) and percent difference between non-vegetated and vegetated scenarios (c, f, i, k). Red and blue colors in (c, f, i, k) indicate wave height increase and decrease by vegetation. Panels from top to bottom are for significant wave periods of 1.5 s, 2 s, 3 s and 4 s, respectively, where offshore depth ho = 0.50 m and mound spacing S = 7.02 m. Waves propagate from left to right. Black dotted lines depict the ramp and mounds in Fig. 3.1...... 38 3.6 Contours of wave energy (in m2) for non-vegetated scenarios (a, d, g), wave energy (in m2) for vegetated scenarios (b, e, h) and percent difference between non-vegetated and vegetated scenarios (c, f, i). Red and blue colors in (c, f, i) indicate wave energy increase and decrease by vegetation. (a, b, c), (d, e, f) and (g, h, i) are for wave energy around the dominant frequency, second harmonic and third harmonic, respectively, where offshore depth ho = 0.50 m, significant wave period Ts = 2 s and mound spacing S = 7.02 m. Panels (j-r) are the same contours with ho = 0.36 m and Ts = 2 s. Waves propagate from left to right. Black dotted lines depict the ramp and mounds in Fig. 3.1. . . 40 3.7 Contours of wave energy (in m2) for non-vegetated scenarios (a, d, g), wave energy (in m2) for vegetated scenarios (b, e, h) and percent difference between non-vegetated and vegetated scenarios (c, f, i). Red and blue colors in (c, f, i) indicate wave energy increase and decrease by vegetation. (a, b, c), (d, e, f) and (g, h, i) are for wave energy around the dominant frequency, second harmonics and third harmonics, respectively, where offshore depth ho = 0.50 m, significant wave period Ts = 1.5 s and mound spacing S = 7.02 m. Panels (j-r) are the same contours with Ts = 4 s. Waves propagate from left to right. Black dotted lines depict the ramp and mounds in Fig. 3.1...... 41

xi 3.8 (a) Percent difference of significant wave height between mound-channel systems with and without vegetation (hollow symbols), and between vegetated mound-channel systems and non-vegetated horizontal bathymetry (filled symbols). Percent difference of wave energy in the first (solid lines), second (dashed lines) and third (dotted lines) harmonics (b) between mound-channel systems with and without vegetation; (c) between vegetated mound-channel systems and non-vegetated horizontal bathymetry. Legends in panel (b) also apply to panel (c). Circles and triangles are for offshore depth ho = 0.50 m and ho = 0.36 m. Significant wave period Ts = 2 s. Negative values indicate reduction by vegetation...... 43 3.9 (a) Percent difference of significant wave height between mound-channel systems with and without vegetation (hollow symbols), and between vegetated mound-channel systems and non-vegetated horizontal bathymetry (filled symbols). Percent difference of wave energy in the first (solid lines), second (dashed lines) and third (dotted lines) harmonics (b) between mound-channel systems with and without vegetation; (c) between vegetated mound-channel systems and non-vegetated horizontal bathymetry. Legends in panel (b) also apply to panel (c). Circles and triangles are for offshore depth ho = 0.50 m and ho = 0.36 m. Mound spacing S = 7.02 m. Negative values indicate reduction by vegetation...... 44

4.1 Planform view (a) and profile (b) of laboratory setup (in m) (from Irish et al. (2014)). The bigger star labels with numbers distinguish the selected ADV/sonic locations for analysis. Waves propagate from left to right. . . . . 51 4.2 Patches of different roughness scenarios. (a) Uniform low roughness (21 cylinders/patch); (b) uniform medium roughness (69 cylinders/patch); (c) non- uniform medium roughness (69 cylinders/patch); (d) uniform high roughness (129 cylinders/patch). For non-uniform roughness in (c), waves coming from left to right and from right to left define low-high roughness and high-low roughness, respectively. (e) and (f) are photos of one individual patch and shoreward view of patch array in the experiments, respectively...... 52 4.3 Experimental water elevation (a- d) and momentum flux (e - h). From left to right are locations in channel (1 and 4) and shoreward/seaward of patches (3 and 5) in Fig. 4.1a, respectively. All three scenarios have the same cylinder number but different within-patch spacings, i.e., uniform medium roughness (solid lines), high-low roughness (dashed lines) and low-high roughness (dotted lines)...... 55

xii 4.4 Simulated momentum flux difference (in %) between control scenario (no roughness) and each of the roughness scenarios. Cool and hot colors indicate reduction and increase cause by roughness patches, respectively. Waves propagate from top to bottom in each pane. Panes from left to right are control vs. low roughness, medium roughness, high roughness, high-low roughness and low-high roughness. Panes from top to bottom are during runup, flow reversal and withdrawal. Dashed line depicts initial still water line. Black circles are roughness patches. Arrows are velocity vectors. Gray depicts no change in momentum flux, and white depicts no inundation...... 56 4.5 Experimental runup heights shoreward of cross-shore channels (black histograms) and shoreward of patches (gray histograms) in different scenarios. Circles depict the simulated alongshore-averaged runup heights, because of the insignificant runup difference at the shoreward edges of patches and channels in the simulations. “Control” represents the scenario with no roughness patches...... 58 4.6 Simulated momentum flux difference (in %) between control scenario (no roughness) and different roughness sizes with medium roughness. Cool and hot colors indicate reduction and increase cause by roughness patches, respectively. Waves propagate from top to bottom in each pane. Panes from left to right are control vs. 0.6-m patches, 1.2-m patches, 1.6-m patches, 2.2-m patches and continuous roughness (between solid lines in e, j and o). Panes from top to bottom are during runup, flow reversal and withdrawal. Dashed line depicts initial still water line. Black circles are roughness patches. Arrows are velocity vectors. Gray depicts no change in momentum flux, and white depicts no inundation...... 59 4.7 Simulation results of maximum momentum flux with patch diameters of 0.8 m (triangles), 1.2 m (circles) and 2.0 m (squares). Dashed lines and dash- dotted lines are continuous roughness scenario and control scenario, respectively. Vertical dotted lines denote the centers of patches. The roughness scenarios correspond to the medium roughness level. (a) Comparison through cross-shore channels. (b) Comparison through patches...... 60 4.8 Fractional area protected from maximum momentum flux, in terms of roughness ratio (between roughness area and total area) and roughness level. Low roughness (triangles), medium roughness (squares) and high roughness (circles) scenarios are all simulated with patch size from 0.6 to 2.2 m. Sveg is the area of vegetation-like roughness, SNV is the area between patches, S is the total area on the slope (S = Sveg + SNV ), and Sd is the area protected from maximum momentum flux (excluding patches). fveg and fNV are friction values for vegetation-like roughness and no-roughness background, respectively. Solid lines represent Eq. 4.4 with different frictions...... 63

xiii 5.1 (a) Bore fronts traced by the algorithm every 5 frames in the medium roughness scenario. Triangles are ADV/sonic locations measured in experiments. Numbers 1 − 6 correspond to the selected ADV/sonic locations in Fig. 4.1 after mirrored into the symmetric sub-domain. (b)-(d) Cross-shore, alongshore and magnitude of bore velocities (in m/s) obtained from bore fronts. Waves propagate from top to bottom...... 80 5.2 Model validation with velocity (a - c) and water depth (d - f) on the slope, corresponding to Locations 2, 4 and 6 in Fig. 4.1a. Solid lines are simulation results, while dashed lines are experimental data. Star labels represent bore speed from the optical technique. Velocity√ is calculated as magnitude of cross- shore and alongshore components (i.e., u2 + v2) during runup (positive) and withdrawal (negative). Correlation values (R2) between measurements and simulations are also shown in each pane. Optical technique and bore velocity ﬁelds are presented in Appendix A...... 81

xiv List of Tables

2.1 Model validation of signiﬁcant wave height ...... 14 2.2 Application of Eq. 2.6 and Eq. 2.8 to ﬁeld scale ...... 25

3.1 Matrix of simulation scenarios and energy transfer across harmonics . . . . . 34

4.1 Matrix of all experimental scenarios ...... 53

xv Chapter 1

Introduction

This dissertation investigates how patchy vegetation influences wave dynamics in nearshore regions, using both laboratory experiments and numerical modeling. In nature, due to various factors, vegetation does not always grow uniformly over the horizontal area. Rather, open spaces with little or no vegetation usually divide the vegetated area into separated patches. Thus, unlike the majority of studies on this subject, which focused on continuous vegetation in planform (having no open spaces), we select a more realistic configuration: patchy vegetation. Coastal regions are an important transition zone connecting land and water. In history, coastlines were originally used to provide services for navy and transportation (Dean and Dalrymple, 2004). Over the years, owing to the desirable environment, tourism entertain- ment and water-related resources, coastal regions have been developed into centers of various businesses. According to Martnez et al. (2007), 63% of the world’s megacities were located along coastlines, and most of them still continue to expand in size. In the meantime, more and more people prefer to settle down in coastal regions. McGranahan et al. (2007) estimated that 10% of the global population (or 13% of the urban population) lived along the coasts less than 10 m above sea level, which accounted for only 2% of the world’s total land area. Though improving quality of life, human activities in these regions might conflict with natural coastal processes. Coastal processes in nature range from normal conditions (e.g., wave, current and tide) to extreme events (e.g., tsunami and storm surge). In general, nature itself is able to manage the equilibrium between water and land; however, with the interaction from human activities, some concerns start to arise. One of the typical threats to coastal development is erosion by sediment transport. For instance, in Louisiana, U.S., the average land loss from 1985 to 2010 was as high as 42.9 km2/year (e.g., Couvillion et al., 2011; Karimpour et al., 2015). Infrastructure along these coastlines is at higher risks of being undermined. Natural disasters, such as tsunamis and storm surges, also pose great threats to coastal communities. Two recent tsunami events in the Indian Ocean (2004) and Japan (2011) killed almost 300,000

1 Yongqian Yang Chapter 1. Introduction 2 people and caused billions of dollars of economic loss (e.g., Lay et al., 2005; Liu et al., 2005; Mori et al., 2011). Hurricane Sandy (2012) and Typhoon Haiyan (2013) further raised public awareness about the vulnerability of coastal regions to flooding hazards (e.g., Gross, 2014; Sutton-Grier et al., 2015). All these destructions, either by moderate or extreme events, are warning us about the necessity of accounting for the impact of coastal processes in coastal engineering practice. With the flourishing development of coastal communities, scientists and engineers have been making efforts since last century to protect coastlines. In history, the application of artificial hard structures, such as breakwaters, levees and seawalls, was the preferred approach for coastal protection (Figure 1.1). These structures are effective in reducing the sediment loss by erosion (e.g., Board et al., 2014; Dean and Dalrymple, 2004) and mitigating the damage by natural hazards (e.g., Irish et al., 2013; Sato et al., 2014; Thomas and Cox, 2011). Yet, hard structures also bring about negative effects to the local and adjacent areas. Ecosystems in the presence of hard structures are usually degraded due to the compromised biological and shoreline processes (e.g., Bilkovic and Roggero, 2008; Toft et al., 2013). Armoring of shoreline may even reduce beach width and cause downdrift erosion (e.g., Basco, 2006; Dean and Dalrymple, 2004; Dugan et al., 2008). Moreover, hard structures are expensive, costing up to millions of dollars for every mile (e.g., Board et al., 2014; Linham et al., 2010). Recently, alternative protection with nature-based infrastructure has become more and more popular. Nature-based features, especially vegetation, are more environmentally friendly and compatible with coastal ecology. In addition, according to Cunniff (2015), coastal protection with vegetation could be more cost-effective than hard structures when used appropriately. Studies on this subject so far have provided engineers with confidence in using vegetation to protect coastlines (Cunniff and Schwartz, 2015). There is sufficient evidence that coastal vegetation can reduce the negative impact of wave activities and mitigate extreme natural hazards. Analytical solutions and empirical models demonstrated the capacity of vegetation in attenuating both regular and irregular waves (e.g., Dalrymple et al., 1984; Kobayashi et al., 1993; Méndezand Losada, 2004; Méndez et al., 1999). Further research with field studies, laboratory experiments and numerical simulations has proven the role of vegetation in reducing wave energy (e.g., Augustin et al., 2009; Morgan et al., 2009; Tang et al., 2015). Post-tsunami surveys by Kathiresan and Rajendran (2005) and Danielsen et al. (2005) showed that vegetation reduced the tsunami- caused damage and deaths as well. Recent studies indicated that the impact of vegetation on wave dynamics depends on hydrodynamic conditions, such as wave frequency (e.g., Anderson and Smith, 2014; Jadhav et al., 2013), energy level (Ondiviela et al., 2014) and current (Paul et al., 2011). Besides, properties of the vegetation itself, such as density and stiffness, also made a difference on the flow characteristics (e.g., Bouma et al., 2005, 2010; Paul and Amos, 2011; Tanaka et al., 2007). On one hand, these studies reveal the potential of vegetation in protecting coastlines. On the other hand, the majority of these studies are on continuous vegetation in planform, while studies on wave dynamics within patchy vegetation are still limited. Yongqian Yang Chapter 1. Introduction 3

(a)

(b) (c)

Figure 1.1: (a) Breakwaters in Norfolk, VA, U.S. (photo by Yongqian Yang); (b) levee in Gretna, LA, U.S. (photo by Infrogmation, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=88220); (c) seawall in Ventnor, Isle of Wight, U.K. (photo by Oikos-team at English Wikipedia, https://commons. wikimedia.org/w/index.php?curid=2746549).

Patchy vegetation commonly exists in nature worldwide (Figure 1.2), usually attributed to the balance of positive interaction and negative competition between plants (e.g., Bertness and Yeh, 1994; Rietkerk et al., 2004; Rietkerk and van de Koppel, 2008). When vegetation was planted in patches in wetlands, Silliman et al. (2015) reported a higher growth rate, and Balke et al. (2012) observed enhanced sediment accretion that induced additional marsh growth. Unlike continuous coverage, patchy vegetation does not provide protection in all situations. Higher risks are likely to occur in the open spaces, or channels, between patches (e.g., Irish et al., 2014; Thuy et al., 2009; Vandenbruwaene et al., 2011). Systematically understanding how ﬂows interact with such vegetation patches is essential to improving the application of nature-based features to coastal protection. To complement our understanding of vegetated ﬂuid dynamics, this dissertation applies both laboratory experiments in a large- scale wave basin and numerical simulations with a Boussinesq model to determine the impact of patchy vegetation on various conditions. In coastal wetlands, vegetation patches can induce variability in bathymetry, leading to the Yongqian Yang Chapter 1. Introduction 4

Figure 1.2: (a) Wetland vegetation growing in patches (Chesapeake Bay Program, http://www. chesapeakebay.net/issues/issue/wetlands); (b) patchy vegetation (marked by red circles) in Gearhart, OR (Google Earth 2014). formation of mounds and channels. To analyze the wave-induced flow, Chapter 2 (Yang et al., 2015) conducts a numerical investigation on the mound-channel wetland systems, whose prototype is in Dalehite Cove, Galveston Bay, TX. Results from a Boussinesq model, COULWAVE, indicate the effects of mound spacing, water depth and wave height on the hydrodynamics. Patchy vegetation on the tops of mounds causes 15% change in significant wave height and reduces shoreward current by 75%. Sizes of the primary circulation adjacent to mounds also decrease in the presence of vegetation patches. Dimensional analysis results in two empirical equations, which may serve as first estimates for the mean seaward current and primary circulation size in mound-channel wetlands. To analyze the impact of mound-channel wetland systems on wave energy of different frequencies, Chapter 3 extends the study of regular waves in Chapter 2 to spectral waves, with periodic mound distribution alongshore. Simulations show energy transfer toward high harmonics in the wetland systems. The impact of patchy wetlands depends on both space and frequency; vegetation causes more attenuation on the high-frequency spectra, while energy amplification occurs in specific locations and harmonics. The bathymetry of mound-channel is the dominant factor in transferring and dissipating wave energy, and vegetation patches provide a fair additional contribution. In Chapter 4, we further our study on the potential of patchy vegetation in mitigating tsunami damage on a slope. Wave-basin experiments were conducted, and a Boussinesq model was used to extend the range of the experiments. Experimental and numerical results reveal transient load amplification in specific locations; however, vegetation patches are capable of reducing the most destructive loads of tsunamis. Within-patch roughness variation, which can result from seasonal variability or vegetation death/regrowth, causes uncertainty on the hydrodynamics around the seaward patches. A logarithmic equation was developed, which may be used to estimate the protected area from extreme hazards by patchy vegetation. In Chapter 5, we summarize the main findings and conclusions of the three projects in this Yongqian Yang Chapter 1. Introduction 5 dissertation, and point out the future work in studying hydrodynamics in the presence of patchy vegetation. Chapter 2

Numerical investigation of wave-induced ﬂow in mound-channel wetland systems

Yongqian Yang1, Jennifer L. Irish1, Scott A. Socolofsky2 1Department of Civil and Environmental Engineering, Virginia Tech, Blacksburg, VA, USA. 2Department of Civil Engineering, Coastal and Ocean Engineering Division, Texas A&M University, College Station, TX, USA. Citation: Yang, Y., Irish, J.L., Socolofsky, S.A., 2015. Numerical investigation of wave- induced ﬂow in mound-channel wetland systems. Coastal Engineering 102, 1-12.

6 Yongqian Yang Chapter 2. 7

2.1 Abstract

Coastal wetlands are an important ecosystem in nearshore regions, but they are also significant in affecting the flow patterns within these areas. Wave-induced flow in wetlands has complex circulation characteristics because of the interaction between waves and plants, especially in discontinuous vegetation. Here, a numerical investigation is performed to analyze the wave-averaged flow in vegetated mound-channel systems. Different water levels, vegetated conditions, and mound configurations are studied with the COULWAVE (Cornell University Long and Intermediate Wave) Boussinesq model. Model simulations show rip currents in the mound-channel systems, whose strength varies with different mound separation distances. The relative influence of vegetation depends on both mound configuration and water level. Approximately a 15% change in significant wave height results as waves propagate over the vegetated mounds, while up to a 75% decrease in the mean shoreward flow speed through vegetation is observed. In addition, vegetation influences the spatial distribution of mean water level within the wetlands. Dimensional analysis shows that rip current strength and primary circulation size depend on mound spacing, water depth, wave height, and vegetation cover.

2.2 Introduction

As a transition region between ocean and land, wetlands are significant ecosystems that maintain water quality, provide natural habitat for a variety of species, and slow down erosion (Gacia and Duarte, 2001; Shutes, 2001; Thullen et al., 2002). Besides its ecological function in coastal regions, wetland vegetation also influences wave dynamics. During the past two decades, studies have elucidated the potential of coastal wetlands to mitigate flow impact in extreme events and protect onshore infrastructure (e.g., Kobayashi et al., 1993; Loder et al., 2009; Shafer et al., 2003; Wamsley et al., 2010). With the projected increase in extreme weather events from global climate change and the rising population at the coast, using vegetation as a natural coastal buffer from wave impact remains an attractive research topic, especially in developing countries with wide coastlines. In previous research, two common methods for studying waves in wetlands are scaled laboratory experiments with artificial or live vegetation (e.g., Anderson and Smith, 2014; Augustin et al., 2009; Bouma et al., 2005, 2010; Vandenbruwaene et al., 2011) and numerical simulations (e.g., Huang et al., 2011; Suzuki et al., 2012). Though these studies are efficient in learning the wave height transformation through vegetation coverage and calibrating the drag effect by vegetation, their bathymetric layouts have been relatively simple. Bathymetry in these studies is either constant depth or a plane slope, while in reality wetlands typically consist of vegetated mounds separated by channels. In addition, no studies have focused on the quantification of vegetation’s effect on the wave- Yongqian Yang Chapter 2. 8 induced flow circulation within wetlands. Rip currents are seaward jet flows from the surf zone with relatively higher velocity. They are commonly observed in nearshore regions with varying bathymetry, especially bar-channel systems. The variability in bathymetry induces alongshore variation of wave breaking around the bar-channel system, causing relatively more intense breaking across the bars. The process of wave pump model for rip current (e.g., Nielsen et al., 2001, 2008) by wave breaking raises water to higher level above the bars, compared with water level in the channels. This mechanism results in variations in significant wave height and mean water level distributions, which provides the primary driving force for alongshore flows feeding rip channels (Dalrymple et al., 2011; MacMahan et al., 2006). Rip currents are important processes to transport coastal pollutants, nutrients and sediments seawards, which may also cause erosion to shorelines. Since both natural and constructed wetlands typically consist of mound-channel systems, it is necessary to study the characteristics of rip current potential within these areas. Though similar to typical rip current phenomenon in bar-channel bathymetry, the circulation characteristics within discontinuous wetlands tend to be more complex. Because of the transient nature of rip currents, field studies with stationary instrument deployments suffer from the difficulty in measuring changing bathymetry and flow patterns simultaneously (e.g., Haller et al., 1997; MacMahan et al., 2006). Basin-scale laboratory experiments could provide controlled conditions with better repeatability, but the tradeoff between measurement resolution and instrument interaction may affect the accuracy of the results. In these aspects, numerical simulation has its edge over field and laboratory studies. Using a basin-scale laboratory experiment and the COULWAVE Boussinesq model with emergent and near-emergent vegetation setups, Augustin et al. (2009) observed that wave height through a continuous rectangular vegetation region decreased more significantly than in the adjacent non-vegetated area. The generated alongshore wave height gradient then attempted to reach equilibrium with energy focusing towards the low wave height area, resulting in locally higher wave height behind the vegetation patch. Bradley and Houser (2009) observed an increase in wave height through a distance of the submerged seagrass in their field experiment. A similar wave height increase could be predicted by the model of Méndez et al. (1999), which incorporated the effect of wave reflection. Bradley and Houser (2009) hypothesized that wave height increase was attributed to the seagrass blades’ obstruction acting like a bathymetric step that decreased wavelength and increased wave height through shoaling. Overall, these various phenomena in previous research imply that wave height evolution within vegetation is case-dependent and difficult to predict. This complexity may be further amplified in complex vegetated mound-channel bathymetry. Moreover, the efficiency of vegetation in wave dissipation is dependent on various parameters, such as stem stiffness, density and incident flow conditions (e.g., Bouma et al., 2005; Ondiviela et al., 2014; Paul et al., 2011; Vandenbruwaene et al., 2015), and significant protection against flow impact is not always guaranteed. For instance, according to a literature review by Ondiviela et al. (2014), seagrass does not protect the shoreline in all cases, and the optimal setups are with shallow depth and low-energy wave conditions. Vandenbruwaene et al. (2011) also reports Yongqian Yang Chapter 2. 9 potential flow acceleration within discontinuous vegetation patches. This paper focuses on a more complicated bathymetric layout with a mound-channel system, whose prototype is Dalehite Cove in Galveston Bay, Texas, US. First, we introduce the laboratory experimental design used for model validation and the numerical model background. Then, model calibration and validation are conducted with experimental data. Third, numerical results of significant wave height, rip current, water level distribution, and swirling strength of the mean flow are analyzed. Finally, two dimensionless relations for these flow phenomena are developed, followed by conclusions.

2.3 Methodology

2.3.1 Wetland Layout

Truong (2011) and Truong et al. (2014) conducted experiments in a 36.6 × 22.9 × 1.5 m wave basin in the Haynes Coastal Engineering Laboratory at Texas A&M University, US (Fig. 2.1). Three concrete conical-frustum mounds with 5.38 m bottom diameter, 2.02 m top diameter and 0.08 m height were constructed in a row 20.55 m from the wavemaker, representing the mounds in Dalehite Cove. The scale factor between the physical model and the prototype was 1 : 6.5, using Froude scaling based on surveys by HDR Engineering, Inc in August 2009. The vegetation was represented by 0.016-m diameter and 0.077-m height rigid wooden dowels affixed to the tops of the mounds and two wave conditions. The total stem number was 154, resulting in a stem density with 48 stems/m2 (Fig. 1 in Truong et al. (2014)). Three distances between mounds’ centers (S = 5.48 m, 7.02 m and 8.66 m), two water levels (0.50 m and 0.36 m), and two wave conditions (wave height 0.17 m and 0.06 m) were tested in the experiments. An instrument array with 19 capacitance wave gauges and 5 Acoustic Doppler Velocimeters were mounted on a moving bridge to map water surface elevation and induced current along cross-shore regions. Both non-vegetated and vegetated mounds were tested for each setup to study the influence of vegetation. More details about the experimental design are described in Truong (2011) and Truong et al. (2014). A reference wave gauge was fixed in the offshore region to estimate the repeatability of the incident wave condition. Most experimental trials had approximately 5% variability in the wave gauge measurements. The accuracy of the Nortek Vectrino ADVs used in the experiment was 0.5% of the measured value plus 1 mm/s uncertainty. For the measured current range in the experiments, the total theoretical uncertainty of ADV measurement was within 1%. More details about the experimental data analyses are described in Truong (2011) and Truong et al. (2014). Yongqian Yang Chapter 2. 10

(a)

(b) 20

ramp 15

10 alongshore (m)

↑ v → u

0 10 15 20 25 30 cross−shore (m)

Figure 2.1: (a) Side view of laboratory setup (in m) (modiﬁed from Truong (2011)); (b) measurement locations of wave gauge locations (∗) for 8.66 m mound separation, scaled from (a) to show the domain of interest.

2.3.2 Numerical Model Theory

In research of wave propagation in shallow and intermediate depth conditions, the Boussinesq- type equations are widely applied in both one- and two-dimensional horizontal applications. In previous studies, Boussinesq modeling was also successfully applied in research of rip current in bar-channel system and jet-like current by bathymetry variability (e.g., Chen et al., 1999, 2000). The numerical model used here, COULWAVE, is originally based on the Boussinesq-type equations in Liu (1994), with several additional terms to consider the eﬀect of bottom friction and wave breaking. This depth-integrated model is applicable to Yongqian Yang Chapter 2. 11

simulation of fully nonlinear and weakly dispersive waves over variable bathymetry (Lynett and Liu, 2002; Lynett et al., 2008). Deﬁning the dimensionless variables as,

√ 0 0 0 0 (x, y) = (x ,y ) , z = z , t = ghot , λ ho λ 0 0 h = h0 , ζ = ζ , p = p , ho ao ρgao (u0,v0) 0 (u, v) = √ , w = w√ , ε gho ε/µ gho

the dimensionless governing equations (continuity and momentum equations) are (Lynett and Liu, 2002):

1 ∂h ∂ζ + + ∇ · [(εζ + h)u ] + H.O.T. = O(µ4), (2.1) ε ∂t ∂t α ∂u α + εu · ∇u + ∇ζ + H.O.T + R − R = O(µ4), (2.2) ∂t α α f b

where h is the local water depth, ζ is the free surface elevation, uα = (uα, vα) is the reference horizontal velocity vector at zα from still water level (Liu, 1994; Nwogu, 1993), Rf is the bottom friction eﬀect, Rb is the wave breaking eﬀect, ε is the ratio between wave amplitude and depth ( ao ) for nonlinearity, µ is the ratio between depth and wavelength ( ho ) for fre- ho λ quency dispersion and H.O.T is the higher order nonlinear and dispersive terms in the order of O(µ2) (e.g., Løvholt et al., 2013; Lynett and Liu, 2002; Lynett et al., 2008, 2002).

ub|ub| The influence of vegetation is accounted for within the bottom friction term, Rf = f h+ζ , where f is the non-dimensional friction coefficient and ub is the horizontal velocity vector at the bed. Such approximation for vegetation is reasonable for bulk roughness, given the difficulty and high computational cost in modeling individual plants in large domains. The higher quadratic bottom friction used to represent vegetation provides more resistance against incident flows, which could slow down wave celerity. In general, f is in the range of 10−3 to 10−2 for a normal seabed (Lynett et al., 2008). Here, the background friction effect of the basin and the influence of vegetation on the mounds are calibrated using the experimental data (Section 2.4). There are three common choices of friction parameters for simulating the vegetation’s effect, Manning coefficient (Loder et al., 2009), drag coefficient (Huang et al., 2011) and non-dimentional Darcy factor (Augustin et al., 2009). For this paper, the non-dimentional Darcy factor employed by Augustin et al. (2009) is used in the simulations. Experimental setups of the three mound configurations, two water levels and two wave conditions are simulated with the model. In addition, to further study the influence of wetland mound-channel systems on flow characteristics, eight additional mound-channel configurations are simulated using the same water levels and wave conditions as the laboratory experiments (Section 2.5). Yongqian Yang Chapter 2. 12

2.4 Model Calibration and Validation

Since this study emphasizes the influence of vegetation on the flow circulation and wave dissipation within mound-channel wetland systems under different conditions, experimental data with two water levels (0.50 m and 0.36 m), three mound separation distances (S = 5.38 m, 7.02 m and 8.66 m) and two wave heights (0.17 m and 0.06 m) in both non-vegetated and vegetated setups are used for model calibration and validation. Regular waves with a 2-s period are used, which is scaled from the prevalent wind-wave range observed in natural coastal wetlands. The Courant number is set as 0.1, and the grid size is chosen as 0.04 m. In order to study the wave-averaged characteristics within these mound-channel systems, each simulation is run for 100 seconds to ensure a sufficient number of waves for time-averaging. In the experiments, one offshore wave gauge was fixed seaward between the wavemaker and the edge of the 1 : 10 ramp in each experimental trial, providing reference records to verify the repeatability of the incident wave conditions from trial to trial. To ensure that the same incident wave condition is used in the numerical model, background friction coefficient is calibrated by best fit of numerical results to the experimental offshore wave gauge records. Figure 2.2 (a) and (b) show the comparison of free surface between the simulation and wave gauge measurement in the offshore region with 0.50-m and 0.36-m water levels. It is observed that, even with the same setup and incident wave condition, the experimental records between trials are slightly different in amplitude (circles and triangles in Fig. 2.2 (a) and (b)), so the simulated incident wave conditions can be regards as identical to experiments. Figure 2.2 (c) and (d) show the comparison of free surface between the simulations and wave gauge measurements at x > 22 m. Though the time series between the two are not perfectly matched in (c) and (d) due to the increased non-linearity effect observed both in the experiments and in the simulations, the corresponding significant wave heights are still in good agreement. Model validation is completed by comparing experimental significant wave heights (Hs) with numerical results. Significant wave height is calculated as four times the standard deviation of free surface time series, which is equivalent to four times the square root of moment of the wave spectra. To ensure analysis only of the stationary condition, the first few seconds of the simulated record are omitted from this calculation. Measurement from positions with repeatable significant wave heights (approximately 5% uncertainty) were used for in model validation.

Percent root mean square of error (%RMSE) of the Hs diﬀerence between experimental and numerical data is used to assess model validation:

q P 2 (Hs,exp−Hs,num) N %RMSE = P × 100%, (2.3) Hs,exp N

where Hs,exp and Hs,num are the experimental and numerical signiﬁcant wave heights, respectively. The vegetation friction coeﬃcients are determined according to the wave height Yongqian Yang Chapter 2. 13

1 (a) 0.5

/ H 0 ζ

−0.5

−1 50 55 60 65 70 75 80 85 90 95 100

1 (b) 0.5

/ H 0 ζ

−0.5

−1 50 55 60 65 70 75 80 85 90 95 100 t (s)

1 (c) 0.5

/ H 0 ζ

−0.5

−1 50 55 60 65 70 75 80 85 90 95 100

1 (d) 0.5

/ H 0 ζ

−0.5

−1 50 55 60 65 70 75 80 85 90 95 100 t (s)

Figure 2.2: Oﬀshore free surface elevation (normalized by incident wave height) of two experimental trials (triangle and circle) and numerical data (solid line) with (a) 0.50-m water level and 0.17-m incident wave height; (b) 0.36-m water level and 0.06-m incident wave height. Free surface elevation (normalized by incident wave height) of two experimental trials (triangle and circle) and numerical data (solid line) at x = 22 m (behind the mounds) with (c) 0.50-m water level and 0.17-m incident wave height; (d) 0.36-m water level and 0.06-m incident wave height. propagation through the vegetated mounds, calibrated as 0.10 for 0.50 m depth and 0.15 for 0.36 m depth. The higher vegetation friction in shallower depth is a result of stronger vegetation resistance through water column, and is consistent with the calibration results in Augustin et al. (2009). The %RMSE values of all validated experimental scenarios are summarized in Table 2.1. In most setups, the validation criteria %RMSE values are around 5%, with RMSE between 0.004 and 0.013 m. In addition, phase lags of free surface are calculatied from 21 spatial location pairs per mound spacing for both the experimental data Yongqian Yang Chapter 2. 14

Table 2.1: Model validation of signiﬁcant wave height

S (m) Vegetated Depth (m) H (m) fveg %RMSE Reﬂection [RMS (m)] channel mound 5.48 No 0.50 0.17 0.001 2.67 [0.005] 5.21% 4.93% 5.48 Yes 0.50 0.17 0.100 4.22 [0.008] 5.28% 5.47% 7.02 No 0.50 0.17 0.001 6.39 [0.013] 5.10% 5.54% 7.02 Yes 0.50 0.17 0.100 5.40 [0.010] 5.29% 4.86% 8.66 No 0.50 0.17 0.001 4.79 [0.010] 3.78% 5.29% 8.66 Yes 0.50 0.17 0.100 4.65 [0.008] 4.58% 5.60% 5.48 No 0.36 0.06 0.001 2.71 [0.004] 5.16% 4.21% 5.48 Yes 0.36 0.06 0.150 3.14 [0.005] 4.96% 3.56% 7.02 No 0.36 0.06 0.001 4.58 [0.004] 5.20% 5.67% 7.02 Yes 0.36 0.06 0.150 4.81 [0.004] 7.59% 4.40% 8.66 No 0.36 0.06 0.001 4.70 [0.004] 3.27% 4.08% 8.66 Yes 0.36 0.06 0.150 4.85 [0.004] 2.30% 5.74%

H: incident wave height; fveg: calibrated friction coeﬃcient of vegetated condition; RMS: root mean square

of diﬀerence between experimental and numerical Hs

and the simulation results. The differences in experimental and modeled phase lags, estimated using the root mean square erro, are about 0.6 rad (or 10%). Given the potential effect of the dynamic wave absorption at the wavemaker and the recirculation currents in the basin due to imperfect symmetry during the experiments, this phase lag difference between experiment and modeling is acceptable. In addition, simulated mean currents through five cross-shore transects between the mounds are compared with ADV measurements. Since the ADVs were used to measure velocity at a single point, at 0.4 times the still-water depth above the bottom, it is not directly comparable with the modeled depth-integrated velocity. Due to the concentration of wave mass transport in the upper water column, especially near the mound tops, ADV measurements below the troughs poorly resolve the induced currents (e.g., Faria et al., 2000; Haller et al., 2002; Svendsen, 2006). Thus, we use correlation statistics to evaluate model performance with respect to the ADV measurements, which will estimate the cross-shore profiles of velocity of experiment and simulation. Among all the experimental setups with 2-s regular waves, 60% and 71% of the cross-shore transects yield p-values lower than 0.10 and 0.15 when the ADV measurements and model results are compared. In this study, p-value represents the probability of rejecting the null hypothesis of non-correlation when the hypothesis is true. With p-value smaller than significance level, the correlation between experiment and simulation is significant (e.g., Ott and Longnecker, 2008). So with the significance level α = 0.10 and α = 0.15 for null-correlation hypothesis test in statistics, 60 − 70% of the modeled cross-shore transects are correlated with the measurements, while the discrepancy in other locations could be attributed to the different data acquisition methods (i.e., point measurement at specific depth by ADV versus depth-integrated velocity by modeling). Yongqian Yang Chapter 2. 15

Based on the validations with signiﬁcant wave height and mean current, the comparison results demonstrate satisfactory model performance.

2.5 Numerical Results

2.5.1 Wave Reﬂection Inﬂuence

To determine if wave reflection is a significant phenomenon in the model setup, a three wave gauge array is used in the numerical model (Isaacson, 1991; Mansard and Funke, 1980). In every simulation, two three-gauge arrays are located in the offshore region aligned with the mound and the channel, respectively. The reflection coefficients in all simulations are less than 7.6% (Table 2.1). Since the reflection coefficient remains low in all setups (similar to Anderson and Smith (2014)), the effect of wave reflection is assumed to be negligible in the following analyses.

2.5.2 Mean Flow Field Characteristics

Mound Spacing Inﬂuence on Current

Variability in bathymetry has a significant influence on rip current scale and strength (e.g., Dalrymple et al., 2011; MacMahan et al., 2006). Here, we analyse the simulation results to determine the influence of the mound-channel configuration on rip currents in wetlands. Figure 2.3 shows the time-averaged velocity fields and the spatial contours of mean water level (MWL) for the three non-vegetated mound configurations with two water levels. Since the overall setups are all symmetric about the centerline of the domain at y = 11.45 m, only the subdomains around the centerline are shown. The wave pump process lifts water above the mounds, leading to MWL gradient towards the channels. Rip currents driven by the wave pumping effect are observed in all setups, with shore-directed currents flowing over the mounds and feeding into along-coast channels behind the mounds. For the cases using a 0.50-m water level, the MWL gradient between wave setdown at and seaward of the mounds (x < 22 m) and wave setup shoreward of the mounds (x > 23 m) becomes more gradual with increasing mound separation. The local mean water depressions in channels are greatest for the narrowest mound separation (5.48 m), which also drives greater rip current strength (discussed later). With increasing mound separation, the wave setup region behind the mounds (warm color in the top panes in Fig. 2.3) is both retreating shoreward and becoming less concentrated in the alongshore direction, leaving wider space for current diffusion. Similarly, these phenomena are observed in the shallower simulations (right panes in Fig. 2.3). For the shallower water level case (0.36 m), the overall offshore wave setdowns and onshore wave setups are 40% and 30% less than those for the 0.50-m depth case, while Yongqian Yang Chapter 2. 16 the local water depressions in the rips are more obvious. These depressions in the shallower depth expand and shift shorewards with wider mound separation due to more channel space for wave energy diffusion. The rip current systems are also dependent on bathymetry (e.g., Brander and Short, 2000; Brander, 1999). To study the relationship between rip current strength and mound separation, additional scenarios with eight new mound separation distances (S = 6.02 m, 6.52 m, 7.52 m, 8.02 m, 9.02 m, 9.72 m, 10.52 m and 11.32 m) are simulated.The mean cross-shore current (U) presented in Fig. 2.4 is averaged in 1-m alongshore bins over the mound ((b) and (e)) in the basin’s centerline and through the channel center between the bottom edges of two adjacent mounds ((a) and (d)). These cross-shore profiles of mean U are shown in Fig. 2.4 for both 0.50-m and 0.36-m water levels with the bathymetry. In shallower depth, the overall rip current amplitudes are less than the deeper setup (Fig. 2.4 (a) and (d)). For both water depths, rip current amplitude decreases with increasing mound separation distance, which illustrates that with more space in the channel for rip current development, the current strength tends to diffuse and become less concentrated (Fig. 2.4 (a) and (d)). The cross-shore locations of maximum rip current shift shoreward as the channel widens. In contrast, the shoreward current amplitude over the mound is less sensitive to mound separation (Fig. 2.4 (b) and (e)). However, the current over the mound persists high further inland with wider mound separation. As the channel widens, it is likely that the weaker rip current steepens the incident waves to a lesser extent. As a result, incident waves may propagate farther inshore before breaking in the wider channels. Others have shown that farther shoreward wave penetration through the rip channel could generate a longshore radiation stress gradient that opposes the longshore pressure gradient (e.g., Haller et al., 2002; MacMahan et al., 2006). According to numerical results in this study, similar opposing alongshore gradients of radiation stress and mean water level for wider mound separations are observed. This phenomenon may reduce the feeder flow into the rip channels shoreward of the mounds as mound separation widens. In turn, the previous feeder flow into the channel, which is redirected by the opposing radiation stress from the wider channel, may stay aligned behind the mound, resulting in higher current speed shoreward of the mound.

Vegetation Eﬀect on Signiﬁcant Wave Height and Mean Current

Figure 2.5 (a), (b), (f) and (g) show the cross-shore distribution of mean U and Hs over the mound and through the channel for the 0.50 m water level setups, with and without vegetation. Wave height is slightly dissipated on the vegetated mound (around x = 20 − 22 m), but shoreward of the mound, Hs becomes higher than in the non-vegetated setups, regardless of the mound spacing (Fig. 2.5 (b)). The current strength over the mound is more sensitive to the roughness on the mound than to the mound separation distance. Unlike Hs, mean U is consistently dampened over the vegetated mound, when compared with the non-vegetated setups (Fig. 2.5 (a)). Through the channel, while the location of rip current maxima tends to move shoreward with increasing mound separation (see Section 2.5.2), Yongqian Yang Chapter 2. 17

Figure 2.3: Time-averaged velocity ﬁelds and mean water levels (in m) of 0.50 m (a - c) and 0.36 m (d - f) water levels in non-vegetated setups (incident waves travel from left to right). Symmetry about the centerline of the domain is obtained in each simulation, so only subdomains around the centerline are shown. Yongqian Yang Chapter 2. 18

5.48m 6.52m 7.02m 8.02m 8.66m 10.52m 0.20 0.20 (a) (d) 0.10 0.10 0.00 0.00 −0.10 −0.10 U (m/s) U (m/s) −0.20 −0.20 −0.30 −0.30 0.40 0.40 (b) (e) 0.30 0.30 0.20 0.20 0.10 0.10 U (m/s) U (m/s) −0.00 −0.00 −0.10 −0.10 0.40 0.40 (c) (f) 0.20 0.20 bed (m) bed (m) 0.00 0.00 16 18 20 22 24 26 16 18 20 22 24 26 cross−shore (m) cross−shore (m)

Figure 2.4: Cross-shore proﬁle of mean current proﬁles through the channel (a and d) and over the mound (b and e) with 0.50-m (a and b) and 0.36-m (c and d) water levels. The legend denotes the mound separation distances. Panes (c) and (f) show the side view of basin bed elevation through the mound centerline. Vertical dotted lines correspond to the edges of the mound, while horizontal dashed lines show U = 0.

vegetation tends to shift the maximum current’s location seaward. With the closest mound separation (5.48 m), since the channel is as narrow as 0.10 m between the adjacent edges of two mounds’ bottoms, the direct damping effect from the vegetated mound extends into the rip, significantly reducing the wave height in the channel. When mounds are separated farther, the extension of direct damping effect from mound vegetation becomes weaker into the channels. At the same time, the weakened current in the wider channels of vegetated setups (Fig. 2.5 (f)) allows waves to break farther inshore, so the corresponding wave heights in the rips are slightly higher (less than 10%) than in the non-vegetated setups (Fig. 2.5 (g)).

Similarly, Fig. 2.5 (c), (d), (h) and (i) show profiles of mean U and Hs for the 0.36- m water level. Mean U over the mound has similar trends as the deeper cases, but the differences in Hs between the non-vegetated and vegetated cases are more significant. With the shallower water level, the higher equivalent roughness results in much greater flow speed dissipation (Fig. 2.5 (c)). Such a sudden and sharp drop in current speed may significantly shorten wavelength within the vegetation on the mounds compared to the non-vegetated case. When the effect of velocity loss within the vegetation is sufficiently strong, the energy of the shortened waves would accumulate in vertical direction, which leads to increasing wave height over and behind the vegetated mounds (Fig. 2.5 (d)). Through the channel, the current does not decrease consistently in the cross-shore direction, as in the deeper cases. Rather, the seaward shifting of maximum current location by vegetation causes 23% − 38% higher velocities for about a 2-m distance in the rip for all mound separations (Fig. 2.5 Yongqian Yang Chapter 2. 19

5.48m, NV 7.02m, NV 8.66m, NV 5.48m, V 7.02m, V 8.66m, V 0.50 0.10 (a) (f) 0.30 −0.10

U (m/s) 0.10 U (m/s) −0.30

−0.10 −0.50 0.30 0.30 (b) (g) 0.20 0.20 (m) (m) s s

H 0.10 H 0.10

0.00 0.00 0.50 0.30 (c) (h) 0.30 0.10

U (m/s) 0.10 U (m/s) −0.10

−0.10 −0.30 0.20 0.20 0.15 (d) 0.15 (i)

(m) 0.10 (m) 0.10 s s H H 0.05 0.05 0.00 0.00 0.40 0.40 (e) (j) 0.20 0.20

bed (m) 0.00 bed (m) 0.00 15 16 17 18 19 20 21 22 23 24 25 15 16 17 18 19 20 21 22 23 24 25 cross−shore (m) cross−shore (m)

Figure 2.5: Cross-shore proﬁles of mean current and signiﬁcant wave height over the mound (a - d) and channel (f - i). Panes (a), (b), (f) and (g) are for 0.50-m water level and 0.17-m incident wave height, while (c), (d), (h) and (i) are in 0.36-m water level and 0.06-m incident wave height. The legend denotes the mound separation distances and vegetated versus non-vegetated conditions. Panes (e) and (j) show the side view of basin bed elevation through the mound centerline. Vertical dotted lines correspond to the edges of and mound, while horizontal dashed lines show U = 0.

(h)), compared with non-vegetated case. In wider channels, the amplitude of rip currents in vegetated cases becomes even higher than the non-vegetated cases. It is likely that the higher resistance of emergent vegetation forces more flow into the channels, especially with wider mound separation that provides more space for channelization. Increasing wave height is observed in all shallower channels in vegetated setups. However, it should be noted that such wave height increase is not caused by the occurrence of farther inshore wave breaking, which is the mechanism in the deeper water level setups. Due to the stronger rip current in the shallow-depth vegetated setups, which is 23% − 38% higher than the non-vegetated case for a 2-m distance in the rip, incident waves in the channel are significantly steepened (30% − 51% increase in significant wave height in Fig. 2.5 (i)); this is similar to the finding of Haller et al. (2002) for bar-rip systems. As a result, wave heights in the vegetated cases in Fig. 2.5 (i) increase over and inshore of the mounds, then decrease immediately due to Yongqian Yang Chapter 2. 20 wave breaking. Figure 2.6 shows the percent change of maximum current amplitude, 4U = Uc,vegetated−Uc,non × Uc,non 100%, caused by vegetation for mound spacings, where Uc is the cross-shore maximum current amplitude. Over mounds, the current amplitude is consistently reduced by vegetation in all configurations. The trends describing current amplitude reductions are not sensitive to the mound separation distance for either of the two water levels. The extent of current- amplitude damping in the 0.36-m depth case (75%) is greater than that for the deeper case (40%), which shows that vegetation resistance in shallower water plays a more significant role in dissipating current over the mounds. In contrast, the percent current-amplitude change through the channels varies with mound separation. In the channels, the percent current- amplitude change trends of the two water depth setups are similar, but the shallower depth case becomes positive in seven of the mound configurations, while the deeper case always remains negative. Thus, with higher roughness on the mound and sufficient channel width, the rip current may be amplified by vegetation. When considering sediment transport, such amplification might result in shoreline erosion or widening of channels.

60 0.50 m depth, mound 0.36 m depth, mound 40 0.50 m depth, channel 0.36 m depth, channel

0 U (%) ∆ −20

−40

−60

−80 5 6 7 8 9 10 11 12 S (m)

Figure 2.6: Percent diﬀerence in mean current between non-vegetated and vegetated setups for diﬀerent mound separations and water levels.

2.5.3 Spatial Circulation Characteristics

To study the time-averaged, spatial circulation characteristics, the simulated mean velocity ﬁeld, rather than the instantaneous one, is used for analysis. Vorticity is the classic parameter used to study circulation structure. However, besides the vortical core, the vorticity also Yongqian Yang Chapter 2. 21

catches shearing motions near boundaries. As a result, the primary rotation vortices are contaminated by this unwanted interference (e.g., Adrian et al., 2000; Nicolau del Roure et al., 2009). Since the large-scale vortices are of interest here, it is preferable to minimize the eﬀect of the boundary shear on the analysis. Swirling strength is another method for identifying vortical structure from velocity ﬁelds (e.g., Adrian et al., 2000; Zhou et al., 1999). Swirling strength is computed from the local velocity gradient tensor,

∂u ∂u ∂x ∂y Dv = ∂v ∂v . (2.4) ∂x ∂y

Dv has a pair of complex conjugate eigenvalues, whose positive imaginary part is the local swirling strength. The reciprocal of swirling strength is the period of a particle trajectory around the axis of the real part. Since pure shear flow has infinite elliptical trajectory, which corresponds to infinite orbit period and zero swirling strength, the non-zero vorticity values in shear layers without local swirling motion are eliminated in the swirling strength field (Adrian et al., 2000). Figure 2.7 (a) - (f) show the swirling strength of time-averaged flow for the S = 5.48 m, 7.02 m and 8.66 m mound separations with the 0.50-m water level. In the following discussion, the size of the primary swirling cores is quantified using a swirling strength threshold of 0.01 s−1. The primary vortices marked by the red boxes in Fig. 2.7 have a clockwise rotation. Both non-vegetated and vegetated setups are analyzed to study the influence of vegetation on the large-scale circulation. Sizes of both the primary swirling cores and the secondary circulations downstream (after x = 25 m) increase with mound separation distance. This increase can be attributed to the larger space for vortex development in the wider channels. In the presence of vegetated mounds, the size of the primary swirling cores decreases, whereas the secondary cores downstream expand. As observed in Fig. 2.5 (a) and (f), cross-shore current amplitudes are reduced by vegetation both over the mounds and in the channels between x = 20 − 23 m. Such velocity dissipation is in the same position as the primary vortex, which accounts for the vortex size reduction. In contrast, the secondary circulations increase in size under the influence of vegetation. This results from the increased reversed shoreward rip current (positive U after x > 24 m in Fig. 2.5 (f)). Since the positive, shoreward current behind the channel is an indication of secondary circulation (Haller et al., 2002), its increase could lead to stronger secondary vortices in vegetated setups. Moreover, the secondary circulations are modified into more circular shapes in the presence of vegetation. Swirling strength of the same mound separations with 0.36-m water level are shown in Fig. 2.7 (g) - (l). Similar increase of the primary vortex size with the same mound separation as the 0.50-m water level is found, but these primary circulations decrease in size more significantly in the presence of vegetation. In Fig. 2.7 (g), (h) and (i), the clockwise-rotating primary swirling cores shown in the red boxes include both the red contoured area as well as the light blue contoured area. In contrast, the light blue contoured areas downstream Yongqian Yang Chapter 2. 22

Figure 2.7: Swirling strength (in s−1) for 0.50-m depth (a - f) and 0.36-m depth (g - l) cases. Panes (a) - (c) and (g) - (i) are non-vegetated setups with different mound separations, while (d) - (f) and (j) - (l) are the corresponding vegetated setups. The red rectangles mark the primary circulations on the middle mounds using a swirling strength threshold of 0.01 s−1. Incident waves travel from left to right. of the marked cores in Fig. 2.7 (j), (k) and (l) are secondary circulations rotating counter- clockwise. Besides the dissipation of the primary vortex, vegetation also forces the expanded secondary circulation seaward. Figure 2.5 (h) shows that the locations of cross-shore current flow reversal are shifted seaward to x = 22 − 24 m by vegetation, which moves the secondary circulations closer to the mounds. In addition, compared with the 0.50-m water level case, the secondary circulations are more irregular in shape, for both non-vegetated and vegetated setups, which implies that the overall circulation field is more complicated in shallower depths. Yongqian Yang Chapter 2. 23

2.6 Discussion

While the simulations here are completed only for a few mound-channel conﬁgurations, water levels and wave conditions, a dimensional analysis is performed to predict the rip current and mean circulation in other similar mound-channel systems for general applicability. To predict rip current amplitude in diﬀerent mound-channel systems, the parameters are analyzed in dimensionless form:

2 Uc S = f1( √ ), (2.5) co hc Hohc

where S is the mound separation distance, co is the deep-water wave celerity by linear wave p g theory (co = k ), Ho is the deep-water equivalent wave height by linear transformation, hc is the depth in the wetland channel and Uc is the rip current amplitude. Figure 2.8 shows Eq. 2.5 with numerical results from all mound configurations. With increasing mound separation distance, the overall trend of the dimensionless rip current amplitude is decreasing, 2 2 until √S > 4200. For √S < 4200, the data approximately follow a logarithmic hc Hohc hc Hohc 2 trend. When √S > 4200, the dimensionless rip current amplitude is more complex, first hc Hohc increasing then decreasing with dimensionless spacing. It can be hypothesized that with sufficiently wide mound separation, rip currents tend to vanish, as shown by the trend of 2 Uc approaching zero with the increasing dimensionless mound spacing, √S . Using eight co hc Hohc mound-channel configurations, S = 6.02 m, 6.52 m, 7.52 m, 8.02 m, 9.02 m, 9.72 m, 10.52 m and 11.32 m, the regression equation shown in Fig. 2.8 is:

U S2 S2 c = 0.029 log( √ ) − 0.272 when √ < 4200 . (2.6) co hc Hohc hc Hohc This formula can be used as a first estimate of the rip current amplitude in wetland mound- 2 channel systems, when √S < 4200. The R2 of the regression equation is 0.931 (for hc Hohc 2 √S < 4200), and 100% of these rip current amplitudes are within 20% of the values hc Hohc predicted by this equation. Simulation with the experimental S = 5.48 m, 7.02 m and 8.66 m are used to validate this regression equation (star symbols in Fig. 2.8), with all simulations 2 of √S < 4200 falling in reasonable range of the prediction. hc Hohc In the previous sections, the friction coefficients for vegetation in the simulations are chosen based on the validation with vegetated experimental data. To study the effect of different vegetated conditions (e.g., how frictional resistance is modified by density, species, flexibility) on the primary circulation, additional simulations with differing friction coefficients are performed using S = 5.48 m, 7.02 m and 8.66 m mound separations. Similarly, a dimensional analysis is conducted as: Yongqian Yang Chapter 2. 24

−0.02

−0.04

−0.06 o

/c −0.08 c U

−0.1

−0.12 0. 50 m d e p t h 0. 36 m d e p t h

2 U c/c o = 0. 029l og ( S /( h cpH oh c)) − 0. 272 −0.14 +/- 20% range validation setups −0.16 0 1000 2000 3000 4000 5000 6000 7000 8000 2 S /(h cpH oh c )

Figure 2.8: Dimensionless relationship between mound separation distance and rip current amplitude. Stars denote simulations for validation.

0.5 C fveg Ho = f2( ), (2.7) hc fc S

where fveg is the vegetation’s friction coeﬃcient, fc is the non-vegetated friction in the wetland channels, and C is the area of the marked swirling cores in Fig. 2.7 (swirling strength > 0.01 s−1). The relation of Eq. 2.7 is shown in Fig. 2.9, and the data follow a power distribution. Using the simulated data shown as hollow circles and triangles in Fig. 2.7, the regression equation is:

C0.5 f H = 10.350 ( veg o )−0.091. (2.8) hc fc S The R2 for this regression equation is 0.523. Equation 2.8, which estimates simulated primary circulation size to within 20%, catches the main size trend. 86% of simulations are within the 20% predictive range. To validate the regression equation shown in Fig. 2.9, additional vegetated simulations are completed with several of the eight additional mound separations discussed in previous sections (stars in Fig. 2.9). The results with fveg = 0.10 for 0.50- m depth and fveg = 0.15 for 0.36-m depth are reasonably represented by Eq. 2.8. As a result, Equation 2.8 can be used to preliminarily estimate the extent of significant circulation as a function of mound-channel configuration. Future studies on the influence of other parameters, such as mound characteristics, might improve the regression. Table 2.2 applies the empirical equations, Eq. 2.6 and Eq. 2.8, to field scale at Dalehite Cove in Galveston Bay, TX, for both normal daily and storm conditions. The predicted rip current amplitudes are within the typical range of rip currents in nature (i.e., generally 0.3−0.6 m/s, Yongqian Yang Chapter 2. 25

0. 50m d e p t h 0. 36m d e p t h 0 . 5 − 0 . 0 9 1 C /h c = 10. 35[ ( f v e g /f c)( H o/S )] +/- 20% range simulations for validation c /h 5 . 0 C

1 10

−2 −1 0 1 10 10 10 10

(fv e g /fc)(H o/S )

Figure 2.9: Dimensionless size of swirling strength versus friction coeﬃcient on the top of mound. Stars denote simulations for validation.

Table 2.2: Application of Eq. 2.6 and Eq. 2.8 to ﬁeld scale

2 0.5 S fveg Ho Uc C 2 S (m) hc (m) Ho (m) √ Uc (m/s) C(m ) hc Hohc fc S co hc 45 1 1.2 1848.6 0.267 −0.054 11.673 −0.431 136.3 45 2 1.6 566.6 0.356 −0.088 11.371 −0.705 517.2 45 3 2.2 262.7 0.489 −0.110 11.046 −0.884 1098.2 40 2 1.6 447.2 0.400 −0.095 11.250 −0.760 506.3 50 3 2.2 698.8 0.320 −0.082 11.481 −0.657 527.2

Ho: oﬀshore wave height; hc: depth in the channels within wetlands.

and up to 2.4 m/s in extreme case), demonstrating the equation yields reasonable estimates for rip current strength in mound-channel wetland systems. Field studies to measure rip current strength and primary circulation over a range of conditions are needed to assess the equations’ performance.

2.7 Summary & Conclusions

A numerical model investigation with COULWAVE is carried out to study the wave-induced ﬂow in wetland mound-channel systems. The layouts with relatively complicated bathymetry provide a more realistic model of natural coastal wetlands. Numerical results show good agreement with experimental data for twelve diﬀerent conditions (i.e. water level, vegetated condition and mound separation), and the parameter set for study is extended to include Yongqian Yang Chapter 2. 26

additional mound-channel setups. Rip currents and feeder flows are observed within the wetland mound-channel systems. Mound separation influences both the rip current strength and the location of its maxima. A logarithmic relation is obtained between normalized rip current strength and normalized 2 mound separation distance for the range of √S < 4200. Though the rip current strength hc Hohc 2 is less predictable when √S > 4200, the rip current tends to vanish when the mound hc Hohc separation is sufficiently wide. Vegetation effects on mean currents and on wave heights interact with each other. Changes in rip currents influence how far wave breaking extends into the channel, which in turn af- fects the mean water level distribution and current pattern in the mound-channel system. Mean cross-shore velocities are always dissipated by vegetation over mounds, but velocities are increased or reduced through the channel as a consequence of the mound vegetation, depending on mound separation and water level. Vegetation reduces wave heights over the mound and in the narrower channel setups for the 0.50-m depth case, while it increases wave height both over the mound and through the channel in the 0.36-m depth case. Because of these complex interactions, in general, small mound separation generates higher rip currents, while the damping effect of vegetation in channels decreases with much larger mound separation. Optimal mound configuration should be chosen, accounting for the compromise between vegetation concentration and flow impact attenuation. Swirling strength indicates that vegetation tends to decrease the primary vortex size in the vicinity of the mounds and expand the secondary circulation inshore, which could be attributed to the variation in mean velocity distribution caused by vegetation. In closing, wetlands are an important ecosystem and coastal buffer zone from extreme events. The results in this paper provide further understanding about how vegetation reduces or amplifies flow impacts within mound-channel wetlands. Since circulation patterns are a significant factor for the long-term stability of these mound-channel systems, the logarithmic and power-form relations for normalized rip current strength and normalized primary vortex size are important for flow estimates to ensure the feasibility of wetland restoration or protection initiatives. These two relationships can be used as first estimate in practical application for current and circulation conditions within discontinuous wetlands, for example constructed mound-channel systems with salt marsh vegetation (e.g., Spartina alterniflora). Further research is needed to understand the influence of other characteristics, such as mound height and shape.

Nomenclature

a wave amplitude

co wave celerity in deep water Yongqian Yang Chapter 2. 27 f friction coeﬃcient h local water depth hc water depth in channel within wetlands k wave number uα reference horizontal velocity (uα, vα) at zα from still water a ε measure of nonlinearity, h ζ free surface µ measure of frequency dispersion, kh C area of primary swirling strength

Dv local velocity gradient tensor H incident wave height

Ho oﬀshore wave height in deep water

Hs signiﬁcant wave height

Rb wave breaking eﬀect

Rf bottom friction eﬀect %RMSE percentile root mean square of diﬀerence between numerical and experimental data S distance between the centers of adjacent mounds

Uc rip current amplitude λ wavelength

Acknowledgements

This material is base on work supported by the National Sea Grant College Program of the U.S. Department of Commerce’s National Oceanic and Atmospheric Administration (Grant No. NA14OAR4170102) and the National Science Foundation (Grant No. CMMI-1206271). This work used resources of Advanced Research Computing at Virginia Tech. Y. Yang would like to express his special thank to Dr. Lynett in University of South California for providing the source code of COULWAVE. Help from staﬀ and students who conducted the experiments in the Haynes Coastal Engineering Laboratory at Texas A&M University is acknowledged. Model data in this study will be provided by the corresponding auther (Yongqian Yang, email: [email protected]) upon request. Chapter 3

Evolution of wave spectra in mound-channel wetland systems

Yongqian Yang1, Jennifer L. Irish1 1Department of Civil and Environmental Engineering, Virginia Tech, Blacksburg, VA 24061, USA. Citation: Yang, Y., Irish, J.L., (in review). Evolution of wave spectra in mound-channel wetland systems. Coastal Engineering.

28 Yongqian Yang Chapter 3. 29

3.1 Abstract

Wetlands characterized by vegetation growing in patches, separated by non-vegetated open spaces (channels), widely exist in coastal regions. Since wave energy is an important factor that influences shoreline and wetland stability and causes damage, understanding wave- spectrum evolution in such patchy vegetation is essential to minimizing erosion and coastal hazard. Here, we conducted a numerical investigation on the evolution of irregular waves across various frequency components in mound-channel wetland systems. Simulations with a Boussinesq model showed the impact of patchy vegetation on wave energy was both frequency- and space-dependent. Energy amplification was induced by mound channel wetland systems in specific harmonics and locations. Compared with uniform bathymetry, the mound-channel systems also induced wave energy transfer toward the higher harmonics, and the phenomenon became more pronounced for the longer-period incident waves. With increasing incident wave period, mound-channel wetland systems had different impacts on the dominant-frequency and high-harmonic energy; attenuation of the dominant-frequency energy decreased with longer incident periods, while the trend in the high-harmonic energy reversed. This study provides insight regarding wave attenuation by wetlands when there is spatial variability in the wetland configuration. The reduced dominant wave energy by both attenuation and energy transfer may imply delayed or decreased sediment erosion in mound-channel wetland systems, which is related to long-term stability of shorelines and coastal wetlands.

3.2 Introduction

The present study investigates how mound-channel wetland systems influence wave energy in the nearshore and estuarine areas. There is evidence that coastal wetlands have various ecological benefits for coastal communities, such as providing habitats for flora and fauna, maintaining water quality and enhancing environmental resilience (e.g., Cimon-Morin et al., 2015; Cunniff, 2015; Karjalainen et al., 2016; Silliman et al., 2012). In addition, wetlands can directly mitigate the physical stress of shoreline erosion and wave activity (e.g., Arkema et al., 2013; Costanza et al., 2008; Gacia and Duarte, 2001; Neubauer et al., 2002). According to Cunniff (2015), such a “natural defense” is also more cost-effective than typical hard structures, such as breakwaters and levees. The subject of wave dissipation by vegetation has attracted numerous studies since the 1980s. Dalrymple et al. (1984) and Kobayashi et al. (1993) derived analytical solutions for the energy decay by vegetation on monochromatic waves, while Méndezet al. (1999) and Méndezand Losada (2004) extended the models to irregular wave application. In the following years, field studies, laboratory experiments and numerical modeling demonstrated the capacity of vegetation for attenuating wave energy (e.g., Augustin et al., 2009; Loder et al., 2009; Morgan et al., 2009; Wamsley et al., 2010). Recently, the role of vegetation on Yongqian Yang Chapter 3. 30 irregular wave attenuation was found to be frequency-dependent. Bradley and Houser (2009) and Anderson and Smith (2014) observed more energy dissipation in the high-frequency components (compared to low frequencies) by both natural and artificial vegetation. In a field study by Jadhav et al. (2013), the drag coefficient of vegetation depended on wave frequency, and they proposed a frequency-dependent curve for velocity attenuation to better parameterize the drag coefficient across the frequency domain. Wu and Cox (2015) concluded that wave steepness and water depth affected wave energy dissipated by vegetation. Some studies also recognized that wave dissipation was related to vegetation properties like stiffness and density (e.g., Bouma et al., 2005; Paul and Amos, 2011), and external factors like current and incident wave energy might undermine vegetation’s capacity to alleviate waves (e.g., Ondiviela et al., 2014; Paul et al., 2011). However, our understanding of coastal wetlands in mitigating natural hazards is not yet as well-established as it is for hard structures (Cunniff, 2015). For instance, studies on wave dynamics in patchy wetlands are still limited. In field settings, patchiness is a common property of coastal wetlands (e.g., Rietkerk et al., 2004; Rietkerk and van de Koppel, 2008). The uncertainty of growth and seasonal variability may result in non-vegetated channels in-between vegetation patches. Silliman et al. (2015) and van Wesenbeeck et al. (2008) reported a higher plant growth rate when vegetation was grouped into patches to maximize the positive species interaction. Under appropriate hydrodynamic and abiotic conditions, Bouma et al. (2009) and Balke et al. (2012) observed enhanced sediment accretion induced by the attenuated hydrodynamic energy inside vegetation patches, which induced additional marsh growth. Yet, the dynamics of wave-spectrum evolution in patchy vegetation, which is relevant to the stability of wetlands and wave energy dissipation, is not well understood. This paper is focused on wave evolution in patchy wetlands characterized by vegetated mounds and unvegetated cross-shore channels (mound-channel wetland systems) using numerical simulations with a Boussinesq model. The mound-channel wetland systems are idealized from a prototype engineered wetland in Dalehite Cove, Galveston Bay, TX. In the following, we introduce the applied methodology and present the simulation results. Further insight into the role of mound-channel wetland systems on wave evolution is provided in the discussion, followed by final conclusions.

3.3 Methodology

3.3.1 Boussinesq Model

The numerical model used in this study is COULWAVE (e.g. Kim and Lynett, 2011), which is based on the depth-integrated Boussinesq-type equations, with sub-models to include the eﬀects of bottom friction, wave breaking and turbulent mixing. This model is fully nonlinear and weakly dispersive, and has been successfully applied in one- and two-dimensional Yongqian Yang Chapter 3. 31 simulations of wave propagation over uneven bathymetry (e.g., Løvholt et al., 2015; Lynett et al., 2010, 2002; Yang et al., 2015). The dimensional governing (continuity and momentum) equations are

∂ζ + ∇ · [(ζ + h)u ] + H.O.T. = O(µ4), (3.1) ∂t α ∂u α + u · ∇u + g∇ζ + R − R − R + H.O.T. = O(µ4), (3.2) ∂t α α f b ev where ζ = free surface elevation, h = local water depth, uα = horizontal velocity vector at zα from still water level and g = gravity. The eﬀects of bottom friction and wave breaking are included in Rf and Rb, and Rev accounts for the vertical and horizontal eddy viscosity of turbulent mixing. H.O.T represents the higher-order nonlinear and dispersive terms on 2 h the order of O(µ ), where µ is the ratio of water depth and wavelength ( λ ). Additional details regarding these terms are described in literature (e.g., Kim and Lynett, 2011; Liu, 1994; Løvholt et al., 2013; Lynett et al., 2002).

3.3.2 Study Domain

In this study, we select the site of Dalehite Cove in Galveston Bay, TX as our prototype, which is composed of constructed vegetated mounds separated by unvegetated channels; vegetation (i.e., higher bottom friction) is specified only at the top of each mound. The mound spacings (S), water depths (ho), incident wave heights (Hi) and significant wave periods (Ts) are selected based on the predominant site conditions with Froude scaling (Truong et al., 2014). We previously investigated the flow characteristics in these mound-channel wetland systems, using laboratory experiments (Truong et al., 2014) and numerical simulations (Yang et al., 2015). These previous studies, however, were limited to regular waves and three mounds alongshore for all scenarios. Here, we (a) use TMA wave spectra to simulate more realistic wave conditions (Hughes, 1984), and (b) assume periodic distribution of mounds in the alongshore direction (Fig. 3.1). Figure 3.2 shows the incident wave spectra with significant wave period Ts = 1.5 to 4.0 s, incident wave height Hi = 0.14 m, and offshore depth ho = 0.50 m. The periodic and infinite distribution of mounds alongshore was simulated by assuming symmetry (depth, free surface and velocity) about the alongshore computational boundaries (i.e., zero normal flux and zero normal gradient at the boundary), which narrowed the domain to save computational time. An absorbing boundary condition was used at the offshore and inshore computational boundaries to eliminate cross-shore wave reflection (e.g., Wei and Kirby, 1995). The effect of vegetation was included in the bottom friction term (Rf ) in Eq. 3.2, which was consistent with other studies (e.g., Augustin et al., 2009; Yang et al., 2015). Hereafter, we refer to the simulations with vegetation represented by higher bottom friction as vegetated scenarios. Validation and calibration of the same model setup with COULWAVE was presented in Yang et al. (2015), and this study will apply these calibrated vegetation coefficients to extend the range of the previous study. Table 3.1 summarizes all Yongqian Yang Chapter 3. 32

simulated scenarios (i.e., mound spacings [S], oﬀshore depths [ho], incident wave heights [Hi] and signiﬁcant periods [Ts]) in this study. For reference, simulations of horizontal bathymetry without mounds, channels or vegetation were also performed with the corresponding depths and wave conditions.

Figure 3.1: (a) Bathymetry (in m) for the 7.02-m mound spacing and 0.50-m offshore depth. Cross-shore channels are along y = ±3.51 and ±10.53 m. Vegetation is represented by higher friction on top of the mounds, marked by black dotted circles. Waves propagate from left to right. The mounds are assumed to distribute periodically and infinitely in the alongshore direction. To save computational time, we only model a narrow alongshore-symmetric portion of the domain, and mirror it into infinity in the alongshore direction. (b) Transect of bathymetry along centerline (y = 0 m). Horizontal bathymetry without mounds and channels (constant depth after x = 17.0 m) is simulated for reference. Yongqian Yang Chapter 3. 33

Figure 3.2: Incident TMA spectra with significant wave period Ts = 1.5 s (solid line), 2.0 s (dashed line), 3.0 s (dash-dot line) and 4.0 s (dotted line). Significant wave height Hi = 0.14 m and offshore depth ho = 0.50 m.

3.3.3 Data Analysis

To study the spatial distribution of wave energy, we used 663 model output locations over a sub-domain of 15 m < x < 30 m in the cross-shore direction and from y = 0 m to the adjacent cross-shore channel. Because of symmetry, this sub-domain can be mirrored alongshore to represent the wider domain. Each simulation contained at least 200 individual waves to provide convergence in the estimates of wave spectra. In addition, to quantify wave energy in the harmonic frequencies, we integrated the wave spectra over a few frequency bins centered around the ﬁrst (f = 1 ), second (f = 2 ) and third (f = 3 ) harmonics to 1 Ts 2 Ts 3 Ts R fu obtain the representative energy, i.e., Spdf, where Sp is the wave spectrum, fi and fu are fi the lower and upper frequencies around the harmonic.

3.4 Results

Figure 3.3 shows the instantaneous free surface and wave-averaged (over two Ts) current in non-vegetated and vegetated scenarios (at time step t = 160 s). Wave shoaling occurs over the shallower mounds, leading to faster wave height damping by wave breaking (x = 21 m). The wave-induced currents toward the centerline (y = 0 m) in Fig. 3.3 (c, d) indicate wave refraction behind the mounds (x = 24 m). Circulation cells similar to rip current systems are observed farther onshore (24 < x < 30 m), with seaward currents in the cross-shore Yongqian Yang Chapter 3. 34

Table 3.1: Matrix of simulation scenarios and energy transfer across harmonics

S (m) ho (m) Hi (m) Ts (s) Energy in harmonics (%) (NV vs. VG) 1st 2nd 3rd 1st 2nd 3rd 5.48 0.50 0.14 2.0 68 22 5 64 20 4 7.02 0.50 0.14 2.0 69 21 5 68 20 4 8.66 0.50 0.14 2.0 70 21 5 70 21 4 10.02 0.50 0.14 2.0 70 20 4 70 20 4 7.02 0.50 0.14 1.5 78 17 2 77 15 2 7.02 0.50 0.14 3.0 55 24 11 53 24 10 7.02 0.50 0.14 4.0 41 28 15 40 28 16 5.48 0.36 0.07 2.0 56 24 10 54 25 8 7.02 0.36 0.07 2.0 57 25 9 56 25 8 8.66 0.36 0.07 2.0 56 26 9 56 27 9 10.02 0.36 0.07 2.0 58 26 9 58 26 9 7.02 0.36 0.07 1.5 70 20 4 70 19 3 7.02 0.36 0.07 3.0 47 24 13 47 23 13 7.02 0.36 0.07 4.0 38 24 15 38 23 15 S: mound spacing; ho: offshore depth at wavemaker; Hi: incident wave height; Ts: significant wave period of incident wave; NV : non-vegetated scenario; VG: vegetated scenario. channels (y = ±3.51 m). The alongshore feeder currents from the shadow zone shoreward of the mounds (x = 27 m) into the channels induce energy amplification in the channels (Fig. 3.3 (a, b) ). Overall, the wave-induced currents in the vegetated scenario are weaker than in the non-vegetated one. The reader is referred to Yang et al. (2015) for a thorough analysis of the wave-induced currents in mound-channel wetland systems.

3.4.1 Signiﬁcant Wave Height

Impact of mound-channel bathymetry

Figure 3.4 (a, d, g) show the planform wave height distribution with various mound spacings (i.e., 5.48 m, 7.02 m and 8.66 m) without vegetation. The offshore depth is 0.50 m, with a 2-s significant wave period. Mound-channel bathymetry has a significant influence on wave breaking, leading to alongshore variability in the significant wave height contours. The decreased depths on the mounds cause stronger wave breaking, reducing wave height behind the mounds. In contrast, areas of increased wave height exist in the cross-shore channels (alongshore boundaries of the sub-domain), which is attributed to the nearshore currents induced by the mound-channel configuration (Fig. 3.3 (c) ). With increasing mound spacing, both the regions of wave height reduction behind the mounds and the regions of wave height amplification in the channels become farther onshore. According to Yang et al. (2015), mound-channel wetlands generated circulation similar to rip-current systems, and larger Yongqian Yang Chapter 3. 35

Figure 3.3: Instantaneous free surface and wave-averaged current in (a, c) non-vegetated scenario and (b, d) vegetated scenario, all at time step t = 160 s. Oﬀshore depth ho = 0.50 m, signiﬁcant wave period Ts = 2 s, incident wave height Hi = 0.14 m and mound spacing S = 7.02 m. Waves propagate from left to right. Black dotted lines depict the ramp and mounds in Fig. 3.1.

mound spacing left a wider space for circulation development shoreward. As a result, the alongshore feeder flows from the mounds’ shadow zones into the channels move shoreward, resulting in wave height amplification farther onshore in the channels. When water depth decreases, the effect of bathymetry on wave propagation becomes more significant. Figure 3.4 (j, m, p) show the wave height distribution for a 0.36-m offshore depth and the same mound spacings. Similar wave height reductions occur behind the mounds. However, unlike the 0.50-m depth, in which the regions of lower wave height widen onshore, these regions in the 0.36-m depth maintain almost a constant width in the cross- shore direction. Moreover, the area of dissipated wave energy behind the mound is not sensitive to the mound spacing. Compared with the deeper scenario, the area of wave height amplification in the channel moves seaward (x < 23 m), and increases when the channel is wider. Yongqian Yang Chapter 3. 36

Figure 3.4: Contours of significant wave height (in m) for non-vegetated scenarios (a, d, g), significant wave height (in m) for vegetated scenarios (b, e, h) and percent difference between non-vegetated and vegetated scenarios (c, f, i). Red and blue colors in (c, f, i) indicate wave height increase and decrease by vegetation. (a, b, c), (d, e, f) and (g, h, i) are for mound spacing of 5.48 m, 7.02 m and 8.66 m, respectively, where offshore depth ho = 0.50 m and significant wave period Ts = 2 s. Panels (j-r) are the same contours with ho = 0.36 m and Ts = 2 s. Waves propagate from left to right. Black dotted lines depict the ramp and mounds in Fig. 3.1. Yongqian Yang Chapter 3. 37

Impact of vegetation

Figure 3.4 (b, e, h) show the significant wave height distribution for the vegetated scenarios (0.50-m offshore depth), while Fig. 3.4 (c, f, i) show the corresponding percent-difference with respect to the non-vegetated scenarios. In the presence of vegetation on the mounds, incident wave breaking occurs slightly farther offshore and stronger. Thus, vegetation reduces wave height on top of the mounds, and the region of wave damping diverges and extends into the outer shadow zones (hereafter, termed “OSZ”; the blue regions angled to centerline behind the mounds (x > 23 m) in Fig. 3.4 (c, f, i) ). For small mound spacing, this dissipation expands into the shoreward sides of the channels, leaving the wave height amplification in the channels next to the mounds (Fig. 3.4 (c) ). With wider mound spacings, the amplified wave height in the channels is shifted seaward in the vegetated scenarios, which is consistent with the seaward movement of vegetation-induced vortices in the wave-induced circulation reported in Yang et al. (2015). In addition, compared with the non-vegetated scenario, the resistance on the vegetated mounds induces stronger wave shoaling and wave refraction, resulting in increased wave height shoreward of the mounds (Fig. 3.4 (c, f, i) ). With a shallower depth of 0.36 m, the relative impact of vegetation becomes more significant as shown in Fig. 3.4 (k, n, q, l, o, r). Vegetation divides the region of low wave height behind the mound into two parts angled to centerline, y = 0 m (Fig. 3.4 (k, n, q) ). In the percent-difference contours, wave height reduction in OSZ is more significant than in the 0.50-m depth scenario. When mound spacing increases, wave height amplification in the channels caused by vegetation widens and expands shoreward. On the other hand, the higher vegetation roughness in the shallower depth causes more dissipation of cross-shore velocity over the mounds (Yang et al., 2015), resulting in more energy accumulated behind the mounds by wave shoaling and wave refraction. Therefore, wave height amplification by vegetation behind the mounds is also more intense than in the 0.50-m depth scenario.

Impact of incident wave period

The simulation results also show the incident wave period (Ts) influences significant wave height distribution. Figure 3.5 shows selected results, but all results exhibit the same trends with respect to Ts. The shortest incident wave generates more localized patterns than the longer-period waves, such as the slight wave height amplification in OSZ (Fig. 3.5 (a, b) ). In the vegetated scenarios, regions of low wave height behind the mounds widen with increasing wave period, and diverge into two separated parts with Ts = 4 s (Fig. 3.5 (k) ). This is similar to the shallower scenario in Fig. 3.4 (n), since the longer wave period approaches the shallow water limit. With longer waves, the effect of vegetation tends to create three regions, i.e., wave height amplification shoreward of the mounds, wave height amplification on the seaward edges of the channels, and wave height damping in OSZ extending into the channels onshore (Fig. 3.5 (k) ). Yongqian Yang Chapter 3. 38

Figure 3.5: Contours of significant wave height (in m) for non-vegetated scenarios (a, d, g, h), significant wave height (in m) for vegetated scenarios (b, e, h, j) and percent difference between non-vegetated and vegetated scenarios (c, f, i, k). Red and blue colors in (c, f, i, k) indicate wave height increase and decrease by vegetation. Panels from top to bottom are for significant wave periods of 1.5 s, 2 s, 3 s and 4 s, respectively, where offshore depth ho = 0.50 m and mound spacing S = 7.02 m. Waves propagate from left to right. Black dotted lines depict the ramp and mounds in Fig. 3.1.

3.4.2 Evolution of Wave Spectra

Transfer of wave energy to higher harmonics

The contours of significant wave height only represent the mean wave energy at each output location in the sub-domain. In order to study the energy evolution of various harmonics over the mound-channel wetland systems, we computed the wave spectra of all 663 output locations and integrated each spectrum over the bins around the first, second and third harmonics (see Section 2.3). Figure 3.6 (a-i) show the wave energy contours of the three harmonics of non-vegetated and vegetated scenarios and the corresponding percent difference, for the 0.50-m depth scenario, while Fig. 3.6 (j-r) show the same results of the 0.36-m depth scenario. While most of the energy remains in the dominant frequency (i.e., first harmonic), considerable portions are transferred into the second (20 − 25%) and third (5 − 10%) harmonics. Mound-channel bathymetry is the dominant factor in inducing wave energy transfer to higher harmonics. At the higher harmonics, vegetation reduces the energy over a larger Yongqian Yang Chapter 3. 39

area ( Fig. 3.6 (f, i, o, r) ). This implies that vegetation is more efficient in dissipating wave energy of higher frequencies, which is consistent with previous studies (e.g., Anderson and Smith, 2014; Bradley and Houser, 2009; Jadhav et al., 2013; Wu and Cox, 2015). However, patchy vegetation does not reduce wave energy in all locations or at all harmonics. Rather, energy amplification by vegetation occurs behind the mounds and in parts of the channels. For the shallower depth (0.36 m offshore), higher vegetation roughness results in larger increases in energy behind the mounds, especially at the higher harmonics (Fig. 3.6 (l, o, r) ). These regions extend farther inshore compared to the 0.50-m depth scenario.

Impact of incident wave period

Figure 3.7 shows selected harmonics results for various incident wave periods (i.e., Ts = 1.5 s and 4 s) for the 0.50-m depth scenario. When wave period increases, the incident wavelength approaches the shallow-water limit, causing the relative eﬀect of the mound- channel bathymetry to become more pronounced. As a result, a larger portion of wave energy is transferred into the higher harmonics for the 4-s wave scenario. In addition, with longer incident wave period, there is less similarity between the contours of signiﬁcant wave height (Fig. 3.5 (j, k) ) and energy at the dominant-frequency (Fig. 3.7 (j, k) ). Here, most energy between x < 18 m and x > 24 m is transferred into the second and third harmonics. This implies that energy transfer of a long wave across frequencies is spatially dependent in mound-channel systems. Moreover, for longer waves, the increase of energy shoreward of the mounds and in the channels due to vegetation is mainly in the higher frequencies (Fig. 3.7 (o, r) ). In contrast, vegetation reduces energy in the higher harmonics in the shorter-wave scenarios over most of the sub-domain (Fig. 3.7 (f, i) ).

3.5 Discussion

3.5.1 Non-uniform spatial distribution of wave energy in mound- channel systems

With continuous vegetation in planform, wave propagation through the vegetation field varies less alongshore. As a result, a single cross-shore transect can reasonably represent the wave evolution (e.g., Anderson and Smith, 2014; Koftis et al., 2013; Paul et al., 2011; Tang et al., 2015). For the mound-channel wetland systems in this study, however, the impact of patchy vegetation is spatially dependent. Vegetated mounds directly attenuate the wave-induced current ( Fig. 3.3 (c, d) and Yang et al. (2015)), which in turn modifies the patterns of wave breaking and wave refraction. This interaction results in wave energy amplification and damping in different regions, rather than a monotonic decay through a vegetation belt (e.g., Eq. 50 in Dalrymple et al. (1984) and Eq. 17 in Kobayashi et al. (1993)). In other Yongqian Yang Chapter 3. 40

Figure 3.6: Contours of wave energy (in m2) for non-vegetated scenarios (a, d, g), wave energy (in m2) for vegetated scenarios (b, e, h) and percent difference between non-vegetated and vegetated scenarios (c, f, i). Red and blue colors in (c, f, i) indicate wave energy increase and decrease by vegetation. (a, b, c), (d, e, f) and (g, h, i) are for wave energy around the dominant frequency, second harmonic and third harmonic, respectively, where offshore depth ho = 0.50 m, significant wave period Ts = 2 s and mound spacing S = 7.02 m. Panels (j-r) are the same contours with ho = 0.36 m and Ts = 2 s. Waves propagate from left to right. Black dotted lines depict the ramp and mounds in Fig. 3.1. Yongqian Yang Chapter 3. 41

Figure 3.7: Contours of wave energy (in m2) for non-vegetated scenarios (a, d, g), wave energy (in m2) for vegetated scenarios (b, e, h) and percent difference between non-vegetated and vegetated scenarios (c, f, i). Red and blue colors in (c, f, i) indicate wave energy increase and decrease by vegetation. (a, b, c), (d, e, f) and (g, h, i) are for wave energy around the dominant frequency, second harmonics and third harmonics, respectively, where offshore depth ho = 0.50 m, significant wave period Ts = 1.5 s and mound spacing S = 7.02 m. Panels (j-r) are the same contours with Ts = 4 s. Waves propagate from left to right. Black dotted lines depict the ramp and mounds in Fig. 3.1. Yongqian Yang Chapter 3. 42

words, the simpliﬁed one-dimensional approaches to predict wave propagation over uniform vegetation are not appropriate for assessing wave conditions in patchy wetlands.

3.5.2 Impact of bathymetry on wave dissipation

To quantify the effect of mound-channel wetland systems on wave evolution, wave height and wave energy are integrated over the sub-domains of the contours in Section 3, i.e., RR RR Hsdxdy and Shdxdy, where Hs is the significant wave height and Sh is the energy in the harmonics. Figure 3.8 (a) shows the wave height difference (in %) between mound- channel systems with and without vegetation and horizontal bathymetry (without vegetation, mounds or channels), where negative values indicate reduction caused by the vegetated mounds. It is observed that smaller mound spacing and shallower depth provide higher reduction in wave height overall in the sub-domain. Mound-channel bathymetry is the dominant factor in reducing the overall wave height, while patchy vegetation provides only a fair contribution. The effect of vegetation alone is less sensitive to the mound spacing. Figure 3.8 (b) shows the percent difference of energy integration in the harmonics between non-vegetated and vegetated mound-channel systems. The effect of vegetation on overall wave energy within subdomain is frequency-dependent, with more dissipation occurring in the higher harmonics. Similar preferential dissipation of high-frequency spectra was reported in other studies with continuous vegetation (e.g., Anderson and Smith, 2014; Jadhav et al., 2013; Wu and Cox, 2015). In our study, however, patchy vegetation does not dissipate wave energy at all harmonics; a slight energy increase (< 4%) is observed in specific harmonics. The combined effect of vegetation plus the mound-channel bathymetry versus the non-vegetated horizontal bathymetry is shown in Fig. 3.8 (c). The energy reduction by the vegetated mounds is more significant for the shallower depth. In the deeper scenario, rather than being dissipated, more energy is transferred into the higher harmonics by the vegetated mounds, leading to increased energy in the second and third harmonics.

3.5.3 Impact of wave period on wave dissipation

Similar spatial integration of wave height and wave energy is performed to show the relationship between incident wave period (Ts) and the wave-spectrum evolution in the sub-domain. In Fig. 3.9 (a), the effect of bathymetry and vegetation is not very sensitive to the incident wave period. Wave height attenuation is not always the largest for the shorter wave-period scenarios; for instance, except for the results shown by the filled circles, wave height damping by mound-channel wetland systems on Ts = 1.5 s is less significant than Ts = 2.0 s. Figure 3.9 (b, c) show the relative effects of vegetation and bathymetry on wave energy in the harmonics. Compared with the non-vegetated mound-channel systems, patchy vegetation causes a slightly higher energy reduction in the higher harmonics (Fig. 3.9 (b) ). However, Yongqian Yang Chapter 3. 43

10 (a)

-10

ho . m wave height veg vs. non-veg, = 0 50

difference (%) -20 veg vs. horizontal, ho = 0.50 m veg vs. non-veg, ho = 0.36 m h . m -30 veg vs. horizontal, o = 0 36 5 6 7 8 9 10 11 mound spacing (m)

10 (b)

-10 1st harmonic, ho = 0.50 m 2nd harmonic, ho = 0.50 m 3rd harmonic, ho = 0.50 m

difference (%) -20 h . m

spectral energy 1st harmonic, o = 0 36 2nd harmonic, ho = 0.36 m h . m -30 3rd harmonic, o = 0 36 5 6 7 8 9 10 11 mound spacing (m)

10 (c)

-10

difference (%) -20 spectral energy

-30 5 6 7 8 9 10 11 mound spacing (m)

Figure 3.8: (a) Percent difference of significant wave height between mound-channel systems with and without vegetation (hollow symbols), and between vegetated mound-channel systems and non-vegetated horizontal bathymetry (filled symbols). Percent difference of wave energy in the first (solid lines), second (dashed lines) and third (dotted lines) harmonics (b) between mound-channel systems with and without vegetation; (c) between vegetated mound-channel systems and non-vegetated horizontal bathymetry. Legends in panel (b) also apply to panel (c). Circles and triangles are for offshore depth ho = 0.50 m and ho = 0.36 m. Significant wave period Ts = 2 s. Negative values indicate reduction by vegetation. Yongqian Yang Chapter 3. 44

10 (a)

-10

ho . m wave height veg vs. non-veg, = 0 50

difference (%) -20 veg vs. horizontal, ho = 0.50 m veg vs. non-veg, ho = 0.36 m h . m -30 veg vs. horizontal, o = 0 36 1 1.5 2 2.5 3 3.5 4 4.5 Ts (m)

10 (b)

-10 1st harmonic, ho = 0.50 m 2nd harmonic, ho = 0.50 m 3rd harmonic, ho = 0.50 m

difference (%) -20 h . m spectral energy 1st harmonic, o = 0 36 2nd harmonic, ho = 0.36 m h . m -30 3rd harmonic, o = 0 36 1 1.5 2 2.5 3 3.5 4 4.5 Ts (m)

10 (c)

-10

difference (%) -20 spectral energy

-30 1 1.5 2 2.5 3 3.5 4 4.5 Ts (m)

Figure 3.9: (a) Percent difference of significant wave height between mound-channel systems with and without vegetation (hollow symbols), and between vegetated mound-channel systems and non-vegetated horizontal bathymetry (filled symbols). Percent difference of wave energy in the first (solid lines), second (dashed lines) and third (dotted lines) harmonics (b) between mound-channel systems with and without vegetation; (c) between vegetated mound-channel systems and non-vegetated horizontal bathymetry. Legends in panel (b) also apply to panel (c). Circles and triangles are for offshore depth ho = 0.50 m and ho = 0.36 m. Mound spacing S = 7.02 m. Negative values indicate reduction by vegetation. Yongqian Yang Chapter 3. 45

compared with the non-vegetated horizontal bathymetry (Fig. 3.9 (c) ), the trends of energy dissipation by the vegetated mound-channel systems are opposite between the dominant frequency and the higher harmonics. Vegetated mound-channel systems reduce more energy in the dominant frequency for waves with lower incident periods (Ts), while the dissipation of the higher-harmonic energy is more eﬃcient for longer-period waves. For the deeper-depth scenario, the vegetated mounds transfer more energy of the shorter incident waves into the high harmonics.

3.5.4 Implications of spectral evolution on sediment transport

For the long-term stability of coastal wetlands, the potential issues of vegetation survival and sediment erosion should be considered. Previous studies illustrated that vegetation grew better in patches (e.g., Silliman et al., 2015; van Wesenbeeck et al., 2008), and the positive feedback of sediment accretion could occur under certain conditions (e.g., Balke et al., 2012; Bouma et al., 2009). According to Diplas et al. (2008), the threshold of sediment motion depended on not only hydrodynamic force magnitude but also duration of peak hydrodynamic force. Previously, Yang et al. (2015) reported the eﬃciency of patchy vegetation in reducing the overall wave-induced ﬂow velocity, which could lead to weaker hydrodynamic force. In this study, the energy transfer toward higher frequencies in mound-channel wetland systems (Tab. 3.1) will reduce the dominant-frequency wave energy, so the duration of dominant force above the threshold of sediment motion may decrease. As a consequence, the reductions in hydrodynamic force magnitude and dominant force duration in mound-channel wetland systems may delay sediment movement, or even reduce the possibility of sediment erosion.

3.6 Conclusions

Patchy wetlands commonly exist in nature due to natural vegetation growth and seasonal variability, and recent studies have also demonstrated higher growth rate and lower erosion when vegetation is grouped in patches. To improve wetland management and minimize marsh loss in engineering practice, it is necessary to further understand the interaction of waves with these mound-channel wetland systems. Wave-spectrum evolution in mound-channel wetland systems is spatially dependent, and the patchy vegetation does not decrease wave energy in all frequency components or in all locations. Even with the same incident wave-energy level, the different wave spectra may result in completely different evolution of wave energy in the frequency domain. Thus, to improve the efficiency of wetlands in attenuating waves and mitigating coastal hazards (e.g., storm surge), the relative scale between bathymetry and incident wave conditions should be considered in engineering practice. Yongqian Yang Chapter 3. 46

The mound-channel bathymetry in this study induces wave energy transfer toward higher frequencies, which may reduce the duration of critical force exerted on sediments, thereby reducing sediment pick-up and subsequent transport. With the contribution of reduced flow velocity by vegetation, mound-channel wetland systems may be more resistant to erosion induced by nearshore processes. This finding may be further applied to the configuration of engineered wetlands to minimize wetlands loss. In closing, this study complements our understanding of the evolution of irregular waves in mound-channel wetland systems. Our findings demonstrate that the effect of vegetated mounds on wave energy is frequency- and space-dependent within wetlands, and is not well characterized by monotonic dissipation during propagation. Future engineering practice on wetland management and restoration should account for the interaction between naturally occurring irregular waves and complex wetland configuration to better design for, and predict shoreline and wetland stability. Due to the complexity of wave dynamics in these systems, future work is needed to understand the influence of other factors, such as multiple rows of mounds, extreme wave conditions, and quantification of sediment movement and subsequent erosion of marsh fringe and inshore shorelines.

Acknowledgements

This material is based upon work supported by the National Oceanic and Atmospheric Administration, U.S. Department of Commerce, under Award No. NA14OAR4170093 to Virginia Sea Grant; and the National Science Foundation via Grant No. CMMI-1206271. The authors acknowledge Advanced Research Computing at Virginia Tech for providing computational resources and technical support that have contributed to the results reported within this paper. The authors would like to thank Ms. K.A. Duhring for sharing her expertise in shoreline protection with wetlands. Y. Yang would like to thank Dr. P.J. Lynett in University of South California for providing the source code of COULWAVE. Comments from Mr. A. Zainali and Mr. R. Sun on applying the appropriate model parameters are acknowledged. Chapter 4

Impact of patchy vegetation on tsunami dynamics

Yongqian Yang1, Jennifer L. Irish1, Robert Weiss2 1Department of Civil and Environmental Engineering, Virginia Tech, Blacksburg, VA 24061, USA. 2Department of Geoscience, Virginia Tech, Blacksburg, VA 24061, USA. Citation: Yang, Y., Irish, J.L., Weiss, R., (in review). Impact of patchy vegetation on tsunami dynamics. Journal of Waterway, Port, Coastal, and Ocean Engineering.

47 Yongqian Yang Chapter 4. 48

4.1 Abstract

Coastal vegetation is capable of mitigating tsunami damage. Yet, the complex tsunami dynamics induced by spatial variability of onshore vegetation are not well understood at present. We conducted laboratory and numerical investigations to study the impact of patchy vegetation on tsunami dynamics. Roughness patches composed of various cylinder numbers and spacings represented different bulk vegetative conditions in the experiments, and a Boussinesq model was applied to extend the range of the experiments. Analysis revealed that roughness patches reduced the maximum momentum flux by up to 80% over most areas, while within-patch roughness variation induced uncertainty on hydrodynamics adjacent to the seaward patches. Dimensional analysis revealed a logarithmic relation between the area protected from extreme momentum flux and the total roughness area. These findings demonstrate that patchy vegetation, with appropriate configuration, can serve as effective as a continuous forest belt in mitigating tsunami hazards.

4.2 Introduction

There is evidence that vegetation along coasts (e.g., forests, mangroves) has helped to reduce tsunami damage (e.g., Kathiresan and Rajendran, 2005; Tanaka, 2009). Most prior studies on this subject have focused on cases where the vegetation is continuous over the impacted area. In reality, however, open spaces with little or no vegetation are common and divide the areas of coastal vegetation into patches. Thus, this study investigates the tsunami dynamics in a coastal area of patchy vegetation with various roughness levels, patch spacings and patch sizes. Tsunamis pose a great threat to public safety and infrastructure in low-lying coastal areas. For example, the tsunami generated by the Sumatra-Andaman earthquake in 2004 killed over 283, 000 people and caused billions of dollars in economic loss (e.g., Lay et al., 2005; Liu et al., 2005; Shaw et al., 2006), and the 2011 Tohoku tsunami inundated over 400 km2 and caused more than 15, 000 deaths in Japan e.g., (e.g., Mori et al., 2011; Sato et al., 2014). Ten percent of the world’s population (13% of its urban population) live along low-lying, tsunami-threatened coasts McGranahan et al. (2007). With the continuing development at the coasts, future tsunami events will likely cause comparatively more damage and casualties. Therefore, for example, the tsunami threat is rising along the Cascadia Subduction Zone (e.g., Atwater et al., 1995; Clague, 1997; Satake et al., 1996; Yu et al., 2014), as more people move to shorelines of Oregon and Washington States. To protect these densely populated communities, governments and scientists have stressed the necessity for solutions to mitigate potential tsunami damage along coastlines. Indirect measures like early tsunami detection and warning systems are effective in timely evacuation, but they are not intended to directly reduce the physical impact of a tsunami as Yongqian Yang Chapter 4. 49 it comes onshore. Historically, direct measures with hard structures, such as seawalls, have been the preferred defense against tsunamis. Although often effective in reducing flooding damage, these costly hard structures have some significant disadvantages, including reduced beach width and increased downdrift erosion (e.g., Basco, 2006; Board et al., 2014; Dean and Dalrymple, 2004). Vegetation, in concert with hard structures and indirect measures, has the potential to lead to more cost-effective, environmentally friendly, and aesthetically pleasing alternatives to tsunami mitigation. In the majority of existing studies, continuous (i.e., non-patchy) vegetation has proven its potential to mitigate coastal hazards. Experiments by (Irtem et al., 2009) and Ismail et al. (2012) demonstrated reduced runup heights behind artificial forests. Bao (2011) and Ander- son and Smith (2014) observed wave energy dissipation by vegetation. According to Yanag- isawa et al. (2010) and Maza et al. (2015), the hydraulic loads of tsunamis also decreased in the presence of mangroves. Some studies also revealed that regions without natural vegetation buffers had more severe damage (Nandasena et al., 2008; Tanaka, 2009; Thuy et al., 2009, e.g.,). In actual populated settings, however, coastal vegetation is not often continuous. Rather, vegetated areas vary in density, and are patchy, having open spaces with little or no growth. These open spaces may arise naturally, as vegetation dies and regrows, or they may be the result of human development (e.g., roads, buildings). Yet, the influence of such patchy vegetation on flow characteristics is not well understood (Irish et al., 2014; Vandenbruwaene et al., 2011; Yang et al., 2015, e.g.,). Some experiments have investigated porous cylinder patches (Rominger and Nepf, 2011; Takemura and Tanaka, 2007; Tanaka and Yagisawa, 2010; Zong and Nepf, 2012, e.g.,), but most of these studies employed one single patch, rather than patch arrays. Because patchy vegetation is so common along coastlines (e.g., Rietkerk et al., 2004; Rietkerk and van de Koppel, 2008), and the inundation behavior within such vegetation is not well understood, understanding how patchy vegetation mitigates tsunami damage is necessary, and will help to ensure better decisions on coastal vegetation planning and management. Post-tsunami surveys provide valuable information about inundation depth, maximum runup, and structural damage (e.g., Liu et al., 2005; Mori et al., 2011; Sato et al., 2014; Tanaka et al., 2007). However, the temporal and spatial flow properties, which are important for hazard analysis, can rarely be determined during surveys. At present, real-time measurements (e.g., velocity and hydraulic load) inland during tsunami events are generally infeasible. In contrast, laboratory experiments and numerical simulations provide controlled conditions and repeatability that allow for the systematic quantification of tsunami dynamics during inundation, especially between obstacles inland. This study investigates how a tsunami behaves when coming ashore through patchy vegetation, and how that behavior varies with roughness level, patch spacing and patch size. We used laboratory experiments to quantitatively investigate flow characteristics during tsunami-like inundation under the influence of different patchy, vegetation-like roughness scenarios, represented by rigid cylinder arrays. Numerical simulations were used to extend the range of the experimental study. Roughness patches were represented by higher bottom Yongqian Yang Chapter 4. 50 friction in the simulations. In the following, we introduce the experimental design and numerical model, as well as the analysis methods. Then, we analyze and discuss the results of various scenarios, followed by the final conclusions.

4.3 Methodology

We previously studied the effects of roughness patches on tsunami-like momentum flux, using the averaged fractional changes between the control and various roughness scenarios Irish et al. (2014). In the experiments, Irish et al. (2014) reported a 30% momentum flux decrease shoreward of the patches during runup, while the cross-shore channels between the patches encountered 5% − 30% higher momentum flux simultaneously. During withdrawal, a 30% momentum flux increase was observed shoreward of the first row of patches (x = 34.0 m) due to the piling up of seaward flow at the patches’ shoreward sides. Only two uniform within-patch roughness scenarios (low roughness and medium roughness) and only fourteen locations were analyzed in Irish et al. (2014). Here we (a) use experimental data to investigate the impact of another higher roughness and within-patch roughness variation, and (b) use numerical simulations to extend the experimental analysis to consider the full inundation time history, a higher planform resolution, and additional patch sizes.

4.3.1 Experimental Design

Large-scale experiments were conducted in the 43.6 × 26.5 × 1.5-m wave basin at the O.H. Hinsdale Wave Research Laboratory at Oregon State University (Fig. 4.1). Patches of subaerial vegetation were represented by 26 staggered cylinder arrays (rigid PVC) with a diameter of 1.2 m installed on the available 1:10 sloping steel beach in the basin. Because of the infeasibility of applying Froude scaling and Reynolds scaling simultaneously in the basin, cylinders could not represent vegetation stems per se in the scaled experiments. Thus, we considered a range of cylinder densities as a proxy for representing a range of bulk vegetative roughness conditions. Similar representation of roughness patches was applied in the simulations. Three uniform within-patch (i.e., constant within-patch cylinder spacing) roughness scenarios were considered; low roughness, medium roughness and high roughness (Fig. 4.2a,b,d). In addition, two scenarios with varying cylinder spacing in the cross-shore direction (i.e., low-high roughness and high-low roughness) were used to study the effect of within-patch roughness variation (Fig. 4.2c). The cylinder arrays (termed roughness patches) were affixed to the basin’s initially dry slope, and became emergent during wave inundation. Open spaces between the patches left clear cross-shore channels with no additional roughness. Measured parameters included offshore surface elevations, velocities and flow depths around the roughness patches, and bore front positions (from which runup height and bore velocity were determined). Yongqian Yang Chapter 4. 51

Figure 4.1: Planform view (a) and proﬁle (b) of laboratory setup (in m) (from Irish et al. (2014)). The bigger star labels with numbers distinguish the selected ADV/sonic locations for analysis. Waves propagate from left to right.

To address the limitations of classic solitary wave as a model for tsunami in the experiments Madsen et al. (2008), we used a 4-s error function to define the full stroke of the wavemaker motion, which generated a solitary-like wave with a longer inundation period (e.g. Baldock et al., 2009; Rueben et al., 2011; Thomas and Cox, 2011). The wave broke near the toe of the slope and evolved to a fully developed bore running toward the shore. The still offshore water level was maintained at 0.730±0.001 m. Five resistance-type wire wave gauges were installed from the wavemaker to the still water line for propagation measurements. Colocated ADV (Acoustic Doppler Velocimeter; 50 Hz) and sonic wave gauges (50 Hz) were mounted adjacent to the roughness patches to measure local flow velocities and water depths in 20 positions. For the control scenario (i.e., no roughness patches), making use of alongshore-uniform flow, only fourteen positions were measured. The ADV/sonic records were ensemble averaged over at least 50 (up to 55) repetitions of each experiment to obtain the mean flow properties. Two high-resolution cameras (Panasonic AW-HE60SN; 60 frames/s) were mounted above Yongqian Yang Chapter 4. 52

Figure 4.2: Patches of diﬀerent roughness scenarios. (a) Uniform low roughness (21 cylinders/patch); (b) uniform medium roughness (69 cylinders/patch); (c) non-uniform medium roughness (69 cylinders/patch); (d) uniform high roughness (129 cylinders/patch). For non-uniform roughness in (c), waves coming from left to right and from right to left deﬁne low-high roughness and high-low roughness, respectively. (e) and (f) are photos of one individual patch and shoreward view of patch array in the experiments, respectively. the basin to record the bore runup. Details about video analysis with optical technique are described in Appendix A. Table 4.1 summarizes all experimental scenarios. A full description of the experimental setup is provided in Irish et al. (2014).

4.3.2 Numerical Model Description and Setup

Despite the controlled conditions and high repeatability of the laboratory experiments, the time and expense of physical experimentation limited the amount of spatial resolution, as well as the number of scenarios that could be tested. Thus, we used numerical simulations to extend the range of the experiments by providing a complementary dataset for analysis. Long-wave theory is widely applied in the simulation of tsunamis. Since both nonlinearity and frequency dispersion are important in tsunami hydrodynamics, we apply the Boussi- nesq model COULWAVE, which is based on the nonlinear depth-integrated Boussinesq-type equations, and includes several sub-models to account for bottom friction and wave breaking (e.g. Løvholt et al., 2013; Lynett et al., 2002). Using wave-basin experiments with the presence of roughness, COULWAVE has been validated for the accurate prediction of water elevation and velocity in Augustin et al. (2009), Park et al. (2013) and Yang et al. (2015). The dimensional continuity and momentum equations are: Yongqian Yang Chapter 4. 53

Table 4.1: Matrix of all experimental scenarios

Scenario Cylinders Within-patch roughness fveg Control (no roughness) N/A N/A 0.003 Low roughness 21 uniform 0.020 Medium roughness 69 uniform 0.065 High roughness 129 uniform 0.120 High-low roughness 69 non-uniform 0.120 − 0.040 Low-high roughness 69 non-uniform 0.040 − 0.120 fveg is the friction coeﬃcient calibrated for the vegetation-like roughness in the simulations, except for the

control scenario that uses fNV (Fig. 4.6).

∂ζ + ∇ · [(ζ + h)u ] + H.O.T. = O(µ4), (4.1) ∂t α ∂u α + u · ∇u + g∇ζ + R − R − R + H.O.T. = O(µ4), (4.2) ∂t α α f b ev where ζ is the free surface elevation, h is the local water depth, uα = (uα, vα) is the reference horizontal velocity vector at zα from still water level, and g is gravity. Rf and Rb are the effects of bottom friction and wave breaking, respectively. Rev accounts for the eddy viscosity of turbulent mixing in horizontal and vertical planes. H.O.T represents the higher order nonlinear and dispersive terms in the order of O(µ2), while µ is the ratio between the water h depth and the wavelength ( λ ). More details about the complete set of governing equations can be found in, e.g., Liu (1994), Lynett et al. (2002), Kim and Lynett (2011) and Løvholt et al. (2013). Rather than resolving the individual cylinders, vegetation was represented as bulk roughness patches in the simulations. A uniform horizontal resolution of 16 cm was selected to sufficiently resolve the scale of the roughness patches. The effect of the vegetation-like roughness ub|ub| was approximated using the bottom friction term, Rf = f h+ζ , where f was the dimensionless friction coefficient and |ub| was the horizontal velocity magnitude at the bottom (derived from uα based on a quadratic relation). Patch areas were represented with a higher friction coefficient (fveg), while all other areas were represented with a background friction coefficient (fNV ) as summarized in Tab. 4.1. We simulated the laboratory experiments with COULWAVE, and validated the simulation results against the experimental data. Model validation with experimental measurements is presented in Appendix B. In addition to the various roughness levels and within-patch roughness variations studied in the experiments, it is recognized that natural coastal vegetation also varies in the degree of patchiness. To better understand the effect of roughness ratio (i.e., area of roughness patches divided by the total area), we simulated additional patch sizes with diameters ranging from 0.6 to 2.2 m at 0.2-m increments. Scenarios with continuous roughness (non-patchy) were simulated for reference. Yongqian Yang Chapter 4. 54

4.3.3 Momentum Flux

Hydraulic load during inundation is one of the most destructive factors of a tsunami. Hy- draulic load exerted on an object can be evaluated as drag force, 1 F = ρC u2A, (4.3) D 2 D where ρ is the fluid density, CD is the drag coefficient, u is the velocity, and A is the wetted area normal to flow direction. In Eq. 4.3, hydraulic load is proportional to momentum flux (i.e., M = ρu2h, where h is the inundated depth). Yeh (2006) concluded that Eq. 4.3 provided a reasonable estimate of tsunami’s hydraulic load given the momentum flux (M) with proper values of CD. Recent studies continued to use momentum flux to estimate the hydraulic load of tsunamis, which has significantly improved understanding of the hydrodynamics of tsunamis over roughness overland (e.g. Linton et al., 2012; Park et al., 2013; Rueben et al., 2014). In this paper, we use momentum flux as a proxy for hydraulic load.

4.4 Results

4.4.1 Impact of Roughness Patches on Momentum Flux

Alongshore variations in inundation were observed in the experimental results. Two locations in the cross-shore channel (Locations 1 and 4 in Fig. 4.1a and Fig. 5.1a) and two locations on the shoreward/seaward sides of patches (Locations 3 and 5) are selected to examine the influence. Figure 4.3 depicts the corresponding results of depth and momentum flux from the three roughness scenarios (uniform medium, high-low and low-high). Interpolation between bore speed from video and the ADV record was used to estimate the momentum flux of the initial aerated flow. Velocity data are not shown, because no significant difference was observed in these three scenarios (about 5% difference). In the seaward edge of the cross-shore channel (Location 1), water rises rapidly in the uniform medium and high-low scenarios, while the lower roughness seaward slows down water accumulation in the low- high scenario (Fig. 4.3a). This delay in depth accumulation by the low-high roughness patches leads to a 40% decrease in the peak momentum flux as shown in Fig. 4.3e. Farther onshore through the cross-shore channel of Location 4, only slight differences exist between the uniform and non-uniform within-patch roughness scenarios (Fig. 4.3b, f), demonstrating that the impact of within-patch roughness variation is less distinct at lower flow depths and speeds. Unlike in the channels, Locations 3 and 5 experience little effect of within-patch roughness variation, except for the slight difference in the multiple water-depth peaks by reflection. Though farther seaward than channel Location 4, Location 3 encounters only 50% of the maximum momentum flux observed at Location 4 (Fig. 4.3f, g); this reveals the capability of roughness patches to reduce extreme momentum flux on their shoreward sides. Yongqian Yang Chapter 4. 55

Figure 4.3: Experimental water elevation (a- d) and momentum ﬂux (e - h). From left to right are locations in channel (1 and 4) and shoreward/seaward of patches (3 and 5) in Fig. 4.1a, respectively. All three scenarios have the same cylinder number but diﬀerent within-patch spacings, i.e., uniform medium roughness (solid lines), high-low roughness (dashed lines) and low-high roughness (dotted lines).

The contours of percent momentum flux difference between the control scenario and roughness scenarios are shown in Fig. 4.4. Because of the strong flooding during initial runup and the reversal of flow direction after maximum inundation, three representative periods (runup, flow reversal and withdrawal) are selected for analysis. During runup (Fig. 4.4a - e), the areas shoreward of patches are sheltered from the strong momentum flux. In the meantime, velocity vectors follow curved paths around the patches in the first two rows (x = 34.0 and 36.2 m), demonstrating that flow channelization amplifies momentum flux between patches (y = ±1.0 m). Except for the low roughness scenario, the other roughness scenarios have similar degrees of momentum flux decrease (∼ 80%) and amplification (∼ 60%), implying that hydraulic load during runup is less sensitive to roughness level when it is above a certain point. When the flow starts to reverse (Fig. 4.4f - j), no evident difference is observed farther inland, but an approximately 200% stronger momentum flux is found in the offshore region (x < 33.0 m). This demonstrates the ability of roughness patches to reflect momentum seaward. The second row of patches (x = 36.2 m) continues to reduce momentum flux, while channelization of stronger loads still exists in between the first two rows (x = 34.0 and 36.2 m, y = ±1.0 m). The shoreward areas sheltered by the first row of patches (x = 34.0 m) Yongqian Yang Chapter 4. 56

Figure 4.4: Simulated momentum flux difference (in %) between control scenario (no roughness) and each of the roughness scenarios. Cool and hot colors indicate reduction and increase cause by roughness patches, respectively. Waves propagate from top to bottom in each pane. Panes from left to right are control vs. low roughness, medium roughness, high roughness, high-low roughness and low-high roughness. Panes from top to bottom are during runup, flow reversal and withdrawal. Dashed line depicts initial still water line. Black circles are roughness patches. Arrows are velocity vectors. Gray depicts no change in momentum flux, and white depicts no inundation. Yongqian Yang Chapter 4. 57

during runup are exposed to 90% − 160% stronger momentum flux in flow reversal. This illustrates a higher transient amplification than that indicated by the time-averaged analysis presented in Irish et al. (2014). During withdrawal (Fig. 4.4k - o), the roughness patches continue to reflect wave seaward, but the offshore areas of increased momentum flux are smaller than during the initial flow reversal. In the cross-shore channels (y = ±1.0 m) adjacent to the first two rows of patches (x = 34.0 and 36.2 m), narrow regions of higher momentum flux are still observed, which is attributed to the release of retained water from the patches. Similar to the initial flow reversal, the momentum flux difference after the second row of patch (x > 37.0 m) is insignificant, and, after a short period of increased momentum flux, the overland protection by the patches on the shoreward side of the first row (x > 34.0 m) is 40% − 90%. Unlike runup and flow reversal, the overall alongshore velocities during withdrawal are weak, indicating the dominance of strong gravity-driven flow during this period.

4.4.2 Impact of Roughness Patches on Runup Height

Inundation overland is another factor related to the extent of damage. Figure 4.5 shows the experimental runup height comparison among the various scenarios, extracted from videos by the optical technique, and averaged over 60 trials for each scenario. Runup analysis is presented for the locations at the shoreward edges of patches and cross-shore channels. The higher roughness levels provide more runup reduction, but the relative benefit appears to diminish with increasing roughness. In addition, for the three medium-roughness scenarios (uniform medium, high-low, and low-high), the two within-patch roughness variation ones offer more runup reduction than the uniform one, especially shoreward of the patches. For the low-high roughness scenario, runup on the shoreward edge of patches is lower than the uniform and high-low scenarios. Along with its weaker momentum flux amplification in the cross-shore channels (Fig. 4.3a), the low-high roughness scenario tends to provide better overall protection against runup height. Overall, the percentage reduction in runup height by the roughness patches is less significant than the reduction of momentum flux, with an approximately 5% − 9% decrease shoreward of patches and a 2% − 5% decrease at the cross-shore channels. Simulated runup heights are also shown in Fig. 4.5. Though the experimental channelization of bore fronts (Fig. 5.1a in Appendix A) is observed in the simulations during runup period, the alongshore variability in maximum inundation is insignificant in the simulations. This is attributed to the model approximation of roughness patches of higher bottom friction. In the experiments, the emergent cylinders obstruct considerable water volume, while in the simulations the increased bottom friction still allows surface flow over the patches. The lack of alongshore variability in the final bore front of simulations demonstrates the model’s limitation in capturing the 3%−4% alongshore variation in maximum inundation. Thus, the simulated runup heights in Fig. 4.5 are averaged in the alongshore direction. On the whole, Yongqian Yang Chapter 4. 58

1.16 Experiment, shoreward of channel 1.14 Experiment, shoreward of patch Simulation, alongshore-averaged 1.12

1.1

1.08

Runup (m) 1.06

1.04

1.02

1 Control Low Medium High-low Low-high High roughness roughness (Medium) (Medium) roughness

Figure 4.5: Experimental runup heights shoreward of cross-shore channels (black histograms) and shoreward of patches (gray histograms) in different scenarios. Circles depict the simulated alongshore-averaged runup heights, because of the insignificant runup difference at the shoreward edges of patches and channels in the simulations. “Control” represents the scenario with no roughness patches. the alongshore-averaged runup heights from the simulations are between the experimental results at the shoreward edges of channels and patches, with relative errors less than 4%. This shows the model’s capability of predicting overall runup.

4.4.3 Impact of Planform Roughness Size on Momentum Flux

Figure 4.6 depicts the percent momentum flux difference between the control scenario and each of 5 roughness sizes (i.e., 0.6 m, 1.2 m, 1.6 m, 2.2 m patch diameters and continuous roughness) under medium within-patch roughness. During runup in Fig. 4.6a - e, the increasing patch size leaves narrower spaces for flow channelization, leading to weaker momentum flux amplification around the second patch row (x = 36.2 m, y = ±1.0 m). With continuous coverage, the roughness region is protected from loads, with only a small fraction on the seaward edge experiencing comparable impact to the control scenario. During flow reversal in Fig. 4.6f - g, larger roughness patches result in a wider offshore area of increased momentum flux, and reduce the load amplification shoreward of the first row of patches (x = 34.0 m). During withdrawal in Fig. 4.6k - n, larger patches eliminate the load amplification in the cross-shore channels (y = ±1.0 m) around the second row (x = 36.2 m) and reflect more energy seaward. Under the continuous roughness scenario, most of the wave energy has been reflected seaward during the earlier flow reversal, and no offshore region with increased loads is found in Fig. 4.6o. Figure 4.7 shows the cross-shore maximum momentum flux through (a) the cross-shore channels and (b) the patches (y = 0.0 m) using three different patch sizes having medium Yongqian Yang Chapter 4. 59

Figure 4.6: Simulated momentum flux difference (in %) between control scenario (no roughness) and different roughness sizes with medium roughness. Cool and hot colors indicate reduction and increase cause by roughness patches, respectively. Waves propagate from top to bottom in each pane. Panes from left to right are control vs. 0.6-m patches, 1.2-m patches, 1.6-m patches, 2.2-m patches and continuous roughness (between solid lines in e, j and o). Panes from top to bottom are during runup, flow reversal and withdrawal. Dashed line depicts initial still water line. Black circles are roughness patches. Arrows are velocity vectors. Gray depicts no change in momentum flux, and white depicts no inundation. Yongqian Yang Chapter 4. 60

1000 )

2 Patch Patch Patch 800 D=0.8 m 600 D=1.2 m D=2.0 m 400 Continuous Control 200

Momentum Flux (kg/s (a) 0 33 34 35 36 37 38 39 40

1000 )

2 Patch Patch Patch 800

600

400

200 (b) Momentum Flux (kg/s 0 33 34 35 36 37 38 39 40 Cross-shore (m) Figure 4.7: Simulation results of maximum momentum ﬂux with patch diameters of 0.8 m (triangles), 1.2 m (circles) and 2.0 m (squares). Dashed lines and dash-dotted lines are continuous roughness scenario and control scenario, respectively. Vertical dotted lines denote the centers of patches. The roughness scenarios correspond to the medium roughness level. (a) Comparison through cross-shore channels. (b) Comparison through patches.

within-patch roughness. The diameter of the patches in the original experiments was 1.2 m. In Fig. 4.7a, the maximum momentum flux through the widest channel (smallest patch size) is almost the same as in the control scenario, with an approximately 4% increase between the first two rows of patches (34.0 < x < 36.2 m) and a slight decrease after the second row (x > 36.2 m). With increasing patch size, momentum flux decreases more rapidly shoreward. Results of the continuous roughness scenario draw the lower limit for the patchy scenarios. Through the patches in Fig. 4.7b, as expected, the larger patches cause more reduction in the maximum momentum flux. With all roughness sizes, the maximum momentum flux decays rapidly and approach the performance of the continuous roughness scenario. This implies that the sheltering effect of roughness becomes less sensitive to patch size when the roughness ratio (i.e., the ratio between roughness area and the total area) approaches continuous coverage. The results from the control scenario and the continuous roughness scenario set the asymptotic limits. Yongqian Yang Chapter 4. 61

4.5 Discussion

Roughness patches shelter most areas from extreme momentum flux, but it also leaves some areas unprotected. The results shown in Fig. 4.4 illustrate the higher potential of damage in the cross-shore channels, which is consistent with previous studies reporting more severe destruction in the open gaps in forests (e.g., Fernando et al., 2008; Tanaka, 2009; Thuy et al., 2009). Additionally, higher momentum flux is observed on the shoreward side of roughness patches during flow reversal, which would undermine the role as a buffer zone against damage. However, closer analysis demonstrates that the momentum flux shoreward of the first row of patches (x = 34.0 m) during flow reversal is more than 85% smaller than the maximum value in the same area during the whole impact period in the control scenario. As a result, the 90% − 160% amplification shoreward of the first patch row (x > 34.0 m) during flow reversal (Fig. 4.4f - j) accounts for only 25% of the maximum momentum flux at the same locations. In contrast, roughness patches reduce the maximum momentum in these areas by up to 80% compared to the control scenario. This supports the use of roughness patches in mitigating the extreme destruction during tsunamis. In nature, the growth of coastal vegetation is more dynamic. It depends on various factors, such as native vegetation species, soil conditions, nutrient supplies and so on. Even within a grouping of same species, the death of old plants and the growth of new ones can also lead to randomness in the spatial coverage. Our experiments involving within-patch roughness variation provide insight into the uncertainty of natural vegetation variability on hydraulic loads. Figure 4.3e demonstrates that within-patch roughness variation has a pronounced influence on flow channelization, with the low-high roughness scenario experiencing 40% lower momentum flux in the seaward edge of the cross-shore channel, compared to the uniform medium roughness scenario. This effect might be leveraged in the design of nature-based infrastructure. Tanaka (2009) and Tanaka et al. (2011) proposed a relevant method for mixing different plant species layers to increase the protection effectiveness of coastal vegetation. Our simulation results of the three medium-roughness scenarios do not show the variability observed in the experiments (i.e., Fig. 4.3e). This implies the uncertainty that within-patch roughness variation introduces on the hydrodynamics. Since vegetation growth is less predictable, and its roughness might vary seasonally, model prediction of hydrodynamics without proper approximation of within-patch roughness variation may have higher uncertainty around the patches, though the overall flow patterns are simulated satisfactorily. To further analyze the effect of patch size on mitigating extreme momentum flux, the scenarios with patch sizes ranging from 0.6 m to 2.2 m were simulated with low-, medium- and high-roughness levels. Figure 4.8 shows the fractional area that experiences lower maximum momentum flux under different within-patch roughness levels and roughness ratios, compared to the control scenario; where Sveg is the area covered by roughness patches, SNV is the area between patches, S is the total area on the slope (S = Sveg + SNV ), and Sd is the area protected from maximum momentum flux (excluding patches). It is observed that higher roughness level is capable of sheltering a slightly larger fraction of the area in the Yongqian Yang Chapter 4. 62 vicinity of roughness patches, especially in the presence of a lower roughness ratio. However, the influence of roughness level is secondary compared to roughness ratio, and the protected fraction tends to converge with increasing roughness level. All simulation results follow a logarithmic distribution with roughness ratio, which confirms the interpretation from Fig. 4.7 that as roughness area is increased the relative benefit in mitigating damage likely di- minishes. Another practical consideration is that a high roughness ratio results in less land Sveg available for coastal development. For instance, with S = 1, which corresponds to a continuous forest, infrastructure is limited to the region behind the forest rather than intermixed with the roughness patches. Using the data in Fig. 4.8, a regression equation is obtained :

f S ( veg )0.026 d = fNV . (4.4) Sveg SNV −0.089 log [3.350 ( S ) ] where log is natural logarithm and the coeﬃcient of determination, R2, is 0.927. For patch Sveg diameter larger than 2.2 m (i.e., S = 0.393), no cross-shore channel exists, which sets the upper limit of validity for Eq. 4.4. This equation may be used as a preliminary estimate of vegetation performance in coastal planning and management.

4.5.1 Conclusions

The intrinsically dynamic feature of coastal vegetation often leads to spatial variability in planform distribution. Understanding the complex tsunami interaction with such variability in onshore environments is essential to the use of coastal vegetation as a natural defense. This study quantifies tsunami dynamics in a more realistic layout at the coasts, patchy vegetation, and provides confidence in its application to coastal protection. The findings demonstrate that patchy vegetation is able to reduce the extreme hydraulic loads of tsunamis. Though some locations experience transiently higher loads, the amplification is insignificant compared with the maximum hydraulic loads in the same areas during the whole inundation. Roughness patches reduce up to 80% of the maximum hydraulic loads in most areas. The protected area by roughness patches is in positive correlation with the total roughness area, but the effectiveness of protection becomes relatively less significant when the roughness ratio approached continuous coverage. Therefore, patches with a certain size, rather than a continuous vegetation belt, may be sufficient for mitigating tsunami damage. The logarithmic relation (Eq. 4.4) developed between the protected areas, roughness level, and roughness ratio can be applied in the design of nature-based infrastructure for tsunami mitigation. Another implication of this relationship between roughness level and protected area is that seasonal changes may not significantly affect the protective role vegetation plays in tsunami mitigation. The results of our study underline the uncertainty in predicting hydrodynamics in patchy vegetation. The experiments show that within-patch roughness variation introduces vari- Yongqian Yang Chapter 4. 63

0.86

0.84

0.82

0.8

0.78

d 0.76 NV S S 0.74

0.72

Low roughness 0.7 Medium roughness High roughness 0.026 0.68 Sd (fveg /fNV ) = −0.089 SNV log [3.350 (Sveg /S) ] 0.66 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Sveg S Figure 4.8: Fractional area protected from maximum momentum flux, in terms of roughness ratio (between roughness area and total area) and roughness level. Low roughness (triangles), medium roughness (squares) and high roughness (circles) scenarios are all simulated with patch size from 0.6 to 2.2 m. Sveg is the area of vegetation-like roughness, SNV is the area between patches, S is the total area on the slope (S = Sveg +SNV ), and Sd is the area protected from maximum momentum flux (excluding patches). fveg and fNV are friction values for vegetation-like roughness and no-roughness background, respectively. Solid lines represent Eq. 4.4 with different frictions. ability in inundation depth, which leads to 40% lower loads in the seaward channel of the low-high roughness scenario. These results may help to explain the deviation between predicted and actual tsunami dynamics in real world, if the within-patch roughness variation is not appropriately considered in simulations. They also help to evaluate the uncertainty in the estimate of hydraulic properties in the presence of roughness patches. In closing, because patchy vegetation commonly exists naturally along coastlines, it is necessary to understand its efficiency in mitigating tsunami damage. Our findings demonstrate both the protective role and the potential vulnerability induced by coastal vegetation patches. Overall, patchy vegetation is beneficial in reducing the most destructive hydraulic loads of tsunamis. Our findings provide insight into evaluating vegetation’s performance in mitigating tsunami impact with spatial variability onshore. As such, the findings herein fill a knowledge gap needed to develop meaningful engineering guidelines for using nature-based infrastructure for tsunami mitigation. The broader benefit of this study is to improve public awareness, hazard warning and risk analysis, which could eventually lessen the impact of Yongqian Yang Chapter 4. 64 coastal hazards to communities. Future work is needed to understand the uncertainty on hydrodynamics introduced by vegetation variability, the influence of broken vegetation (and resulting debris) on the flow, and the role of vertical plant structure on the flow. Finally, further development of predictive models for early warning and coastal planning is needed to better resolve smaller-scale vegetated flow characteristics.

Acknowledgements

This material is based on work supported by the National Science Foundation (Grant No. CMMI-1206271). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. The authors acknowledge Advanced Research Computing at Virginia Tech for providing computational resources and technical support that have contributed to the results reported within this paper. The authors would like to especially thank Dr. P. J. Lynett (University of South California) for providing the source code of COULWAVE, and thank Mr. T. Irish for his comments on editing the paper. Help from staff and students during the experiments in the Hinsdale Wave Research Laboratory at Oregon State University is gratefully acknowledged. Chapter 5

Conclusions

Using vegetation to mitigate natural hazards is a sustainable way for coastal development in the future. Previous studies have proven the eﬃciency of continuous vegetation in reducing wave energy, while we extend the study to patchy vegetation that has open spaces. Since patchy vegetation commonly exists in nature due to the spatial and seasonal variability of growth, understanding the wave dynamics in vegetation patches is essential to the application of nature-based infrastructure to coastal protection. This dissertation investigates the impact of patchy vegetation on wave evolution, using laboratory experiments and numerical simulations. Both normal wave conditions (Chapter 2 and Chapter 3) and extreme events (Chapter 4) are used to evaluate the eﬀectiveness of patchy vegetation. The main conclusions can be summarized as follows:

• Vegetation patches significantly attenuate wave-induced currents and the corresponding circulation in mound-channel wetland systems, especially over the mounds. The seaward current strength and primary circulation size are in logarithmic and power- form relations, respectively, to wave conditions and bathymetric parameters in the wetlands. • Wave-spectrum evolution in mound-channel wetland systems is space- and frequency- dependent, with more attenuation on the high-frequency spectra and increased energy in specific locations/harmonics. This demonstates a distinction with continuous vegetation, which dissipates wave energy over frequency and space. • Unlike continuous vegetation, in the presence of open spaces between vegetation patches, vulnerability associated with transiently higher loads exists in some locations. With appropriate configuration, however, patchy vegetation is efficient at mitigating the most destructive loads of tsunamis. The protected area from extreme hydraulic loads follows a logarithmic relation with the ratio of vegetated land.

Numerical results from Boussinesq model in Chaper 2 show the patterns of wave-induced

65 Yongqian Yang Chapter 5. Conclusions 66 current and circulation in mound-channel wetland systems, selected from prototype in Dale- hite Cove, Galveston Bay, TX. Similar to classic bar-channel bathymetry in previous studies, the more complicated mound-channel systems induce rip-current circulation in the wetlands. Patchy vegetation on the tops of mounds has more significant effects on current than wave height; shoreward current over patchy vegetation decreases by 75%, while significant wave height only changes by about 15%. The modified current patterns by patchy vegetation results in changes in circulation, with smaller primary vortex around the mounds and expanded secondary vortex downstream. Dimensional analysis reveals that the magnitude of current can be quantified using a logarithmic equation (Eq. 2.6) with wave and bathymetric parameters. Similarly, the primary circulation size can be estimated using a power-form equation (Eq. 2.8). These two relations provide a way to evaluate wetland condition in engineering practice. A further numerical investigation in Chapter 3 extends the study in Chapter 2 to spectral wave conditions. Though previous studies have noted the frequency-dependent attenuation of wave energy by continuous vegetation, few of them observe amplified energy induced by vegetation. Our results indicate that spatial variability within vegetation causes more complex interaction between the various wave harmonics. Mound-channel wetland systems not only attenuate wave energy but also induce energy transfer across the frequency domain, leading to increased energy in specific locations or harmonics. Overall, compared to unvegetated horizontal bathymetry, the mound-channel wetland systems in our study are capable of attenuating wave energy significantly. Furthermore, the energy transfer from dominant frequencies to high harmonics may reduce the duration of critical force exerted on sediments, thereby reducing sediment pick-up and subsequent transport. Along with the reduced current magnitude observed in Chapter 2, mound-channel wetland systems may be more beneficial to the long-term stability of wetlands against erosion induced by nearshore processes. Applying both laboratory experiment and Boussinesq modeling, we evaluate the performance of patchy vegetation in extreme events, tsunamis, in Chapter 4. Depending on the size and roughness level of vegetation patches, the maximum runup of tsunami decreases by about 10%. Since coastal infrastructure is usually constructed at higher elevations, this runup reduction is significant in mitigating the flooding damage. Using momentum flux as a proxy for hydraulic loads, we demonstrate that patchy vegetation is able to reduce the maximum tsunami loads by up to 80% in most areas. The protected land area by patchy vegetation is in positive correlation with vegetated area. However, the effectiveness becomes relatively less significant when the vegetated ratio approached continuous coverage, according to a logarithmic equation (Eq. 4.4) from dimensional analysis. The secondary effect of roughness level in the logarithmic equation implies that seasonal changes of vegetation density may not significantly influence the protective role vegetation plays in tsunami mitigation. These findings prove the effectiveness of patchy vegetation against natural hazards. We point out the importance of accounting for the potential negative effects of patchy vegetation as a coastal defense. When arranged properly, vegetation patches may behave similarly, or even Yongqian Yang Chapter 5. Conclusions 67 more effectively, compared to continuous wetlands/forests. This dissertation may provide renewed guidance on how to harness the benefits of vegetation patches in coastal protection, while minimizing the negative effects. We hope our results will improve public awareness of coastal hazards, and facilitate the application of nature-based infrastructure to engineering practice. We recognize that knowledge gaps still exist in sedimentation and debris flow in patchy vegetation. Our study neglects the effect of morphological changes on the flow. This assumption is valid in short period of hours or days, but the process of sedimentation may start to play a role in long term, which will influence the stability of wetlands. During extreme events like tsunamis, the possibility of broken vegetation or infrastructure increases significantly, and the resulting debris in the flow can lead to sequent destruction farther ashore. In addition, the limitation of grid refinement in COULWAVE, mainly due to the stability requirement, constrains its application when higher grid resolution is required. In the future, more work is needed to quantify sediment movement under the effect of energy transfer across frequencies within mound-channel wetland systems. Broken debris during extreme events should be included in experimentation and numerical modeling to account for the extra hazard to patchy vegetation and infrastructure. The steep topography (1:10) in Chapter 4 helped to restain the maximum tsunami inundation ashore, so varying topographic slopes should be modeled in future experiments/simulations to comprehensively evaluate patchy vegetation in mitigating tsunami damage. Finally, further model development is needed to better resolve smaller-scale vegetated flow characteristics. References

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5.1 Appendix A

5.1.1 Optical Technique for Estimating Bore-front Velocity

Tsunami bores can cause devastating damage to coastal communities (e.g., Linton et al., 2012; Palermo et al., 2009; Yeh, 1991). Yet, due to the high aeration level of bores, ADV was not capable of measuring velocities during this initial inundation (e.g., Baldock et al., 2009; Linton et al., 2012; Rueben et al., 2014, 2011). Previous studies used optical techniques to trace bore fronts in videos and compute bore speed from cross-shore displacement between sequential frames (e.g., Park et al., 2013; Rueben et al., 2014, 2011). The assumption of cross- shore dominant flow in these studies, however, neglected the alongshore velocity component. In the presence of roughness patches, the induced alongshore velocity could be of the same order-of-magnitude as cross-shore component in some regions, and should not be neglected. Assuming bore propagation in the orthogonal direction of bore front curvature, Song (2013) developed another optical technique that was capable of extracting the two-dimensional bore front velocities from the video frames. Song (2013) validated the results with the analytical solution for a propagating cosine function, showing less than 5% error when a resolution of 1 cm/pixel was used. Following the assumption in Song (2013), we further developed the algorithm for more complicated lighting conditions and scenarios, and applied the algorithm to our rectified videos (1-cm/pixel resolution). Using a video frame of the dry slope as a reference, the bore fronts in videos were isolated and detected automatically by the algorithm by subtracting the reference frame from each instantaneous frame. The results were ensemble-averaged over 60 repetitions for each experimental scenario. Runup height, defined as the elevation of the maximum flooding location (e.g., Synolakis, 1987), was calculated directly from the maximum bore inundation on the 1:10 slope. Finally, the algorithm calculated the orthogonal motion between each two sequential bore fronts, which provided the two-dimensional velocities along every bore front after being divided by the time interval.

78 Yongqian Yang Chapter 5. Conclusions 79

5.1.2 Experimental Bore Front Data

As detected by the optical algorithm, Fig. 5.1a shows representative ensemble-averaged bore fronts for the medium roughness scenario, while Fig. 5.1b - d show the corresponding averaged bore velocity fields. Roughness patches dissipate cross-shore bore velocity more significantly on the shoreward sides of the patches than through the cross-shore channel, while strong alongshore variability is induced in the wakes shoreward of patches. Overall, the contours of cross-shore velocity (Fig. 5.1b) and velocity magnitude (Fig. 5.1d) are similar. Two cross-shore stripes with very low values exist in the wakes of the cross-shore velocity field (the two brightest areas in Fig. 5.1b), which are less intense in the velocity magnitude field (Fig. 5.1d). The locations of these two areas coincide with the areas of increased alongshore velocity (both positive and negative values) in Fig. 5.1c. Thus, the reduced cross-shore velocities are compensated by the induced alongshore component in Fig. 5.1d. This implies that the alongshore component of bore speed is not negligible in the presence of roughness patches, especially in the wake regions. Since hydraulic loads are proportional to the square of velocity magnitude (Eq. 4.3), neglecting alongshore velocity can lead to an underestimation of hydraulic loads. The optical results fall in a reasonable range (10%−15%) with regard to linearly extrapolated magnitudes from the ADV records (Fig. 5.2). Therefore, linear interpolation between ADV data and bore speed from the optical technique appears to give a reasonable estimate of the missing ADV records in the aerated flow during initial inundation. Such interpolation is needed to evaluate the full time series of experimental momentum flux, and validate simulation results. Based on the alongshore-symmetric setup, the ADV/sonic locations are mirrored into the sub-domain shown in Fig. 5.1a for bore velocity extraction at each location.

5.2 Appendix B

5.2.1 Model Calibration and Validation

Model calibration was performed for the friction coefficients of Rf in Eq. 4.2. Background friction of no-roughness area was calibrated by matching simulation results with experimental data in the control scenario, i.e., 3% errors in offshore water elevations and 1% error in runup height. Roughness friction coefficients were calibrated with respect to the ADV/sonic measurements on the slope. √ Figure 5.2 shows model validation by velocity magnitudes ( u2 + v2, positive in runup and negative in withdrawal) and water depths on the slope for control scenario. For velocity, R2 (square of correlation coefficient) values were above 0.95 in 86% of ADV/sonic locations. For water depth, R2 values were above 0.85 in 93% of ADV/sonic locations. The L1 norms of error were mostly below 0.10 m/s and 0.02 m for velocity and water depth, respectively. Yongqian Yang Chapter 5. Conclusions 80

Figure 5.1: (a) Bore fronts traced by the algorithm every 5 frames in the medium roughness scenario. Triangles are ADV/sonic locations measured in experiments. Numbers 1 − 6 correspond to the selected ADV/sonic locations in Fig. 4.1 after mirrored into the symmetric sub-domain. (b)-(d) Cross-shore, alongshore and magnitude of bore velocities (in m/s) obtained from bore fronts. Waves propagate from top to bottom.

The higher predicted water depth on the slope can be attributed to a variety of reasons. Firstly, the slope in the wave basin consisted of steel boards (3.3 × 3.3 m) with narrow seams (1-cm wide). Though all the seams were filled with foam adhesive, water might leak slightly during inundation, leading to less water volume on the slope. Secondly, ADV/sonic mounts interfered with flow. During experiments, the inundation extent shoreward of the ADV/sonic area was about 0.3 m shorter than the adjacent area under cameras. Thirdly, in experimental data processing, low-pass filtering and ensemble-averaging might smooth out some transient peaks of leading bores (e.g., Baldock et al., 2009), resulting in underestimated mean water depth. Taking these factors into account, the simulated water depths on the slope are reasonable. The order of deviation on water depth prediction is consistent with those obtained by Park et al. (2013), which applied the same Boussinesq model with a similar wave-basin setup. Yongqian Yang Chapter 5. Conclusions 81

4 4 4 (a) Simulation (b) Simulation (c) Simulation 3 Experiment 3 Experiment 3 Experiment Bore speed Bore speed Bore speed 2 2 2

1 1 1

0 0 0

velocity (m/s) -1 velocity (m/s) -1 velocity (m/s) -1 R2= 0.992 R2= 0.992 R2= 0.963 -2 -2 -2

-3 -3 -3 10 12 14 16 18 20 10 12 14 16 18 20 10 12 14 16 18 20 t (s) t (s) t (s)

0.16 0.16 0.16 0.14 (d) Simulation 0.14 (e) Simulation 0.14 (f) Simulation Experiment Experiment Experiment 0.12 0.12 0.12

0.1 R2= 0.941 0.1 R2= 0.923 0.1 R2= 0.961 0.08 0.08 0.08

depth (m) 0.06 depth (m) 0.06 depth (m) 0.06

0.04 0.04 0.04

0.02 0.02 0.02

0 0 0 10 12 14 16 18 20 10 12 14 16 18 20 10 12 14 16 18 20 t (s) t (s) t (s)

Figure 5.2: Model validation with velocity (a - c) and water depth (d - f) on the slope, corresponding to Locations 2, 4 and 6 in Fig. 4.1a. Solid lines are simulation results, while dashed lines are experimental data. Star labels represent bore speed from√ the optical technique. Velocity is calculated as magnitude of cross-shore and alongshore components (i.e., u2 + v2) during runup (positive) and withdrawal (negative). Correlation values (R2) between measurements and simulations are also shown in each pane. Optical technique and bore velocity ﬁelds are presented in Appendix A.

For the roughness patches, friction coefficients were calibrated with respect to ADV/sonic measurements. With increasing roughness, the zero-crossing moments in velocity records were different, and multiple reflection peaks occurred in the sonic gauge data. To capture this flow-roughness interaction in the simulations, roughness frictions were calibrated to maximize the correlation between measured and simulated data. In roughness scenarios, R2 values were above 0.90 for velocity in 72% − 100% of locations, with L1 norm of error mostly below 0.15 m/s. For water depth, R2 values were above 0.80 for 74% − 95% of locations, with L1 norm of error mostly within 0.02 m. Overall, the model performance is satisfactory. The higher predicted water depths imply that COULWAVE simulation tends to overestimate flooding depth, so decisions based on the simulation results tend to be more conservative. The friction coefficients are summarized in Tab. 4.1.