1 ATTENUATION OF SOLITARY WAVE BY ... - Journals

ATTENUATION OF SOLITARY WAVE BY PARAMETERIZED FLEXIBLE MANGROVE MODELS Agnieszka Strusińska-Correia1, Semeidi Husrin2 and Hocine Oumeraci1 The systematic laboratory investigation on tsunami attenuation by flexible mangrove models was performed in order to improve the knowledge on tsunami-coastal forest interaction. A sophisticated parameterization method, based on structural and bio-mechanical properties of a mature mangrove (Rhizophora sp.), was developed for the construction of the mangrove models under assumption of stiff and flexible structure. The forest model examined in the laboratory experiments consisted of the selected flexible mangrove models, arranged in different configurations, which was impacted by a tsunami-like solitary wave of varying height, propagating in different water depths. Based on the envelopes of max. wave height and wave forces induced on single tree models, wave evolution modes were determined to identify the source of wave attenuation. The results indicate the dependence of wave transmission on the observed wave evolution modes and relative forest width: the highest transmission coefficient is attributed to nonbreaking waves (ca. 0.78 and 0.55 for forest width of 0.75 and 3.0 m, respectively), while the lowest transmission coefficient corresponds to wave breaking in front of/in the forest model (ca. 0.5 and 0.3 for forest width of 0.75 and 3.0 m, respectively). eywords: mangroves; parameterization method; solitary wave; wave attenuation; laboratory experiments

INTRODUCTION

The positive role of coastal vegetation in the preservation of coastal ecosystems and in the prevention of the inland from flooding due to storms and cyclones is undisputed – coastal forests have been employed to enhance stabilization of the coastal zone (particularly dunes), to protect the adjacent fields from salt spray and wind, to support fisheries and to dissipate energy of short-period waves (e.g. Badola and Hussain 2005, Wolanski 2007, Mazda et al. 1997b). The recent tsunami events in 2004 and 2011 have attracted public attention to another aspect of the protective role of a coastal forest, in particularly mangroves, namely tsunami mitigation. In many of post-tsunami field survey reports (e.g. Kathiresan and Rajendran 2005, EJF 2006, Yanagisawa et al. 2009), lower casualties and property losses were claimed due to the presence of a dense mangrove forest. However, a detailed insight into the local tsunami hydrodynamics, local topography-bathymetry features and pre-tsunami forest conditions was very often ignored in these reports, what might have led to overestimation of the performance of mangrove forests during the 2004 Indian Ocean Tsunami. Definitely, performance of a coastal forest is conditioned by several factors such as vegetation characteristics (vegetation type, age, health state, density, width of the green belt), tsunami parameters (height, period, angle of impact), local morphology and soil properties, and is limited by the magnitude of the tsunami event and the tree resistance to wave impact. Although some vegetation zones were found intact after the recent tsunami events, most of them, particularly those facing directly an open sea, were moderately to heavily damaged by tilting, trunk/branches breakage and uprooting (e.g. Shuto 1987, Latief and Hadi 2006, Yanagisawa et al. 2009). The influence of the above-mentioned parameters on the effectiveness of a mangrove forest in tsunami mitigation has not been addressed in previous experimental investigations. Particularly the lack of a comprehensive parameterization method for the development of a tree model under consideration of structural and bio-mechanical tree properties is the main disadvantage of these studies, enabling comparison of the experimental results. The geometry of mangrove trees was either idealized by using single cylinders representing tree trunk (and thus neglecting the roots and the canopy) or modeled by means of material of very different properties than the prototype (dimensions, stiffness, etc.). Fig. 1 shows selected mangrove models, examined in previous studies. The parameterization approach applied to the development of a tree model determines the hydrodynamic performance of the forest model considered and the processes accompanying wave-tree interaction. Inappropriate assumptions on structural and bio-mechanical properties of the tree as well as too strong simplification of tree structure may lead to gaining incorrect experimental data and wrong assessment of the damping characteristics of the forest.

1

2

Hydromechanics and Coastal Engineering, Technical University Braunschweig, Beethovenstr. 51a, Braunschweig, Lower Saxony, 38106, Germany Research Institute of Coastal Resources and Vulnerability, Ministry of Marine and Fisheries Affairs, Padang-Painan Km.16, Padang, West Sumatera, 25245, Indonesia

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COASTAL ENGINEERING 2014

Figure 1. Examples of parameterized mangrove models from previous studies: a) cylinder-shaped model by Massel et al. 1999, b) porous model by Harada and Imamura 2000, c) wire-made model by Istiyanto et al. 2003, d) model by Kongko 2004 with cylinders representing roots, trunk and canopy (after Husrin 2013).

In this paper, the effectiveness of a parameterized mangrove forest in attenuation of a solitary-like tsunami wave is discussed, based on laboratory experiments performed for different forest configurations, water depths and incident wave conditions. The approach proposed for the parameterization of mangrove Rhizophora sp., accounting for physical tree properties, represents the core of this study. DEVELOPMENT OF APPROACH FOR PARAMETERIZATION OF MANGROVES

Considering the wave damping properties of a mangrove in respect to its geometry and biomechanical properties, Rhizophora sp. with a very dense, wide root system and a well-developed canopy represents mangroves that are most suitable for the purposes of this study (see Fig. 2a). Tree resistance to flow depends largely on tree growth stage, during which tree dimensions, root/canopy density and trunk elasticity change greatly. In order to ensure maximum tree resistance to flow, a mature Rhizophora sp. was considered in the parameterization method. Development of a generic parameterization approach was conditioned by the necessity of use of simple mangrove models in the experiments and the reduction of the effort spent on the preparation of the experimental set-up. Unlike the previous studies, the simplification of mangrove geometry, particularly the complex 3D root system and the canopy, was based on both structural and biomechanical properties of a mangrove, under condition of same hydraulic losses in the prototype and the model. The tree characteristics (i.e. dimensions, trunk elasticity, root and canopy density) was defined using data available from previous studies, extended by own field measurements performed on a young, mid age and mature Rhizophora apiculata by Semeidi Husrin in Angke Kapuk Protected Forest Region on Java Island in Indonesia (see Husrin 2013 for more details). When determining a typical geometry of a mature Rhizophora sp., shown in Fig. 2b, other available field data by e.g. Mazda et al. 1997a, Istiyanto et al. 2003, Harada and Kawata 2005 were additionally used. In the literature, values of Young modulus, defining the elasticity of the trunk, range from 8.27 × 109 N/m2 for 17% of moisture content for Rhizophora sp. (Hawa 2005) to 20.03 × 109 N/m2 for mangroves (Vallam et al. 2011). Young modulus of 13.6 × 109 N/m2 (for moisture content of ca. 15%) was obtained from deflection tests of wooden probes, performed in the framework of own field surveys. Concept of a submerged root ratio Vm/V, introduced by Mazda et al. (1997a), was adopted to define the density of the root system as a function of water depth (where Vm represents the volume of submerged roots and V the water control volume). This method required counting of the roots at selected water levels, which in case of the field work by Mazda et al. (1997a) were limited to the tidal level of 0.5 m and were extended up to ca. 1.5 m in own field surveys. Canopy density was specified using Leaf Area Index (LAI), which represents a ratio of a total onesided leaves area to the downward projected area of a canopy. By estimating the number of leaves on mangrove main branches, leaves area and number of the branches, LAI of 1.3, 3.3 and 2.9 was determined for a young, mid-age and mature tree, respectively, in own field measurements. In the literature, LAI of ca. 7 was reported for mangroves by Green and Clark (2000), while Clough et al. (2000) underlined its dependency on tree age (LAI > 5.0 for mangroves younger than 5 years, LAI ca. 1.8 for 36 year old mangroves). LAI of 4.5 was considered in this study.

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COASTAL ENGINEERING 2014 3.75 m

canopy

b)

http://1.bp.blogspot.com/‐8Sml4yn3onI/TtBlaTrxu‐ I/AAAAAAAAQcA/qng3m23ZmCA/s400/Rhizophora‐stylosa‐1.jpg

trunk

0.15 m

MHWL

roots

0.5, 1.0, 1.5, 2.5 m 2.0 m

10.0 m

5.5 m

a)

0.125 m 3.75 m

Figure 2. Mature mangrove Rhizophora sp. in natural habitat (a) and its geometry (b).

Based on the defined structural and bio-mechanical properties of a mature Rhizophora sp., two parameterization approaches were developed in order to determine the contribution of each structural tree element (i.e. the root system, the trunk and the canopy) to wave attenuation, depending on tsunami flow depth:  Stiff structure assumption, in which the tree model consisted of a parameterized root system and a stiff trunk. The stiff mangrove model was submerged maximally up to the top of the trunk, what corresponded to tsunami of a moderate magnitude (see Strusińska-Correia et al. 2013).  Flexible structure assumption, in which the tree model consisted of a parameterized root system (identical to the one in the stiff structure assumption), a flexible trunk and a canopy. In this case, stronger tsunami flooding conditions were reproduced in the laboratory by using higher water levels, reaching the top of the mangrove canopy. Stiff structure assumption

In order to compare the properties of a mangrove prototype and a mangrove model, three real-like models of a different root density (model group A with low density, model group B with medium density and model group C with high density) were constructed at a scale of 1:20 (Fig. 3). The trunk and the roots were modeled using a modeling clay, hardened in an oven. The relationship between the submerged root volume ratio and root submergence, plotted in Fig. 4a, agrees very well with the pattern determined by Mazda et al. (1997a). Geometry of these models is provided in Tables 1 and 2. In the next step, three parameterized models for each real model were introduced, accounting for a varying frontal root area Af (i.e. the area perpendicular to flow direction) with changing root submergence (see Fig. 3). The nature-like-shaped trunk and the roots were replaced in these models by steel and plastic cylinders of varying number, diameter and height (see Tables 1 and 2). Based on results of experiments performed at a scale of 1:20 (Froude similitude law) under quasisteady flow conditions, which aimed at a comparison of the properties of the real and the parameterized stiff mangrove models in terms of drag coefficient, reduction of flow velocity and hydraulic gradient, model A2 was selected as the best representation of the mangrove prototype. Detailed information on these experiments is provided in Husrin (2013). Flexible structure assumption

The stiff mangrove model A2 was further modified into the flexible model by introducing a trunk and a canopy. Similarly to the stiff structure parameterization procedure, a real flexible mangrove model was constructed first to provide a reference for the parameterized flexible models (Fig. 4b and Table 3). The canopy and trunk in this model was made of plastic branches with leaves, resulting in a Leaf Area Index of 4.5. The parameterization of the mangrove prototype under flexible structure assumption was performed in two stages in order to determine the representative properties of the canopy and the trunk. In the first step, the five tree models were equipped with a stiff trunk, while the

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canopy properties (density and frontal area) varied by controlling the volume of the fibrous material used (see Fig. 4b and Table 3). The models were examined under quasi-steady flow conditions in terms of current-induced forces (see Husrin 2013 for more details). Based on the comparison of the experimental data, canopy model M2FS was selected for the construction of the entirely flexible mangrove models (see Fig. 4b and Table 3). The trunk in the three flexible models was made of Polytetrafluoroethylene (PTFE), which is the only feasible material with elasticity (0.5 × 109 N/m2 at model scale 1:25) fitting to the aforementioned range of the Young modulus for mangrove trunks. Density of this material (ca. 2000 kg/m3) is however double as compared to mangrove trunk density (ca. 1000 kg/m3). Comparative analysis of the deflection pattern of the flexible models (see Husrin 2013) indicated that model M2FF is the best representation on the mangrove prototype. a) Side view

b) Plan view

“Real” model

Increasing root density (Vm/V) A1

A1

Parameterized model

B1

C1

C1

Decreasing frontal area (Af)

B1

A2

B2

C2

A3

B3

C3

A4

B4

C4

Figure 3. Developed stiff mangrove models: a) side view, b) plan view. The root model applied to the flexible mangrove models is marked in red frame.

b) Flexible mangrove models

16

Model group A

14

Model group B

Stiff trunk

Model group C

M1FS

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Nakama-Gawa (Japan), Mazda et al. ((1997) 1997) Coral Creek (Australia), Mazda et al. ((1997) 1997)

8 6 4 2 0 0.00

0.10

0.20

0.30

0.40

Parameterized model

Water depth h [cm]

12

“Real” model

a) Root density

Same density and frontal area

M2FS

30% less dense, same frontal area

M3FS

M4FS

M5FS

50% less dense, same frontal area

30% less dense, 50% less dense, 30% less frontal 50% less frontal area area

Flexible trunk M1FF

M2FF

M3FF

Submerged root volume ratio Vm/V [-] Same density, 8% less frontal area

30% less dense, 8% less frontal area

50% less dense, 8% less frontal area

Figure 4. Relationship between mangrove root density and root submergence (a) and constructed flexible mangrove models (b). The selected flexible model is marked in red frame.

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COASTAL ENGINEERING 2014 Table 1. Properties of stiff mangrove models at model scale of 1:20 (height and diameter in cm). Structural part Trunk

Root type I Root type II Root type III Root type IV Root type IV

Model group A A1 A2 1 1 15 15 1 1 9 12 12.5 0.6 0.5 26 0 10 0.4 0.5 20 20 7.5 0.35 0.5 25 28 5.0 0.3 0.5 74 2.5 0.5

No. Height Diameter No. Height Diameter No. Height Diameter No. Height Diameter No. Height Diameter No. Height Diameter

A3 1 15 1 4 12.5 1.0 0 10 1.0 4 7.5 1.0 8 5.0 1.0 18 2.5 1.0

A4 1 15 1 2 12.5 1.5 0 10 1.5 2 7.5 1.5 4 5.0 1.5 4 2.5 1.5

Model group B B1 B2 1 1 15 15 1 1 12 20 12.5 0.6 0.5 40 12 10 0.4 0.5 40 28 7.5 0.35 0.5 63 80 5.0 0.3 0.5 46 2.5 0.5

B3 1 15 1 8 12.5 1.0 0 10 1.0 8 7.5 1.0 8 5.0 1.0 20 2.5 1.0

Model group C C1 C2 1 1 15 15 1 1 16 96 12.5 0.6 0.5 40 0 10 0.4 0.5 40 44 7.5 0.35 0.5 150 52 5.0 0.3 0.5 474 2.5 0.5

B4 1 15 1 4 12.5 1.5 0 10 1.5 0 7.5 1.5 8 5.0 1.5 10 2.5 1.5

C3 1 15 1 24 12.5 1.0 0 10 1.0 12 7.5 1.0 12 5.0 1.0 66 2.5 1.0

C4 1 15 1 12 12.5 1.5 0 10 1.5 0 7.5 1.5 12 5.0 1.5 20 2.5 1.5

Table 2. Frontal area of stiff mangrove models for relative root submergence h/hmdl = 0.05-0.15 at model scale of 1:20 (hmdl denotes total mangrove model height). A1: 30.6-61.8 cm2 B1: 34.7-70.1 cm2 C1: 56.9-115.1 cm2

A2: 50.1-86.6 cm2 B2: 65.1-119.1 cm2 C2: 72.6-142.9 cm2

A3: 47.5-75.0 cm2 B3: 47.5-125.0 cm2 C3: 74.3-148.2 cm2

A4: 41.3-66.3 cm2 B4: 45.0-110.0 cm2 C4: 84.0-171.1 cm2

Table 3. Characteristics of flexible mangrove models (model scale of 1:25). Model ReMS M1FS M2FS M3FS M4FS M5FS 116.16 87.10 Total submerged 165.20 174.20 116.16 87.10 volume [cm3] Canopy width [m] 0.150 0.135 0.135 0.135 0.095 0.068 Canopy frontal 0.0291 0.0297 0.0297 0.0297 0.0208 0.0148 area [m2]

M1FF 174.20

M2FF 116.16

M3FF 87.10

0.124 0.0273

0.124 0.0273

0.124 0.0273

EXPERIMENTAL SET-UP Experimental facility

The laboratory investigation on solitary wave attenuation by the parameterized mangrove forest was conducted in a 2 m – wide wave flume at the Leichtweiss-Institute for Hydromechanics and Coastal Engineering at the Technical University of Braunschweig in Germany. The flume is approximately 90 m long and 1.25 m deep and is equipped with a piston type wave maker (see Fig. 5a). The model was scaled according to Froude similitude law, using a scale of 1:25. a)

WG1-WG4

WAVE MAKER

SWL

SWL

0.42m

1.08m

WG9-WG15

WG5-WG8

9.19m

0.76m

0.42m

0.5m

1.08m

0.76m

0.5m 0.5m

h=0.815m 31.97m

10.0m

b) B=3.0 m

13.71m

8.33m

c)

0.42m 0.33m

1.1m

FOREST

1.08m

ADV2 h r=0.415m

BEACH MODEL 2.0m

0.42m

0.76m

0.51m

ADV1

h=0.595m

WG16-WG19

B

d)

Figure 5. Experimental set-up: a) arrangement of measuring devices, b) forest model of width of B=3.0 m, c) force transducer connected to mangrove model, d) installation of force transducer in forest model.

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Mangrove forest model and beach model

In order to investigate the conditions most favorable for wave attenuation, maximum possible forest density was considered in this test series, corresponding to ca. 44 trees/m2. This density was achieved by arranging the tree models in shifted rows, consisting of 12 and 13 mangrove models (see Figs. 5b and 6). 62 and 250 mangrove tree models were used to construct forest model of width of B = 0.75 m and B = 3.0 m, respectively. A proper modelling of a bathymetry/topography as well as applied wave force measurement technique (described in more details in the following section) required placement of the forest model on an elevated ground. A horizontal plywood platform, representing a beach model of height of ca. 0.41 m and a seaside slope of 1:20, was constructed for this purpose. The toe of the beach model was placed at a distance of ca. 23.7 m from the wave maker, while the front of the forest model was 33.97 m from the wave generator and 2.0 m behind the end of the beach slope, as shown in Fig. 5a. a) B=0.75 m B=0.75m T13 T1

T38 T39

T15

T40

T16 T4

T41

T17

T42

T6 FTS1 T7 FTS2

T19 FTS3

T56 T44

FTS6

T69

T57 FTS7

FTS8

T45

T9

T46

T10

T47

T23 T11

T48

T12

T73

T49

T25

T50

T87

T148

T123 T136 T137

T100

T150

T125

T234 T247 T235

T198

T223 T211

T248 T236

T199

T175

T246

T222 T210

T187

T162

T245 T233

T221 T209

T186 T174

T244 T232 FTS11

T220 T208

T197

T173 T161

T149

T124

T195

T185

T160

T219 T207

T196

T172

T243 T231

T194

T184

T159

T242 T230

T218 T206

T183 T171

T147 T135

T112

T170 T158

T134

T111 T99

T182

T146

T122

T98

T75

T133

T110

T157 T145

T120

T217 T205

T193

T181 T169 FTS10

T241 T229

T192

T156 T144

T121 T109

T86 T74

T62

T37

T132

T97 T85

T61

T36 T24

T119 T107 FTS9 T108

T84

T60

T35

T131

T216 T204

T180 T168

T240 T228

T191

T167 T155

T143

T106

T96

T72

T130 T118

T215 T203

T179

T239 T227

T190

T166

T238 T226

T214 T202

T178

T154 T142

T117

T95 T83

T59

T34 T22

T94 T82

T71

T129

T105 T93

T70

T58

T33 T21

T92

T81

T141

T116 T104

T80 T68

T32 FTS5

T20

T8

T67

T43 T31 FTS4

T91

T165 T153

T213 T201

T189 T177

T152

T128

T188 T176

T164

T140

T115

B=0.75m

T163 T151

T139 T127

T103

T79

T55

T30 T18

T90

T66

T126 T114

T102

T78

T54

T29

T5

T65

T138

T113 T101

T89 T77

T53

T28

B=0.75m

T88 T76

T64 T52

T27

T3

T63 T51

T26 T14

T2

B=0.75m

T224 T212

T249 T237

T200

T225

T250

b) B=3.0 m B=0.75m T13 T1

T38

T14

T39

T16

T41

T17 T5

T42

T18 T6 FTS1 T7 FTS2

T19

T43 T31 FTS3

T44

T20

T8

T45

T21

T10 T23

T48

T24 T12

T49

T25

T74 T62

T50

T98

T75

T100

T149

T124 T137

T112 T125

T150

T247 T235

T223

T199

T248 T236

T224 T212

T200

T246 T234

T222

T211

T187 T175

T221

T198

T174

T245 T233

T210

T186

T162

T244 T232 FTS11

T209 T197

T173

T243 T231 FTS10

T219 T220

T196

T185

T161

T218

T208

T184 T172

T148 T136

T195

T171

T160

T206 FTS9

T242 T230

T207

T183

T159 T147

T123

T99 T87

T146

T135

T111

T170 T158

T134 T122

T194

T182

T157

T217

T193 FTS8

T241 T229

T205

T181 T169

T216

T192

T168 T156 FTS7

T145

T121

T110

T86

T132 T133

T109 T97

T73 T61

T37

T96

T85

T144

T120 T108

T84 T72

T60

T36

T95

T71

T131

T119 T107 FTS6

T240 T228

T204

T180

T239 T227

T215

T191

T167 T155

T143

T118 T106

T94

T83

T59 T47

T35

T11

T70

T46 T34

T22

T93 T81 FTS5

T130

T214

T203

T179

T238 T226

T202 T190

T166

T142

T117

T189

T178

T154

T213 T201

T177 T165

T153

T129

T105

T82

T58

T33

T9

T69

T57

T32

T92

T164

T141

T116 T104

T80 T68

T56 FTS4

T128

T188 T176

T152 T140

T115

T91

T67

T127

B=0.75m

T163 T151

T139

T114

T103

T79

T55

T30

T126

T102 T90

T66 T54

T29

T89

T78

T138

T113 T101

T77 T65

T53

T28

T4

T64

T40

B=0.75m

T88 T76

T52

T27 T15

T3

T63 T51

T26

T2

B=0.75m

T249 T237

T225

T250

Figure 6. Arrangement of mangrove tree models (green squares marked as T1 - T250) and force transducers (orange squares marked as FT1 - FT11) in forest model of width of: a) 0.75 m, b) 3.0 m.


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Measuring technique

The pattern of wave propagation in front of, in, and behind the mangrove forest model was recorded by means of 19 wire-type wave gauges (WG), which arrangement is presented in Fig. 5a. Three wave gauges were placed within the forest model: wave gauge WG13 at the front, WG14 in the middle and WG15 at the rear tree row. In addition to the wave profile analysis, the pattern of wave forces induced on single tree models was examined by means of force transducers (FT), developed at the LWI for the purposes of this investigation (Figs. 5c and d). The force transducers are capable of measuring positive and negative wave forces up to 60 N, exerted in the direction of wave propagation. In each forest model configuration, 11 force transducers were employed within the forest, and in case of the shorter forest model (B = 0.75 m), also behind the forest as depicted in Fig. 6. Two Acoustic-Doppler velocimeters (ADV), installed at the beginning and at the end of the forest model, measured horizontal flow velocity in the direction of wave propagation (see Fig. 5a). Experimental programme

For each of the considered configurations of the mangrove forest model (i.e. forest width of 0.75 m and 3.0 m), varying water depth conditions and solitary wave height were examined, what resulted in a total number of 50 tests. In order to investigate the influence of the submergence of the mangrove tree model on solitary wave attenuation, total water depth in front of the beach model h was varied from 0.595 m to 0.815 m (with an increment of 0.055 m), which corresponded to the tree model submergence range of dr = 0.18 - 0.40 m. As shown in Fig. 7, the tree submergence covered the entire height of tree canopy, with the lowest submergence reaching the canopy bottom and the highest one reaching canopy top. For each water level, solitary waves of five different nominal incident heights (Hi,nom = 0.04, 0.08, 0.012, 0.016 and 0.20 m) were generated. 0.124 m

h=0.815 m (dr=0.400 m) 0.055 m

0.22 m

0.055 m

0.40 m

0.055 m

(other root height: 0.02, 0.04, 0.06 m)

0.10 m

0.08 m

0.055 m

h=0.760 m (dr=0.345 m)

h=0.705 m (dr=0.290 m)

h=0.650 m (dr=0.235 m)

h=0.595 m (dr=0.180 m)

0.008 m

0.005 m

upper surface of beach model 0.15 m × 0.15 m

Figure 7. Examined water depth conditions in respect to the geometry of flexible mangrove model.

ANALYSIS OF EXPERIMENTAL RESULTS Classification of wave evolution modes

Due to the fact that two sources of wave energy attenuation were observed in the conducted tests, namely the wave-forest interaction and wave breaking process, introduction of wave evolution modes into the data analysis was very crucial for the proper assessment of the forest damping performance. In case of tests with nonbreaking solitary waves, which dominated in the performed test series, the reduction of wave energy was solely due to wave propagation in the forest model. In contrast, in the experiments under broken wave conditions, both the forest model and the bathymetry/topography contributed to wave attenuation. The classification of the wave evolution modes was based both on the generation of wave breaking and the location of the breaking point in respect to the geometry of the beach-forest model. The following wave evolution modes (EM) were distinguished:

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1. 

Nonbreaking solitary waves disintegrating into solitons: Nonbreaking waves (EM1): a solitary wave train, consisting of waves of decreasing height (solitons), was generated as a result of the wave fission process due to the change of the water depth over the beach model (see Fig. 8a). 2. Breaking solitary waves disintegrating into solitons:  Waves breaking between the end of the beach slope and the beginning of the forest model (region 2) and disintegrating into solitons (EM3), as illustrated in Fig. 8b.  Waves breaking in the forest model (region 3) and disintegrating into solitons (EM4), shown in Fig. 8c.  Waves breaking behind the forest model (in region 4) and disintegrating into solitons (EM5), depicted in Fig. 8d. Evolution mode EM2, in which wave broke over the beach slope (in region 1), was not observed in the performed test series. As shown in Fig. 9, the wave evolution modes were governed predominantly by the incident solitary wave height and the water depth, and partially by the width of the forest model (to distinguish between wave breaking induced in and behind the forest model).

region 3

region 2

Water free surface elevation η [m]

0.14

a) Nonbreaking waves (EM1) region 1

region 4

dr h

hr

forest model

wave shoaling wave fission wave fission 8.33m

2.0m

0.12 0.10

development of wave fission

0.06 0.04 0.02 0.00

86

90

88


region 3

region 4

dr h

hr wave shoaling 8.33m

wave breaking 2.0m

forest model broken wave

region 4

forest model

wave shoaling 2.0m

8.33m

wave breaking B

broken wave

d) Waves breaking behind forest model (EM5) region 1

region 2

region 3

region 4

dr h

forest model

hr wave shoaling 8.33m

2.0m

B

wave breaking

Figure 8. Classification of wave evolution modes.

wave fission

dr=0.18m hr=0.415m

broken wave

0.20 0.16


0.12

Hi,nom=0.20m B=3.0m h=0.595m dr=0.18m

0.08 0.04 0.00

95

94

93

92

96

97

98

99

100

101

0.28

WG14 WG11 WG17 WG9 WG13 WG19 WG15

generation of wave breaking

0.24 0.20 0.16

broken wave

Hi,nom=0.20m B=3.0m h=0.76m dr=0.345m

B=3.0m

h=0.76m

dr=0.345m hr=0.415m


0.12 0.08 0.04 0.00 -0.04

wave fission

94

96

95

98

97

102

101

100

99

Time t [s]


hr

WG18

B=3.00m

Time t [s]


region 3

WG10 WG13 WG9 WG11 WG14

h=0.595m

-0.04 91

wave fission

dr h

102

0.24

0.32

region 2

100

98

96


0.28

B

c) Waves breaking in forest model (EM4) region 1

94

92

Time t [s]

0.32

region 2

WG19

dr=0.18m hr=0.415m

B

b) Waves breaking in front of forest model (EM3) region 1

WG15

B=3.00m

h=0.595m

0.08

-0.02 84

wave fission

WG10 WG13

generation of wave fission

Hi,nom=0.08m B=3.0m h=0.595m dr=0.18m

0.28 0.24 0.20 0.16

WG14 WG16 WG11 WG15 WG19 WG9 WG13

broken wave


dr=0.40m

Hi,nom=0.20m B=3.00m h=0.815m dr=0.40m

h=0.815m

B=3.00m

hr=0.415m


0.12 0.08 0.04 0.00 -0.04 76

77

78

79

80

81

Time t [s]

82

83

84

85

9

0.24

EM1 EM3 EM4 EM5

a) B=0.75 m 0.20 0.16 0.12 0.08 0.04 0.00 0.540

0.595

0.650

0.705

0.760

0.815

0.870

Nominal solitary wave height Hi,nom [m]

Nominal solitary wave height Hi,nom [m]

COASTAL ENGINEERING 2014 0.24

EM1 EM3 EM4 EM5

b) B=3.0 m 0.20 0.16 0.12 0.08 0.04 0.00 0.540

0.595

Water depth h [m]

0.650

0.705

0.760

0.815

0.870

Water depth h [m]

Figure 9. Observed wave evolution modes as a function of water depth conditions and solitary wave height in case of forest width of: a) B = 0.75 m, b) B = 3.0 m.

Evolution of wave height

Effectiveness of the forest model in wave attenuation was analyzed first in terms of solitary wave height reduction, which was governed forest width, water level and incident wave height. For this purpose, maximum solitary wave height was determined for each performed experiment. Exemplary results of this analysis, plotted in Fig. 10 for both forest model configurations and extreme water level conditions examined, clearly indicate four regions of different wave behavior. Solitary wave height remained constant over the horizontal part of the flume and increased as a result of shoaling process over the slope of the beach model. Depending on the evolution mode, the wave height decreased either in front of the forest model due to wave breaking process (wave evolution mode EM3), or in the forest model (EM1 and EM4), where particularly significant wave height reduction was observed for the wider forest model. The wave height in front of the forest model yielded: ca. 0.05 m for Hi,nom = 0.04 m, 0.1 m for Hi,nom = 0.08 m, 0.15 - 0.20 m for Hi,nom = 0.12 m, 0.20 - 0.25 m for Hi,nom = 0.16 m and 0.23 - 0.27 m for Hi,nom = 0.20 m for all examined water depths. These wave heights were attenuated as follows at the end of the forest model of width of 0.75 m: ca. 0.02 - 0.04 m for Hi,nom = 0.04 m, 0.07 m for Hi,nom = 0.08 m, 0.11 m for Hi,nom = 0.12 m, 0.12 - 0.16 m for Hi,nom = 0.16 m and 0.14 - 0.20 m for Hi,nom = 0.20 m for all examined water depths. As a result of a longer propagation distance in case of the forest model of width of 3.0 m, further wave height reduction was observed at the rear tree row: ca. 0.03 m for Hi,nom = 0.04 m, 0.05 m for Hi,nom = 0.08 m, 0.06 - 0.10 m for Hi,nom = 0.12 m, 0.07 - 0.16 m for Hi,nom = 0.16 m and 0.08 - 0.24 m for Hi,nom = 0.20 m for all examined water depths. The pattern of solitary wave height behind the forest model was generally more irregular for higher water levels and forest model of B = 0.75 m due to the more intensive process of solitary wave fission and triggering of wave breaking behind the forest (EM5). Evolution of wave forces induced on single mangrove models

Pattern of maximum wave forces exerted on the single mangrove models was analyzed in a similar way to the envelope of the maximum solitary wave height. Fig. 11 presents exemplarily the development of the forces in the forest for representative experiments, in which point 0.0 m on the horizontal axis represents the beginning of the forest model. The magnitude of the wave forces was governed by the water depth and wave height conditions and the resulting evolution mode – the forces decreased with the increasing submergence depth of the tree models and on the other hand they became larger for greater wave heights, e.g. ca. 1 N for Hi,nom = 0.04 m, 5 - 6.5 N for Hi,nom = 0.08 m, 7 - 15 N for Hi,nom = 0.12 m, 10 - 24 N for Hi,nom = 0.16 m and 13 - 27 N for Hi,nom = 0.20 m for all examined water depths. The highest forces were exerted at the frontal tree row at the direct impact of the wave. A general trend of the decrease of the wave forces with wave propagation in the forest model was observed (see FT1 - 7 for B = 0.75 m and FT1 - 11 for B = 3.0 m in Fig. 11). A smaller force reduction was attributed to the narrow forest model due to the shorter wave propagation distance and thus weaker interaction with the tree models. The forces recorded at the end of this forest model corresponded well to that measured by force transducers FT4 in forest of width of 3.0 m and yielded: ca. 0.7 - 1 N for Hi,nom = 0.04 m, 3 - 4 N for Hi,nom = 0.08 m, 6 - 9 N for Hi,nom = 0.12 m, 9 - 15 N for Hi,nom = 0.16 m and 10 - 15 N for Hi,nom = 0.20 m for all examined water depths. Further reduction of the forces (between FT4 and FT10/11) was observed within the wide forest model.

10

COASTAL ENGINEERING 2014 0.35 Hi,nom=0.04m (EM1)

Max. height of solitary wave Hs,max [m]

a) B=0.75m, h=0.595m

Hi,nom=0.08m (EM1)

0.30

Hi,nom=0.12m (EM5)

B=0.75m 0.25

Hi,nom=0.16m (EM4) Hi,nom=0.20m (EM3)

0.20 0.15 0.10 0.05 WG 5,7+8

WG 2‐4

0.00 10

15

20

WG 9‐19

25

30

35

40

45

40

45

Horizontal distance from wave maker x [m] 0.35 Hi,nom=0.04m (EM1)

Max. heiht of solitary wave Hs,max [m]

b) B=0.75m, h=0.815m

Hi,nom=0.08m (EM1)

0.30

Hi,nom=0.12m (EM1)

B=0.75m

Hi,nom=0.16m (EM1)

0.25

Hi,nom=0.20m (EM1)

0.20

0.15

0.10

0.05 WG 2‐4

0.00 10

WG 5,7+8

15

20

WG 9‐19

25

30

35

Horizontal distance from wave maker x [m] 0.35 B=3.0m


c) B=3.0m, h=0.595m


0.30

Hi,nom=0.12m (EM1) Hi,nom=0.16m (EM4) Hi,nom=0.20m (EM3)

0.25 0.20 0.15 0.10 0.05 WG 5,7+8

WG 2‐4

WG 9‐19

0.00 10

15

20

25

30

35

40

45

Horizontal distance from wave maker x [m] 0.35 B=3.0m


c) B=3.0m, h=0.595m


0.30

Hi,nom=0.12m (EM1) Hi,nom=0.16m (EM4) Hi,nom=0.20m (EM3)

0.25 0.20 0.15 0.10 0.05 WG 5,7+8

WG 2‐4

WG 9‐19

0.00 10

15

20

25

30

35

40

45

Horizontal distance from wave maker x [m]

Figure 10. Envelopes of maximum solitary wave height for: a) B = 0.75 m and h = 0.595 m, b) B = 0.75 m and h = 0.815 m, c) B = 3.0 m and h = 0.595 m, d) B = 3.0 m and h = 0.815 m.

11

COASTAL ENGINEERING 2014 35 Hi,nom=0.04m (EM1)

Max. force exerted on tree model Fmax [N]

a) B=0.75m, h=0.595m

Hi,nom=0.08m (EM1)

30

Hi,nom=0.12m (EM5)

FT1,2 FT3

25

Hi,nom=0.16m (EM4)

End of forest model

Hi,nom=0.20m (EM3)

FT4

20

FT5

FT6,7 FT10

FT8

15

FT9 FT11

10

5

0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Horizontal distance from beginning of forest model [m]

Max. force exerted on tree model Fmax [N]

16

FT1,2

Hi,nom=0.04m (EM1)

b) B=0.75m, h=0.815m

Hi,nom=0.08m (EM1)

14

Hi,nom=0.12m (EM1)

FT3

End of forest model

12

FT6,7

FT4

Hi,nom=0.16m (EM1)

FT10

Hi,nom=0.20m (EM1)

FT9 FT8

10

FT11

8 6 4 2 0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Horizontal distance from beginning of forest model x' [m] 35

Max. force on tree model Fmax [N]

FT1,2

c) B=3.0m, h=0.595m


30

Hi,nom=0.12m (EM1)

FT4

Hi,nom=0.16m (EM4)

FT3

25

Hi,nom=0.20m (EM3)

20

End of forest model FT5

15

10 FT6

5

FT7

FT8

FT9 FT10,11

0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Horizontal distance from beginning of forest model x' [m] 16 FT1,2

Hi,nom=0.04m (EM1)

d) B=3.0m, h=0.815m

Hi,nom=0.08m (EM1)

Max. force on tree model Fmax [N]

14


12

FT3

Hi,nom=0.20m (EM5)

10

FT4 FT6

8

End of forest model

FT8 FT9

FT7

FT10,11

6 4 2 0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Horizontal distance from beginning of forest model x' [m]

Figure 11. Envelopes of maximum wave forces exerted on single mangrove models for: a) B = 0.75 m and h = 0.595 m, b) B = 0.75 m and h = 0.815 m, c) B = 3.0 m and h = 0.595 m, d) B = 3.0 m and h = 0.815 m.

12


The range of the wave forces at the end of this forest model was as follows: ca. 0.4 - 0.8 N for Hi,nom = 0.04 m, 1.2 - 2.2 N for Hi,nom = 0.08 m, 2 - 4 N for Hi,nom = 0.12 m, 2.4 - 6 N for Hi,nom = 0.16 m and 2.8 - 7.5 N for Hi,nom = 0.20 m for all examined water depths. The additional contribution of the breaking process to wave attenuation in the forest can be clearly seen in Figs. 11a and c, what resulted in a greater reduction of the wave forces as compared to the nonbreaking waves. In case of the narrow forest model, the data measured by the force transducers placed behind the forest model (FT8 - 11) indicate a slight increase and then decrease of the forces to the value behind the forest model, particularly for larger wave heights. Due to the limited number of the constructed force transducers, analysis of this force pattern behind forest model of B = 3.0 m was not possible and requires further investigation. Wave transmission

Due to the disintegration of the incident solitary wave into a soliton train, wave transmission coefficient was calculated as a function of wave energy as postulated by Liu and Cheng (2001). Wave energy was considered as a sum of kinetic and potential wave energy (Longuet-Higgins and Fenton 1974):

Etot  Ek  E p ,

(1)

determined at wave gauge WG13 as total energy of incident wave and at WG15 as total energy of transmitted wave. The energy components are expressed as follows:  

Ek  0 .5  

 u dzdx, 2

(2)

  h



E p  0.5   g   2 dx.

(3)



Approach by Al-Banaa und Liu (2007) was used to transform the energy components from spatial into temporal domain: t2 

Ek  0.5  c   u 2 dzdt,

(4)

t1  h

t2

E p  0.5  g  c   2 dt,

(5)

t1

in which dx = c·dt. The horizontal particle velocity can be defined after Munk (1949) as:

uc

 h 

,

(6)

with solitary wave speed calculated as:

c  g h  H .

(7)

In Eqs. 1-7, c denotes the wave celerity [m/s], Ek the kinetic wave energy [J/m], Ep the potential wave energy [J/m], g the gravitational acceleration [m/s2], h the water depth [m], H the wave height [m], u the horizontal particle velocity [m/s] and η the water free surface elevation [m]. Figure 12 shows the relationship between computed wave transmission coefficient Kt and relative forest width B/L with corresponding wave evolution modes. Two very clear data clouds can be distinguished in this graph: one for forest width of B = 0.75 m with the transmission coefficient ranging from ca. 0.48 to 0.78 and another for forest width of B = 3.0 m with Kt = 0.29 - 0.56. The lowest wave transmission was attributed to waves breaking in front of and in the forest model (EM3 and EM4, respectively) due to the combined wave energy dissipation through the wave-tree model

13


Transmission coefficient in terms of wave energy Kt [‐]

interaction and the turbulence at breaking. Nonbreaking waves (EM1) were dominant in the performed test series, resulting in much higher transmission coefficient as compared to the broken waves. A better performance of the forest model can be also observed for smaller water depths, particularly when comparing the data for a constant wave height. h

1.0

Kt 

0.9 0.8

EM1

E tot,WP15 WG15 E tot,WP13 WG13

0.6 0.5

[-]

0.04 m

0.08 m

0.16 m

0.20 m

0.705 m 0.760 m

0.4

0.815 m

EM1 EM1

EM1

EM5 EM1 EM1

EM1

EM4

EM4 EM1

EM1 EM1

EM1

EM1

EM4

EM1

0.3

EM1

B = 0.75 m

0.2

0.12 m

0.650 m

EM1

EM1 EM1 EM1 EM1 EM1 EM1 EM4 EM1 EM4 EM1 EM1 EM1 EM1 EM1 EM1 EM1 EM1 EM1 EM4 EM4 EM1 EM3 EM1 EM5 EM4

0.7

Hnom

0.595 m

EM1

EM4 EM4

EM3

EM4

B = 3.0 m

L2

0.1

2.12h H/h

0.0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Relative forest width [m] Relative forest widthB/L B/L gen[-]

Figure 12. Wave transmission coefficient as a function of relative forest width.

CONCLUSIONS

Consideration of the most important physical properties of the selected mangrove species as well their dependency on the tree age makes the parameterization approach presented in this paper more reliable than those proposed in the previous studies. Although it was developed for a specific tree species, the assumptions made and the systematic parameterization procedure itself can be applied to other types of coastal vegetation. However, there are two shortcomings of the parameterization procedure to be mentioned: firstly, experimental modelling of a tree failure (e.g. trunk breakage or uprooting) under wave impact is not possible and secondly, the trunk model, despite same elasticity as mangrove wood, has density that is double density of the prototype. The idealized forest conditions assumed in these experiments, namely the maximum forest density, healthy mangrove trees of idealized resistance to wave attack, result in overestimation of the attenuation performance of the forest model. As indicated by the results, wave energy reduction by 70% was attributed to the widest forest of B = 3.0 m (75 m in prototype) in case of the weakest flow depth conditions examined. In case of larger flow depths, reaching the top of the canopy, wave transmission is reduced to ca. 40 - 50%. Despite such a large forest width, relatively poor performance of the forest model was observed, which is, in fact, even poorer when considering the horizontal scale of a real tsunami and laboratory limitations in generation of long waves. Moreover, execution of such large vegetation zones at the coast would be very difficult in many regions due to the limited availability of the land. The effectiveness of the narrower forest model of B = 0.75 m (18.75 m in prototype) is too low (between 20 and 50%) in order to consider the mangrove forest as a defense barrier against tsunami. Despite the low performance in attenuation of extreme tsunami, planning and maintenance of coastal green belts is highly recommended due to the coast stabilization functions and protection from flooding, mentioned before in the introductory part of this paper, as well as due to the life-saving role and debris-stoppage reported from the recent tsunami events. ACKNOWLEDGMENTS

The TAPFOR project was performed in the framework of the project "Tracing Tsunami impacts on- and offshore in the Andaman Sea Region (TRIAS)", funded by the Deutsche Forschungsgemeinschaft (DFG) and the Office of the Research Council of Thailand (NRCT) and partly by the DFG within the Graduate College of TU Braunschweig "Risk Management of Natural and Civilization Hazards on Buildings and Infrastructure" (GRK 802).

14


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