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48 3 (29.9) * ** *** (1975) (28) NOWT-PARIVer5.3 * ** *** 239-826 3-1-1 46-844-542 Fax46-841-3888 e-mail:hirayama@pari.go.jp - 23 -

REPORT OF THE PORT AND AIRPORT RESEARCH INSTITUTE Vol.48, No.3 (Sep.29) Evaluation of Design Wave Condition for Seawall on Coral Reef Calculated in Boussinesq-type Wave Transformation Model Katsuya HIRAYAMA* Kazuto HARUO** Ichiro MIYAZATO*** Synopsis Wave overtopping rate for a designed seawall can be evaluated in the diagrams proposed by Goda (1975) using the equivalent offshore wave height and the water depth in front of the seawall. Moreover, Miyakuni et al. (28) suggested that the wave set-up and the surf-beat should be added to the design water depth for the seawall on a coral reef flat. The evaluation of such a design condition on the surf, however, is much difficult because the wave transformation is complicated in the target area because of wave breaking and run-up on spatial topography in the reef area. In this study, the evaluation of the surf condition is carried out by using the Boussinesq-type wave transformation model developed by Hirayama and Hiraishi (25), which can reproduce wave dissipating, wave set-up and surf-beat generated in wave breaking zone on a complicated coral reef bathymetry. Thus, the design wave height can be directly calculated and the design water level can be evaluated with the calculated wave set-up and surf-beat height. Additionally, the wave overtopping rate on the designed seawall is calculated by using Goda s diagram in order to verify the applicability of this procedure for seawall design in an actual coral reef. Key Words: Boussinesq model, coral reef, overtopping rate, seawall design, wave set-up, surf-beat * Head, Wave Group, Coastal and Ocean Eng. Research Division, Marine Environment and Eng. Dept. ** Researcher, Wave Group, Coastal and Ocean Eng.Research Division, Marine Environment and Eng. Dept. *** Visiting Engineer, Wave Group, Coastal and Ocean Eng. Research Division, Marine Environment and Eng. Dept. 3-1-1 Nagase, Yokosuka, Kanagawa 239-826 Japan Phone+81-46-844-542 Fax+81-46-841-3888 e-mail:hirayama@pari.go.jp - 24 -

23 27 27 28 3 31 32 32 33 38 4 4 43 46 47 47 47 48 49 58-25 -

1991 24,25 NOWT-PARIVer5.3 28 28 CADMAS-SURF NOWT-PARIVer5.3 1977 NOWT-PARIVer5.3 Great Barrier Reef Marine Park, 21-27 -

5m h d h η bar H L1/3 h d =h+η bar +ah L1/3 H L1/3 H L1/3 H L1/3_S h d =h+η bar +ah L1/3_S a h d hη bar αh L1/3 αh L1/3 H L1/3 h d η bar h a=.5 a=.7 a=.5.7 a a H L1/3_I h d =h+η bar +a*bh L1/3_I H L1/3_S = bh L1/3_I 2b=2-28 -

b=2 28 h d = h+η bar +.7H L1/3_S = h+η bar +1.4H L1/3_I a=.7b=2 h d = h+η bar +.5H L1/3_S = h+η bar +1.H L1/3_I a=.5b=2 H K d K r H 28 K s 1974 H 1/3 271975 K sb 26 H =H 1/3 / K sb H 1/3 H hd tanθ H h/h 4. Yes No H =K d K r H Ks 1974 Ksb 1975 H H 1/3 H 2 H1/3/Ks H1/3/Ksb H Yes H H hd tanθ H H1/3/Ks No H 1/3 H H =H 1/3 / K s H Yes H No - 29 -

h d tanθ H h/h 4 K s h/h 4 H 1/3 /H H 1/3 H H H H H 28 H H 1/3 h d tanθ H K s H 1/3 K s H H H H 1984 3 7% 1982 1975 1977 (1975 H 1/3x η barx - 3 -

1992 22 H L1/3 1975 ζ H L1/3 4.4* ζ NOWT-PARIVer5.3 NOWT-PARIVer5.325 (a) Line1; Y=+8m (b)line2; Y=+55m (c)line3; Y=+6m (d)line4; Y=-5m - 31 -

29 3s3s H 1/3 H L1/3 η bar 28 3s 3s H 1/3 H L1/3=H L1/3_I η bar h d= h+η bar + H L1/3*a H = H 1/3 / K s h d 2.5km 2.km 25m 1km NOWPHAS - 32 -

NOWPHAS 2,5m NOWPHAS NOWPHAS1998225 WSW NNW N W NNWWSW6 D.L. H.H.W.L. +3.2 +3.2 +3.1 +3.1 H.W.L. +2.1 +2.1 +1.9 +1.9 L.W.L. ±. ±. +.1 +.1 5-33 -

NOWPHAS NOWPHAS5 NNWNOWPHAS 5 Smax = 5 2 dx=dy=5.m H.H.W.L.=D.L.+3.2m NOWPHAS NOWPHAS H 1/3 [m] T 1/3 [s] Smax [deg.] N 8.7 13.6 16 NNW 8.23 13.3 11 337 NW 9.9 13.8 16 315 WNW 1.42 15.1 6 293 W 9.92 14.5 8 27 WSW 9.34 14.1 9 248-34 -

S(f) [m 2 sec] 18 NNW 16 14 12 1 8 6 4 2..1.2 Frequency(Hz) 29 NNW H 1/3 [m ] T 1/3 [s] Sm ax [deg.] N 8.93 13.2 19 5 NNW 8.24 13.1 13 335 NW 9.48 14.1 14 317 W NW 1.11 14.9 1 31 W 9.48 14.5 11 281 W SW 8.23 14.2 13 26 NE N s Ns512 2 NNW NNW - 35 -

[s] L /2 [m] [m] [m] N 13.66 146 4. 3. 1/1 NNW 13.29 138 35. 35. 1/1 NW 13.94 152 3. 3. 1/1 WNW 14.9 173 3. 3. 1/2 W 14.58 166 4. 4. 1/1 WSW 14.12 156 4. 4. 1/1 [m ] I [m ] J [m ] I J N 5. 374 69 748 138 1/1.1 NNW 5. 33 75 66 141 1/1.1 NW 5. 27 75 54 141 1/1.1 W NW 5. 32 68 64 136 1/2.5 W 5. 44 637 88 1274 1/1.1 W SW 5. 436 576 872 1152 1/1.1 [m] IMAX JMAX IS I I1 IE JS J J1 JE N 5. 842 1464 2+1 2+46 2+799 2+838 2+1 2+41 2+1421 2+146 1,232,688 NNW 5. 754 1494 2+711 2+75 2+1451 2+149 1,126,476 NW 5. 634 1494 2+591 2+63 2+1451 2+149 947,196 WNW 5. 734 1444 2+691 2+73 2+141 2+144 1,59,896 W 5. 92 1358 2+859 2+898 2+1315 2+1354 1,224,916 WSW 5. 966 1236 2+923 2+962 2+1193 2+1232 1,193,976 1m.1.4 21 λ αβdh - 36 -

λ α β d[m] V[m^3] 5.5 21 2.2 2.71 2 32.5 21 2.2 2.32 12.5 2.5 21 2.2 2. 8 16.5 21 2.2 1.85 6.3 12.5.5 21 2.2 1.71 5 5.5 21 2.2 1.26 2 5.575 21 2.2 2.79 21.739 4.575 21 2.2 2.89 17.391 α β 12 1.7 21 2.2-37 -

NOWT-PARI Ver.5.3 Δt 1/4 WNWW Δt 1/8 24P4P271m NNW NNW NNW - 38 -

(a) P33 (b) P44 (c) P16 NNW NNW P33P44P16 P33P44P16 3s H 1/3 η bar H L1/3 WNW - 39 -

H S1/3(m) HL1/3(m) η bar(m) (a) 1.6 1.4 N NNW NW WNW 1.2 W WSW 1..8.6.4.2. (b).8.7.6.5.4.3 N NNW.2 NW WNW.1 W WSW..7.6.5.4.3.2.1. (c) N NNW NW WNW W WSW (d) P4P27 ±5% 2 b b=2 2 b=2-4 -

hd(m) 4.5 h d h+η bar +.5*H L1/3 4. 3.5 3. N NNW 2.5 NW WNW W WSW 2. H '(m) 1..9 h d h+η bar +.5*H L1/3.8.7.6.5.4.3.2.1. N NNW NW WNW W WSW (a) a=.5 (a) a=.5 hd(m) 4.5 h d h+η bar +.7*H L1/3 4. 3.5 3. N NNW 2.5 NW WNW W WSW 2. H '(m) 1..9 h d h+η bar +.7*H L1/3.8.7.6.5.4.3.2.1. N NNW NW WNW W WSW (b) a=.7 (b) a=.7 b=2 a=.5.72 a a=.5.7 P9P15 h (1)(3) aa=.5.7 a=.528.7 1975 a NOWT-PARI Ver5.3 3s 3s H L1/3_I H L1/3_S a=.5 a=.7 7:3-41 -

β 1= β 1> N N ηbar[m], HL1/3 [m] b1.5.6.4.2.2.4.6 4 5 6 7 8 9 1 11 12 13 14 15 16 17 18 19 2 21 22 23 24 25 26 27 Point 2 4 6 8 1 12 T L1/3[s] ηbar[m] HL1/3[m] Sqrt(B1) TL1/3[s] ηbar[m], HL1/3 [m] b1.5 1.4 1.2 1.8.6.4.2.2.4 4 5 6 7 8 9 1 11 12 13 14 15 16 17 18 19 2 21 22 23 24 25 26 27 Point 2 4 6 8 1 12 TL1/3[s] ηbar[m] HL1/3[m] Sqrt(B1) TL1/3[s] η bar[m], HL1/3 [m] b1.5.7.6.5.4.3.2.1.1 NNW 4 5 6 7 8 9 1 11 12 13 14 15 16 17 18 19 2 21 22 23 24 25 26 27 2 4 6 8 1 12 TL1/3[s] ηbar[m] HL1/3[m] Sqrt(B1) TL1/3[s] η bar[m], HL1/3 [m] b1.5 1.2 1.8.6.4.2.2.4 NNW 4 5 6 7 8 9 1 11 12 13 14 15 16 17 18 19 2 21 22 23 24 25 26 27 2 4 6 8 1 12 TL1/3[s] ηbar[m] HL1/3[m] Sqrt(B1) TL1/3[s] Point Point NW NW η bar[m], HL1/3 [m] b1.5.8.6.4.2.2.4 4 5 6 7 8 9 1 11 12 13 14 15 16 17 18 19 2 21 22 23 24 25 26 27 2 4 6 8 1 12 TL1/3[s] ηbar[m] HL1/3[m] Sqrt(B1) TL1/3[s] η bar[m], HL1/3 [m] b1.5 1.6 1.4 1.2 1.8.6.4.2.2.4 4 5 6 7 8 9 1111213141516171819221222324252627 2 4 6 8 1 12 14 TL1/3[s] ηbar[m] HL1/3[m] Sqrt(B1) TL1/3[s] Point Point η bar[m], HL1/3 [m] b1.5.8.6.4.2.2.4 WNW 4 5 6 7 8 9 1 11 12 13 14 15 16 17 18 19 2 21 22 23 24 25 26 27 2 4 6 8 1 12 TL1/3[s] ηbar[m] HL1/3[m] Sqrt(B1) TL1/3[s] η bar[m], HL1/3 [m] b1.5 1.5 1.5.5 WNW 4 5 6 7 8 9 1 11 12 13 14 15 16 17 18 19 2 21 22 23 24 25 26 27 2 4 6 8 1 12 TL1/3[s] ηbar[m] HL1/3[m] Sqrt(B1) TL1/3[s] Point Point η bar[m], HL1/3 [m] b1.5.7.6.5.4.3.2.1.1 W 4 5 6 7 8 9 1111213141516171819221222324252627 2 4 6 8 1 12 TL1/3[s] ηbar[m] HL1/3[m] Sqrt(B1) TL1/3[s] η bar[m], HL1/3 [m] b1.5 1.4 1.2 1.8.6.4.2.2.4 W 4 5 6 7 8 9 1 11 12 13 14 15 16 17 18 19 2 21 22 23 24 25 26 27 1 2 3 4 5 6 7 8 9 1 TL1/3[s] ηbar[m] HL1/3[m] Sqrt(B1) TL1/3[s] Point Point η bar[m], HL1/3 [m] b1.5.6.5.4.3.2.1.1.2 WSW 4 5 6 7 8 9 1 11 12 13 14 15 16 17 18 19 2 21 22 23 24 25 26 27 2 4 6 8 1 12 TL1/3[s] ηbar[m] HL1/3[m] Sqrt(B1) TL1/3[s] ηbar[m], HL1/3 [m] b1.5 1.2 1.8.6.4.2.2 WSW 4 5 6 7 8 9 1 11 12 13 14 15 16 17 18 19 2 21 22 23 24 25 26 27 1 2 3 4 5 6 7 8 9 TL1/3[s] ηbar[m] HL1/3[m] Sqrt(B1) TL1/3[s] Point Point - 42 -

1 β1 = η 1 N 3 N rms i= 1 ( ηi η ) 3 1.2 1. β 1=.5 β 1 a=.5a=.7 NNW η bar (m) ah L1/3 (m) h d (m).8.6.4.2..9.8.7.6.5.4.3.2.1. 4. 3.8 3.6 3.4 3.2 3. 2.8 2.6 2.4 2.2 2. 4 7 1 13 16 19 22 25 (a) (a=.7) (a=.5) 4 7 1 13 16 19 22 25 (a=.7) (a=.5) (b) (a=.7) (a=.5) 4 7 1 13 16 19 22 25 (c) (a=.7) (a=.5) 1.2 1..8 (a=.7) (a=.5) (a=.7) (a=.5) H' (m).6.4.2. 4 7 1 13 16 19 22 25 (m) (d) NNW - 43 -

a 2 35cma 2cm a 6cm H 1/3_x(m) H 1/3_x (m) H 1/3_x (m) H 1/3_x (m) 5. 4. 3. 2. Line1 84 P29 H1/3 H1/3 H1/3 P4 1. P4. -6 4 14 24 34 44 54 64 74 84 94 2.5 2. 1.5 1..5 Line3 984m P31 (a) H1/3 H1/3 H1/3. -6 4 14 24 34 44 3. 2.5 2. 1.5 1..5 (b). -5 5 15 25 35 45 55 65 75 6. 5. 4. 3. 2. 1. Line5 1584m P33 Line7 2184m P35 P46 P1 H1/3 H1/3 H1/3 P44 (c) P16 H1/3 H1/3 H1/3 1 8 6 4 2 2 4 6 8 m 4 35 3 25 2 15 1 5 5 1 m 22 17 12 7 2 3 8 m. -6 4 14 24 34 44 54 64 74 84 94 14 114 124 134 m (d) NNW P22 1 8 6 4 2 2 4 6 8 1-44 -

q(m 3 /m/s) 1.E+ 1.E 3 1.E 6 1.E 9 1.E 12 1.E 15 1.E 18 1.E 21 1.E 24 1.E 27 1.E 3 4 7 1 13 16 19 22 25 a=.5 q=21 4 D.L.+5.m (a) a=.5 q(m 3 /m/s) 1.E+ 1.E 3 1.E 6 1.E 9 1.E 12 1.E 15 1.E 18 1.E 21 1.E 24 1.E 27 1.E 3 4 7 1 13 16 19 22 25 a=.7 q=2 1 4 D.L.+5.m (b) a=.7 NNW q(m 3 /m/s) q(m 3 /m/s) 1.E+ 1.E 3 a=.5 q=2 1 4 1.E 6 1.E 9 1.E 12 1.E 15 1.E 18 1.E 21 N NNW 1.E 24 NW WNW 1.E 27 W WSW 1.E 3 (a) a=.5 1.E+ 1.E 3 a=.7 q=2 1 4 1.E 6 1.E 9 1.E 12 1.E 15 1.E 18 1.E 21 1.E 24 1.E 27 1.E 3 N NNW NW WNW W WSW (b) a=.7-45 -

Line Line Line1357 1 2 Line5NNW Line3 Line1Line7 2cm a a P162.7 5% 21-4 m 3 /m/s P15NW a a=.7 a=.53.4 1-4.23-46 -

- 47 - NOWT-PARIVer5.3 29 1/2 a=.5.7 29421 28 55 pp831-835. 1975 143pp59-16. 1975 144 44p. 1974 21 pp57-63. 1977 No.27832p. 1982 212 pp151-25. 1984 31 pp542-546. 1991 31 pp21-67p. 1992 No.723176p. 21

41pp3-3. 22 No.136 162p 24 51pp11-15. 25 52pp11-15. 26 53pp.76-71 28 55 pp.796-8 29 28 24pp951-955. a b d dt, Δt f h h d H 1/3 H L1/3 H L1/3_I H L1/3_S H K s N s tanθ α β η bar θ λ ζ - 48 -

(a) N (b) NNW (c) NW (d) WNW (e) W (f) WSW NOWT-PARI - 49 -

S(f) [m 2 sec] S(f) [m 2 sec] S(f) [m 2 sec] 18 16 14 12 1 8 6 4 2..1.2 Frequency(Hz) S(f) [m 2 sec] 18 NNW 16 14 12 1 8 6 4 2..1.2 Frequency(Hz) (a)n (b)nnw 18 NW 16 14 12 1 8 6 4 2..1.2 Frequency(Hz) S(f) [m 2 sec] 18 WNW 16 14 12 1 8 6 4 2..1.2 Frequency(Hz) (a)nw (b)wnw 18 W 16 14 12 1 8 6 4 2..1.2 Frequency(Hz) S(f) [m 2 sec] 18 WSW 16 14 12 1 8 6 4 2..1.2 Frequency(Hz) (a)w (b)nsw - 5 -

5. 4. G 2 [m 2 ] 3. 2. 1.. 9 45 45 9 Deg.() (a) N (b) NNW 5. 5. 4. 4. G 2 [m 2 ] 3. 2. G 2 [m 2 ] 3. 2. 1. 1... 9 45 45 9 Deg.() 9 45 45 9 Deg.() (c) NW (d) WNW 5. 5. 4. 4. G 2 [m 2 ] 3. 2. G 2 [m 2 ] 3. 2. 1. 1.. 9 45 45 9 Deg.() (e) W. 9 45 45 9 Deg.() (f) WSW - 51 -

- 52 -

- 53 -

N NNW NW 1-54 -

WNW NW WSW 2-55 -

ap29p33p36 bp4p44p47 NNW 1-56 -

cp4p19p25 NNW 2-57 -

NOWT-PARI Ver5.3 2km4km St.3 St.1St.2St.4St.5 7/158/6 87 7/1622 88 7/2531 12/421 St.4 SW NOWPHAS - 58 -

NOWPHAS 7 7/17 7/19 9s 1.52.5m SWWN 22527 7/17 15: 7/17 18: 7/18 6: 7/18 15: (a) 7 28 7 16 22 7/28 3: 7/28 6: 7/29 13: (b) 8 28 7 25 31 NOWPHAS - 59 -

St.1 St.2 St.3 St.4 St.5 D.L D.L-28.2m D.L-2.3m D.L-28.5m D.L+.4m D.L-4.4m 7/17 15: 7/17 18: 7/18 6: 7/18 15: 7/28 3: 7/28 6: 7/29 13: (a) 7/17 15: 7/17 18: 7/18 6: 7/18 15: 7/28 3: 7/28 6: 7/29 13: (b) St.1St.5 28/7/158/6-6 -

8 7/26 7/28 12s 7/29 11s 1.53.m SWN 225 O 1 K 1 S 2 M 2 D.L. D.L =- 1.346(m)B.1 St.1St.5 D.L. B.1 St.4 1.746m 7/19 14 7/3 12 7/18 15 D.L.+.45m 5cm 7/17 15 7/18 15 7/28 6 7/29 13 St.4 St.4.5s 72 FFT 496 34 St.1St.5 St.1St.3 St.5 St.4 (1) SW St.3 St.3 34 2 3 4 25 3-61 -

NOWT-PARI H 1/3 T 1/3 Smax 28717 216 1.83 8.9 73.69 15: SW 28717 212 2.12 9.6 71 1.71 18: SSW 28718 214 1.94 8.6 7 2. 6: SW 28718 226 1.57 8.6 73.45 15: SW 28728 211 2.47 11.2 67 1.85 3: SSW 28728 211 2.18 1.5 68 1.15 6: SSW 28729 218 1.5 8.6 72.77 13: SW H 1/3 T 1/3 [m] [deg.]n Smax D.L. T 1/3 [s] DT [s] TTIN [s] TDEL [s] TSVE [s] TEND [s] 28.7.17 15: 8.9.2 45..225 225. 495. 28.7.17 18: 9.6.2 45..225 225. 495. 28.7.18 6: 8.6.2 45..225 225. 495. 28.7.18 15: 8.6.2 45..225 225. 495. 28.7.28 3: 11.2.3 6..3 3. 546. 28.7.28 6: 1.5.3 6..3 3. 546. 28.7.29 13: 8.6.2 45..225 225. 495..225.3s 8192 5m 1/81/1 5m 4m 6s 5s f=.2-62 -

(2) St.1St.5 53s.33.2Hz 3s.33Hz 28/7/17 15: - 63 -

.2Hz =5s 53s.33.2Hz 3s.33Hz 28/7/17 18: - 64 -

(a) 17 15 18 15 29 13 53s.33.2Hz 3s.33Hz 28/7/18 6: - 65 -

St.3.8Hz 12.5s St.3 53s.33.2Hz 3s.33Hz 28/7/18 15: - 66 -

St.1 St.2 St.1.8Hz St.4 53s.33.2Hz 3s.33Hz 28/7/28 3: - 67 -

St.5.8.2Hz 512.5s.8 12.5s St.4 53s.33.2Hz 3s.33Hz 28/7/28 6: - 68 -

(b) 17 18 18 6 28 3 53s.33.2Hz 3s.33Hz 28/7/29 13: - 69 -

St.3.8Hz 12.5s St.3 St.2.8Hz St.1 St.4 St.4 St.5.8.2Hz 512.5s.8 12.5s St.4 (c) 28 6 St.3.8Hz 12.5s St.1 St.2.8Hz St.1 St.4 St.5-7 -

.8.2Hz 512.5s.8 12.5s St.4 (3) St.1St.5.2.33Hz= 53s.33Hz = 3s - 71 -

.2Hz = 5s (a) 17 15 18 15 29 13 St.3 St.1St.2-72 -

St.4 St.5 St.3 St.1St.2 3s St.1 St.5 St.4 St.5 (b) 17 18 18 6 28 3 St.3 St.2 St.1 St.4 St.5 St.3 St.1St.2 St.4 St.5 (c) 28 6 St.3 St.2 St.1 St.4 St.5 St.3 St.1St.2 St.4 St.5-73 -

D.L.+3.2m - 74 -

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