Wave Transmission over Rubble-Mound Submerged Breakwaters
Abstract
:1. Introduction
2. Materials and Methods
2.1. Experimental Setup
2.2. Numerical Model
2.3. Breaker Type Classification
2.3.1. Regular Waves
2.3.2. Irregular Waves
3. Results
4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
# | T (s) | Hi (m) | Kt | Breaker Type | |
---|---|---|---|---|---|
SPB1 F = 0.10 m | 1 | 1 | 0.078 | 0.85 | x |
2 | 1.15 | 0.066 | 0.98 | x | |
3 | 1.3 | 0.08 | 0.76 | x | |
4 | 1.45 | 0.122 | 0.89 | S | |
5 | 1.85 | 0.145 | 0.79 | S | |
SPB2a F = 0.05 m | 6 | 1 | 0.098 | 0.72 | S |
7 | 1.15 | 0.141 | 0.50 | P | |
8 | 1.25 | 0.051 | 0.45 | O | |
9 | 1.25 | 0.066 | 0.53 | O | |
10 | 1.25 | 0.096 | 0.57 | P | |
11 | 1.45 | 0.079 | 0.80 | S | |
12 | 1.6 | 0.083 | 0.61 | O | |
13 | 1.7 | 0.125 | 0.55 | P | |
14 | 1.85 | 0.107 | 0.47 | O | |
15 | 2 | 0.045 | 0.49 | O | |
16 | 2 | 0.052 | 0.50 | O | |
17 | 2 | 0.08 | 0.46 | O | |
18 | 2.2 | 0.152 | 0.36 | P | |
SPB2a F = 0.10 m | 19 | 1 | 0.078 | 0.85 | x |
20 | 1 | 0.113 | 0.88 | x | |
21 | 1.15 | 0.066 | 0.98 | x | |
22 | 1.3 | 0.07 | 0.90 | x | |
23 | 1.3 | 0.08 | 0.76 | S | |
24 | 1.45 | 0.12 | 0.93 | x | |
25 | 1.45 | 0.13 | 0.80 | S | |
26 | 2 | 0.14 | 0.57 | S | |
SPB2b F = 0.05 m | 27 | 1 | 0.093 | 0.60 | P |
28 | 1.25 | 0.087 | 0.41 | P | |
29 | 1.25 | 0.097 | 0.48 | S | |
30 | 1.5 | 0.081 | 0.68 | S | |
31 | 1.5 | 0.089 | 0.66 | S | |
32 | 1.5 | 0.095 | 0.63 | S | |
33 | 1.6 | 0.08 | 0.56 | S | |
34 | 1.6 | 0.082 | 0.59 | S | |
35 | 1.7 | 0.118 | 0.47 | P | |
36 | 1.85 | 0.11 | 0.39 | P | |
37 | 2 | 0.045 | 0.51 | O | |
38 | 2 | 0.075 | 0.49 | O | |
39 | 2.1 | 0.062 | 0.52 | O | |
SPB2b F = 0.10 m | 40 | 1 | 0.085 | 0.87 | x |
41 | 1.25 | 0.173 | 0.49 | P | |
42 | 1.3 | 0.065 | 0.91 | x | |
43 | 1.5 | 0.094 | 0.77 | S | |
44 | 1.6 | 0.075 | 0.67 | O | |
45 | 1.6 | 0.141 | 0.63 | S | |
46 | 1.8 | 0.115 | 0.61 | S | |
47 | 2 | 0.093 | 0.45 | O | |
48 | 2.2 | 0.108 | 0.67 | S | |
SPB3a F = 0.05 m | 49 | 1 | 0.07 | 0.79 | x |
50 | 1.15 | 0.105 | 0.58 | S | |
51 | 1.25 | 0.094 | 0.96 | x | |
52 | 1.3 | 0.082 | 0.88 | S | |
53 | 1.45 | 0.141 | 0.50 | P | |
54 | 1.6 | 0.112 | 0.54 | S | |
55 | 1.7 | 0.131 | 0.68 | S | |
56 | 1.85 | 0.074 | 0.73 | x | |
57 | 2 | 0.052 | 0.79 | x | |
58 | 2 | 0.084 | 0.86 | x | |
59 | 2.2 | 0.138 | 0.63 | O | |
SPB3a F = 0.10 m | 60 | 1 | 0.073 | 0.99 | x |
61 | 1.25 | 0.122 | 0.89 | S | |
62 | 1.3 | 0.089 | 0.99 | x | |
63 | 1.45 | 0.159 | 0.63 | S | |
64 | 1.5 | 0.126 | 0.78 | x | |
65 | 1.5 | 0.15 | 0.69 | S | |
66 | 1.8 | 0.079 | 0.89 | x | |
67 | 1.8 | 0.105 | 0.90 | x | |
68 | 2 | 0.088 | 0.77 | x | |
SPB3b F = 0.05 m | 69 | 1 | 0.066 | 0.83 | S |
70 | 1.15 | 0.053 | 0.87 | x | |
71 | 1.15 | 0.101 | 0.54 | P | |
72 | 1.3 | 0.079 | 0.86 | S | |
73 | 1.45 | 0.145 | 0.44 | P | |
74 | 1.5 | 0.115 | 0.59 | P | |
75 | 1.6 | 0.102 | 0.57 | S | |
76 | 1.7 | 0.123 | 0.74 | S | |
78 | 1.8 | 0.07 | 0.77 | x | |
79 | 2 | 0.075 | 0.81 | O | |
80 | 2.1 | 0.057 | 0.88 | x |
# | T (s) | Hs (m) | Kt | |
---|---|---|---|---|
SPB1 F = 0.10 m | 1 | 1 | 0.066 | 0.82 |
2 | 1.15 | 0.079 | 0.8 | |
3 | 1.3 | 0.086 | 0.8 | |
4 | 1.3 | 0.102 | 0.75 | |
5 | 1.45 | 0.087 | 0.82 | |
6 | 1.5 | 0.095 | 0.82 | |
7 | 1.6 | 0.102 | 0.81 | |
8 | 1.85 | 0.102 | 0.78 | |
9 | 2 | 0.107 | 0.77 | |
SPB2a F = 0.05 m | 10 | 1 | 0.064 | 0.69 |
11 | 1.15 | 0.063 | 0.70 | |
12 | 1.15 | 0.074 | 0.66 | |
13 | 1.25 | 0.04 | 0.73 | |
14 | 1.25 | 0.052 | 0.69 | |
15 | 1.25 | 0.07 | 0.67 | |
16 | 1.25 | 0.083 | 0.63 | |
17 | 1.3 | 0.049 | 0.71 | |
18 | 1.3 | 0.087 | 0.62 | |
19 | 1.45 | 0.062 | 0.71 | |
20 | 1.45 | 0.095 | 0.61 | |
21 | 1.6 | 0.073 | 0.66 | |
22 | 1.6 | 0.113 | 0.56 | |
23 | 1.7 | 0.092 | 0.54 | |
24 | 1.85 | 0.087 | 0.55 | |
25 | 2 | 0.046 | 0.61 | |
26 | 2 | 0.075 | 0.55 | |
27 | 2.2 | 0.073 | 0.55 | |
SPB2a F = 0.10 m | 28 | 1 | 0.065 | 0.83 |
29 | 1.15 | 0.076 | 0.82 | |
30 | 1.3 | 0.093 | 0.75 | |
31 | 1.3 | 0.11 | 0.71 | |
32 | 1.3 | 0.124 | 0.67 | |
33 | 1.45 | 0.092 | 0.77 | |
34 | 1.45 | 0.108 | 0.73 | |
35 | 1.6 | 0.12 | 0.68 | |
36 | 1.7 | 0.116 | 0.66 | |
37 | 1.7 | 0.129 | 0.64 | |
38 | 1.85 | 0.107 | 0.64 | |
39 | 2 | 0.109 | 0.65 | |
SPB2b F = 0.05 m | 40 | 1 | 0.063 | 0.63 |
41 | 1.15 | 0.075 | 0.60 | |
42 | 1.25 | 0.037 | 0.70 | |
43 | 1.25 | 0.061 | 0.64 | |
44 | 1.45 | 0.089 | 0.57 | |
45 | 1.6 | 0.109 | 0.51 | |
46 | 1.7 | 0.113 | 0.50 | |
47 | 1.85 | 0.099 | 0.49 | |
48 | 2 | 0.039 | 0.62 | |
49 | 2 | 0.07 | 0.53 | |
50 | 2 | 0.11 | 0.48 | |
51 | 2.2 | 0.115 | 0.48 | |
SPB2b F = 0.10 m | 52 | 1 | 0.063 | 0.79 |
53 | 1.15 | 0.076 | 0.74 | |
54 | 1.3 | 0.107 | 0.65 | |
55 | 1.45 | 0.09 | 0.73 | |
56 | 1.6 | 0.117 | 0.64 | |
57 | 1.7 | 0.124 | 0.60 | |
58 | 1.85 | 0.106 | 0.60 | |
59 | 2 | 0.109 | 0.60 | |
60 | 2 | 0.122 | 0.60 | |
SPB3a F = 0.05 m | 61 | 1 | 0.049 | 0.80 |
62 | 1.15 | 0.06 | 0.78 | |
63 | 1.15 | 0.077 | 0.70 | |
64 | 1.25 | 0.043 | 0.91 | |
65 | 1.25 | 0.068 | 0.78 | |
66 | 1.3 | 0.099 | 0.65 | |
67 | 1.45 | 0.073 | 0.73 | |
68 | 1.45 | 0.099 | 0.62 | |
69 | 1.6 | 0.115 | 0.57 | |
70 | 1.7 | 0.088 | 0.67 | |
71 | 1.7 | 0.115 | 0.62 | |
72 | 1.85 | 0.079 | 0.71 | |
73 | 1.85 | 0.097 | 0.68 | |
74 | 2 | 0.044 | 0.80 | |
75 | 2 | 0.07 | 0.73 | |
76 | 2 | 0.103 | 0.68 | |
77 | 2.2 | 0.106 | 0.70 | |
SPB3a F = 0.10 m | 78 | 1 | 0.053 | 0.85 |
79 | 1.15 | 0.06 | 0.88 | |
80 | 1.3 | 0.085 | 0.82 | |
81 | 1.3 | 0.101 | 0.74 | |
82 | 1.3 | 0.115 | 0.72 | |
83 | 1.45 | 0.092 | 0.77 | |
84 | 1.45 | 0.105 | 0.70 | |
85 | 1.6 | 0.126 | 0.67 | |
86 | 1.7 | 0.122 | 0.74 | |
87 | 1.85 | 0.104 | 0.74 | |
88 | 2 | 0.111 | 0.74 | |
89 | 2.2 | 0.109 | 0.80 | |
SPB3b F = 0.05 m | 90 | 1 | 0.042 | 0.83 |
91 | 1.15 | 0.056 | 0.86 | |
92 | 1.25 | 0.031 | 1.00 | |
93 | 1.25 | 0.06 | 0.85 | |
94 | 1.3 | 0.068 | 0.78 | |
95 | 1.3 | 0.099 | 0.64 | |
96 | 1.45 | 0.072 | 0.74 | |
97 | 1.45 | 0.097 | 0.63 | |
98 | 1.6 | 0.115 | 0.58 | |
99 | 1.7 | 0.086 | 0.71 | |
100 | 1.7 | 0.113 | 0.65 | |
101 | 1.85 | 0.094 | 0.71 | |
102 | 2 | 0.043 | 0.84 | |
103 | 2 | 0.07 | 0.77 | |
104 | 2 | 0.109 | 0.66 | |
105 | 2.2 | 0.107 | 0.71 | |
SPB3b F = 0.10 m | 106 | 1 | 0.043 | 0.95 |
107 | 1.15 | 0.06 | 0.92 | |
108 | 1.3 | 0.102 | 0.76 | |
109 | 1.45 | 0.093 | 0.78 | |
110 | 1.6 | 0.121 | 0.72 | |
111 | 1.7 | 0.12 | 0.77 | |
112 | 1.7 | 0.132 | 0.76 | |
113 | 2 | 0.11 | 0.78 | |
114 | 2.2 | 0.12 | 0.78 |
# | T (s) | Hi (m) | Kt | |
---|---|---|---|---|
SPB2a F = 0.05 m | 10 | 1 | 0.067 | 0.97 |
11 | 1 | 0.099 | 0.76 | |
12 | 1.25 | 0.063 | 0.67 | |
13 | 1.25 | 0.082 | 0.67 | |
14 | 1.25 | 0.119 | 0.59 | |
SPB2a F = 0.10 m | 28 | 1 | 0.063 | 0.95 |
29 | 1 | 0.082 | 0.96 | |
30 | 1.25 | 0.059 | 0.88 | |
31 | 1.25 | 0.082 | 0.79 | |
32 | 1.25 | 0.117 | 0.99 | |
SPB2b F = 0.05 m | 40 | 1 | 0.058 | 0.93 |
41 | 1 | 0.102 | 0.73 | |
42 | 1.25 | 0.061 | 0.56 | |
43 | 1.25 | 0.08 | 0.54 | |
44 | 1.25 | 0.122 | 0.52 | |
SPB2b F = 0.10 m | 52 | 1 | 0.061 | 0.92 |
53 | 1 | 0.08 | 0.94 | |
54 | 1.25 | 0.063 | 0.62 | |
55 | 1.25 | 0.08 | 0.66 | |
56 | 1.25 | 0.123 | 0.73 | |
SPB3a F = 0.05 m | 61 | 1 | 0.062 | 0.98 |
62 | 1 | 0.106 | 0.81 | |
63 | 1.25 | 0.065 | 0.69 | |
64 | 1.25 | 0.084 | 0.71 | |
65 | 1.25 | 0.119 | 0.78 | |
SPB3a F = 0.10 m | 78 | 1 | 0.062 | 0.97 |
79 | 1 | 0.102 | 0.98 | |
80 | 1.25 | 0.058 | 0.88 | |
81 | 1.25 | 0.079 | 0.89 | |
82 | 1.25 | 0.124 | 0.97 | |
SPB3b F = 0.05 m | 90 | 1 | 0.061 | 0.85 |
91 | 1 | 0.102 | 0.70 | |
92 | 1.25 | 0.062 | 0.58 | |
93 | 1.25 | 0.084 | 0.62 | |
94 | 1.25 | 0.123 | 0.53 | |
SPB3b F = 0.10 m | 106 | 1 | 0.06 | 0.92 |
107 | 1 | 0.104 | 0.96 | |
108 | 1.25 | 0.064 | 0.70 | |
109 | 1.25 | 0.084 | 0.71 | |
110 | 1.25 | 0.122 | 0.86 |
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Model | SPB1 | SPB2a | SPB2b | SPB3a | SPB3b |
---|---|---|---|---|---|
B (m) | 0.30 | 0.28 | 0.40 | 0.25 | 0.35 |
Dn50 (m) | 0.10 | 0.08 | 0.08 | 0.06 | 0.06 |
F (m) | 0.10 | 0.05, 0.10 | 0.05, 0.10 | 0.05, 0.10 | 0.05, 0.10 1 |
Regular Waves | |||||
No of tests | 5 | 21 | 22 | 20 | 12 |
T (s) | 1.0–1.85 | 1.0–2.2 | 1.0–2.2 | 1.0–2.2 | 1.0–2.2 |
Hi (m) | 0.078–0.145 | 0.045–0.152 | 0.045–0.173 | 0.052–0.15 | 0.053–0.145 |
Irregular Waves | |||||
No of tests | 9 | 30 | 21 | 29 | 27 |
Tp (s) | 1.0–2.0 | 1.0–2.2 | 1.0–2.2 | 1.0–2.2 | 1.0–2.2 |
Hs (m) | 0.066–0.102 | 0.04–0.124 | 0.039–0.124 | 0.043–0.122 | 0.031–0.132 |
Sub Area | Breaker Type |
---|---|
if ξm < 2.35 and R ≥ T1 | Plunging 1 |
if ξm < 2.35 and T1 > R > T2 | Spilling 1 |
if ξm ≥ 2.35 and R > T2 | Other |
if R ≤ T2 | Non-breaking |
Sub Area | Breaker Type |
---|---|
R ≥ T1 | Plunging |
T1 > R > T2 | Spilling+ |
R ≤ T2 | Non-breaking |
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Repousis, E.; Roupas, I.; Memos, C. Wave Transmission over Rubble-Mound Submerged Breakwaters. J. Mar. Sci. Eng. 2023, 11, 1346. https://doi.org/10.3390/jmse11071346
Repousis E, Roupas I, Memos C. Wave Transmission over Rubble-Mound Submerged Breakwaters. Journal of Marine Science and Engineering. 2023; 11(7):1346. https://doi.org/10.3390/jmse11071346
Chicago/Turabian StyleRepousis, Elpidoforos, Ioannis Roupas, and Constantine Memos. 2023. "Wave Transmission over Rubble-Mound Submerged Breakwaters" Journal of Marine Science and Engineering 11, no. 7: 1346. https://doi.org/10.3390/jmse11071346
APA StyleRepousis, E., Roupas, I., & Memos, C. (2023). Wave Transmission over Rubble-Mound Submerged Breakwaters. Journal of Marine Science and Engineering, 11(7), 1346. https://doi.org/10.3390/jmse11071346