High-Resolution Wave Energy Assessment in Shallow Water Accounting for Tides
Abstract
:1. Introduction
2. Wave Modelling in the Portuguese Nearshore
3. Study of the Tide and Wind Influences in the High Resolution Computational Domain
4. Results and Discussion
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Nomenclature | Significance |
---|---|
Δx/Δy | Resolution in the geographical space |
Δθ | Resolution in the directional space |
Δt | Time resolution |
nf | Number of frequencies in the spectral space |
nθ | Number of directions in the spectral space |
ngx | Number of grid points in x direction |
ngy | Number of grid points in y direction |
np | Total number of grid points |
wave | Wave forcing |
wind | Wind forcing |
tide | Tide forcing |
cur | Current field input |
gen | Generation by wind |
wcap | Whitecapping process |
quad | Quadruplet nonlinear interactions |
tri | Triad nonlinear interactions |
dif | Diffraction |
bfr | Bottom friction |
set up | Wave induced set up |
br | Depth induced wave breaking |
SWAN Model | Origin | Δx × Δy | Δθ (°) | Mode | nf | nθ | ngx × ngy = np | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Level I Iberian | XO1 = −11° W YO1 = 35° N | 0.05 × 0.1 (°) | 10 | nonstat | 29 | 36 | 100 × 100 = 10,000 | |||||
Level II Coastal | XO2 = −10.25° W YO2 = 38.25° N | 0.02 × 0.02 (°) | 10 | nonstat | 29 | 36 | 75 × 90 = 6750 | |||||
Level III Local | XO3 = −9.75° W YO3 = 39.2° N | 0.005 × 0.005 (°) | 10 | nonstat | 29 | 36 | 161 × 161 = 25,921 | |||||
Level IV High Resolution | XO4 = −9.315° W YO4 = 39.398° N | 25 × 25 (m) | 5 | stat | 34 | 36 | 112 × 96 = 10,752 | |||||
Input/Process | Wave | Wind | Tide | Cur | Gen | Wcap | Quad | Tri | Dif | Bfr | Set up | Br |
Level I Iberian | X | X | 0 | 0 | X | X | X | 0 | 0 | X | 0 | X |
Level II Coastal | X | X | 0 | 0 | X | X | X | 0 | 0 | X | 0 | X |
Level III Local | X | X | X | 0 | X | X | X | X | X | X | X | X |
Level IV High Resolution | X | X | X | 0 | X | X | X | X | X | X | X | X |
Case Study | Hs (m) | Tp (s) | |||
---|---|---|---|---|---|
CSI (total average) | 2.0 | 10.1 | |||
CSII (winter average) | 2.43 | 11.0 | |||
CSIII (high waves) | 4.5 | 15.0 | |||
CSIV (extreme conditions) | 8.7 | 18.0 | |||
Mean Wave Direction (°) Nautical Convention | Wind Conditions | ||||
Wind Velocity (m/s) | Wind Direction (°) | ||||
Dir1 | 270 | W0 (no wind) | 0 | - | |
W7 (average wind) | 7 | FW (following wind) | 305 | ||
OW (opposite wind) | 90 | ||||
W22 (high wind) | 22 | FW (following wind) | 305 | ||
OW (opposite wind) | 90 | ||||
Dir2 | 300 | W0 (no wind) | 0 | - | |
W7 (average wind) | 7 | FW (following wind) | 305 | ||
OW (opposite wind) | 120 | ||||
W22 (high wind) | 22 | FW (following wind) | 305 | ||
OW (opposite wind) | 120 | ||||
Dir3 | 330 | W0 (no wind) | 0 | - | |
W7 (average wind) | 7 | FW (following wind) | 305 | ||
OW (opposite wind) | 150 | ||||
W22 (high wind) | 22 | FW (following wind) | 305 | ||
OW (opposite wind) | 150 | ||||
Tide Level | T1 | T2 | T3 | T4 | T5 |
(m)-above the hydrographic zero | 0.16 | 1.1 | 2.04 | 2.98 | 3.92 |
CS1 | P3 | P4 | P5 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Hs | Hsw | Pw | Hs | Hsw | Pw | Hs | Hsw | Pw | |||
m | m | kW/m | m | m | kW/m | m | m | kW/m | |||
D1 | W0 | T1 | 1.07 | 0.67 | 5.16 | 1.08 | 0.66 | 5.26 | 1.06 | 0.64 | 5.06 |
T5 | 1.06 | 0.65 | 5.15 | 1.07 | 0.65 | 5.22 | 1.06 | 0.64 | 5.07 | ||
W7-FW | T1 | 1.25 | 0.77 | 6.91 | 1.26 | 0.77 | 7.03 | 1.24 | 0.75 | 6.76 | |
T5 | 1.24 | 0.75 | 6.90 | 1.25 | 0.75 | 6.98 | 1.24 | 0.74 | 6.78 | ||
W7-OW | T1 | 1.09 | 0.67 | 5.19 | 1.09 | 0.66 | 5.27 | 1.07 | 0.65 | 5.06 | |
T5 | 1.07 | 0.65 | 5.17 | 1.08 | 0.65 | 5.23 | 1.07 | 0.64 | 5.08 | ||
W22-FW | T1 | 3.68 | 2.21 | 57.89 | 3.68 | 2.19 | 58.44 | 3.62 | 2.13 | 55.91 | |
T5 | 3.64 | 2.15 | 57.70 | 3.66 | 2.15 | 57.98 | 3.62 | 2.11 | 56.07 | ||
W22-OW | T1 | 1.78 | 0.97 | 12.01 | 1.83 | 0.99 | 12.90 | 1.84 | 1.00 | 13.10 | |
T5 | 1.80 | 0.97 | 12.44 | 1.84 | 0.99 | 13.17 | 1.85 | 1.00 | 13.35 | ||
D2 | W0 | T1 | 1.35 | 0.84 | 8.21 | 1.36 | 0.83 | 8.32 | 1.33 | 0.81 | 7.97 |
T5 | 1.34 | 0.82 | 8.19 | 1.35 | 0.82 | 8.25 | 1.33 | 0.81 | 8.00 | ||
W7-FW | T1 | 1.51 | 0.93 | 10.11 | 1.52 | 0.93 | 10.24 | 1.49 | 0.90 | 9.81 | |
T5 | 1.49 | 0.91 | 10.08 | 1.51 | 0.91 | 10.16 | 1.49 | 0.89 | 9.85 | ||
W7-OW | T1 | 1.36 | 0.84 | 8.21 | 1.37 | 0.83 | 8.31 | 1.34 | 0.81 | 7.96 | |
T5 | 1.35 | 0.82 | 8.18 | 1.36 | 0.82 | 8.25 | 1.34 | 0.81 | 7.99 | ||
W22-FW | T1 | 3.89 | 2.34 | 65.04 | 3.89 | 2.32 | 65.66 | 3.82 | 2.26 | 62.75 | |
T5 | 3.85 | 2.29 | 64.79 | 3.87 | 2.28 | 65.05 | 3.82 | 2.24 | 62.87 | ||
W22-OW | T1 | 1.47 | 0.80 | 7.28 | 1.48 | 0.79 | 7.38 | 1.47 | 0.77 | 7.08 | |
T5 | 1.45 | 0.78 | 7.28 | 1.47 | 0.78 | 7.34 | 1.46 | 0.77 | 7.12 | ||
D3 | W0 | T1 | 1.47 | 0.91 | 9.71 | 1.48 | 0.91 | 9.82 | 1.45 | 0.88 | 9.40 |
T5 | 1.45 | 0.89 | 9.68 | 1.47 | 0.89 | 9.74 | 1.45 | 0.88 | 9.43 | ||
W7-FW | T1 | 1.63 | 1.01 | 11.78 | 1.64 | 1.00 | 11.90 | 1.61 | 0.97 | 11.39 | |
T5 | 1.61 | 0.98 | 11.74 | 1.62 | 0.98 | 11.81 | 1.61 | 0.96 | 11.44 | ||
W7-OW | T1 | 1.48 | 0.91 | 9.70 | 1.49 | 0.91 | 9.81 | 1.46 | 0.88 | 9.39 | |
T5 | 1.46 | 0.89 | 9.67 | 1.47 | 0.89 | 9.74 | 1.46 | 0.88 | 9.43 | ||
W22-FW | T1 | 3.96 | 2.39 | 67.65 | 3.97 | 2.37 | 68.25 | 3.90 | 2.31 | 65.21 | |
T5 | 3.92 | 2.33 | 67.40 | 3.94 | 2.33 | 67.62 | 3.89 | 2.29 | 65.35 | ||
W22-OW | T1 | 1.51 | 0.83 | 7.66 | 1.53 | 0.83 | 7.74 | 1.52 | 0.80 | 7.37 | |
T5 | 1.49 | 0.81 | 7.64 | 1.52 | 0.81 | 7.68 | 1.52 | 0.80 | 7.41 |
CS2 | P3 | P4 | P5 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Hs | Hsw | Pw | Hs | Hsw | Pw | Hs | Hsw | Pw | |||
m | m | kW/m | m | m | kW/m | m | m | kW/m | |||
D1 | W0 | T1 | 1.28 | 1.00 | 7.77 | 1.28 | 0.99 | 7.91 | 1.25 | 0.96 | 7.57 |
T5 | 1.26 | 0.97 | 7.80 | 1.27 | 0.98 | 7.90 | 1.25 | 0.96 | 7.65 | ||
W7-FW | T1 | 1.46 | 1.13 | 9.97 | 1.46 | 1.12 | 10.15 | 1.43 | 1.09 | 9.72 | |
T5 | 1.44 | 1.10 | 10.01 | 1.45 | 1.10 | 10.13 | 1.43 | 1.08 | 9.81 | ||
W7-OW | T1 | 1.32 | 1.02 | 8.16 | 1.32 | 1.02 | 8.29 | 1.30 | 0.99 | 7.93 | |
T5 | 1.30 | 1.00 | 8.19 | 1.31 | 1.00 | 8.28 | 1.29 | 0.98 | 8.01 | ||
W22-FW | T1 | 3.82 | 2.30 | 62.75 | 3.83 | 2.28 | 63.41 | 3.76 | 2.22 | 60.64 | |
T5 | 3.78 | 2.24 | 62.51 | 3.80 | 2.24 | 62.82 | 3.76 | 2.20 | 60.75 | ||
W22-OW | T1 | 2.00 | 1.42 | 16.48 | 2.03 | 1.43 | 17.35 | 2.03 | 1.42 | 17.30 | |
T5 | 2.00 | 1.40 | 16.90 | 2.03 | 1.42 | 17.65 | 2.03 | 1.42 | 17.65 | ||
D2 | W0 | T1 | 1.67 | 1.30 | 13.13 | 1.66 | 1.29 | 13.30 | 1.63 | 1.25 | 12.70 |
T5 | 1.64 | 1.27 | 13.17 | 1.65 | 1.27 | 13.28 | 1.62 | 1.24 | 12.83 | ||
W7-FW | T1 | 1.80 | 1.39 | 15.10 | 1.79 | 1.38 | 15.30 | 1.76 | 1.34 | 14.61 | |
T5 | 1.77 | 1.36 | 15.15 | 1.78 | 1.36 | 15.27 | 1.75 | 1.33 | 14.75 | ||
W7-OW | T1 | 1.67 | 1.30 | 13.13 | 1.67 | 1.29 | 13.29 | 1.64 | 1.25 | 12.69 | |
T5 | 1.63 | 1.27 | 13.17 | 1.65 | 1.27 | 13.27 | 1.63 | 1.24 | 12.82 | ||
W22-FW | T1 | 4.15 | 3.15 | 78.44 | 4.14 | 3.12 | 79.26 | 4.05 | 3.03 | 75.53 | |
T5 | 4.09 | 3.07 | 78.65 | 4.09 | 3.06 | 78.99 | 4.03 | 3.00 | 76.15 | ||
W22-OW | T1 | 1.73 | 1.23 | 11.70 | 1.74 | 1.22 | 11.79 | 1.73 | 1.19 | 11.22 | |
T5 | 1.71 | 1.21 | 11.72 | 1.72 | 1.20 | 11.78 | 1.71 | 1.18 | 11.35 | ||
D3 | W0 | T1 | 1.83 | 1.42 | 15.77 | 1.82 | 1.41 | 15.95 | 1.78 | 1.37 | 15.22 |
T5 | 1.80 | 1.39 | 15.82 | 1.81 | 1.39 | 15.93 | 1.78 | 1.36 | 15.38 | ||
W7-FW | T1 | 1.95 | 1.51 | 17.74 | 1.94 | 1.49 | 17.94 | 1.90 | 1.45 | 17.12 | |
T5 | 1.92 | 1.47 | 17.80 | 1.92 | 1.47 | 17.92 | 1.90 | 1.44 | 17.30 | ||
W7-OW | T1 | 1.83 | 1.42 | 15.76 | 1.83 | 1.41 | 15.94 | 1.79 | 1.37 | 15.20 | |
T5 | 1.80 | 1.39 | 15.82 | 1.81 | 1.39 | 15.92 | 1.79 | 1.36 | 15.37 | ||
W22-FW | T1 | 4.24 | 3.23 | 82.18 | 4.23 | 3.19 | 83.02 | 4.14 | 3.10 | 79.09 | |
T5 | 4.18 | 3.15 | 82.45 | 4.19 | 3.14 | 82.76 | 4.13 | 3.08 | 79.76 | ||
W22-OW | T1 | 1.83 | 1.32 | 13.25 | 1.84 | 1.31 | 13.38 | 1.82 | 1.27 | 12.72 | |
T5 | 1.80 | 1.29 | 13.29 | 1.82 | 1.29 | 13.36 | 1.81 | 1.26 | 12.85 |
CS3 | P3 | P4 | P5 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Hs | Hsw | Pw | Hs | Hsw | Pw | Hs | Hsw | Pw | |||
m | m | kW/m | m | m | kW/m | m | m | kW/m | |||
D1 | W0 | T1 | 2.44 | 2.31 | 32.75 | 2.41 | 2.27 | 33.29 | 2.33 | 2.19 | 31.57 |
T5 | 2.39 | 2.25 | 33.69 | 2.37 | 2.23 | 34.09 | 2.32 | 2.17 | 32.70 | ||
W7-FW | T1 | 2.53 | 2.38 | 34.75 | 2.49 | 2.34 | 35.33 | 2.41 | 2.26 | 33.51 | |
T5 | 2.47 | 2.32 | 35.75 | 2.45 | 2.30 | 36.17 | 2.39 | 2.24 | 34.70 | ||
W7-OW | T1 | 2.47 | 2.33 | 33.33 | 2.44 | 2.29 | 33.87 | 2.36 | 2.21 | 32.11 | |
T5 | 2.42 | 2.27 | 34.29 | 2.40 | 2.25 | 34.68 | 2.34 | 2.19 | 33.26 | ||
W22-FW | T1 | 4.54 | 4.21 | 109.68 | 4.48 | 4.14 | 111.41 | 4.33 | 3.99 | 105.34 | |
T5 | 4.44 | 4.10 | 112.73 | 4.40 | 4.06 | 113.60 | 4.29 | 3.95 | 108.73 | ||
W22-OW | T1 | 3.01 | 2.75 | 46.59 | 2.97 | 2.70 | 47.22 | 2.89 | 2.62 | 44.76 | |
T5 | 2.96 | 2.69 | 47.96 | 2.93 | 2.66 | 48.35 | 2.87 | 2.59 | 46.38 | ||
D2 | W0 | T1 | 3.14 | 2.97 | 54.08 | 3.10 | 2.92 | 54.76 | 3.00 | 2.81 | 51.82 |
T5 | 3.07 | 2.90 | 55.63 | 3.05 | 2.86 | 56.09 | 2.98 | 2.79 | 53.70 | ||
W7-FW | T1 | 3.19 | 3.01 | 55.54 | 3.14 | 2.95 | 56.25 | 3.04 | 2.85 | 53.23 | |
T5 | 3.12 | 2.93 | 57.13 | 3.09 | 2.90 | 57.61 | 3.02 | 2.83 | 55.15 | ||
W7-OW | T1 | 3.19 | 3.01 | 55.52 | 3.14 | 2.95 | 56.22 | 3.04 | 2.85 | 53.20 | |
T5 | 3.12 | 2.93 | 57.11 | 3.09 | 2.90 | 57.58 | 3.02 | 2.83 | 55.13 | ||
W22-FW | T1 | 5.06 | 4.61 | 133.41 | 5.03 | 4.56 | 136.70 | 4.88 | 4.40 | 129.46 | |
T5 | 4.99 | 4.52 | 138.28 | 4.95 | 4.48 | 139.18 | 4.84 | 4.37 | 133.25 | ||
W22-OW | T1 | 3.24 | 2.99 | 54.63 | 3.20 | 2.93 | 55.21 | 3.10 | 2.83 | 52.16 | |
T5 | 3.18 | 2.91 | 56.14 | 3.16 | 2.88 | 56.52 | 3.09 | 2.81 | 54.04 | ||
D3 | W0 | T1 | 3.55 | 3.36 | 69.04 | 3.50 | 3.29 | 69.91 | 3.39 | 3.18 | 66.08 |
T5 | 3.47 | 3.27 | 70.98 | 3.44 | 3.23 | 71.49 | 3.36 | 3.15 | 68.42 | ||
W7-FW | T1 | 3.60 | 3.40 | 70.71 | 3.55 | 3.33 | 71.59 | 3.43 | 3.22 | 67.67 | |
T5 | 3.52 | 3.31 | 72.69 | 3.49 | 3.27 | 73.21 | 3.41 | 3.19 | 70.06 | ||
W7-OW | T1 | 3.56 | 3.36 | 69.03 | 3.50 | 3.29 | 69.89 | 3.39 | 3.18 | 66.06 | |
T5 | 3.48 | 3.27 | 70.96 | 3.45 | 3.23 | 71.47 | 3.37 | 3.15 | 68.40 | ||
W22-FW | T1 | 5.27 | 4.81 | 145.20 | 5.27 | 4.78 | 150.01 | 5.11 | 4.62 | 142.18 | |
T5 | 5.23 | 4.74 | 152.12 | 5.19 | 4.70 | 153.03 | 5.08 | 4.58 | 146.51 | ||
W22-OW | T1 | 3.57 | 3.31 | 66.78 | 3.53 | 3.25 | 67.54 | 3.43 | 3.13 | 63.75 | |
T5 | 3.49 | 3.22 | 68.62 | 3.47 | 3.19 | 69.07 | 3.39 | 3.10 | 66.03 |
CS3 | P3 | P4 | P5 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Hs | Hsw | Pw | Hs | Hsw | Pw | Hs | Hsw | Pw | |||
m | m | kW/m | m | m | kW/m | m | m | kW/m | |||
D1 | W0 | T1 | 4.07 | 3.94 | 94.21 | 4.01 | 3.87 | 95.84 | 3.86 | 3.72 | 90.59 |
T5 | 3.97 | 3.84 | 97.64 | 3.93 | 3.80 | 98.71 | 3.83 | 3.69 | 94.45 | ||
W7-FW | T1 | 4.08 | 3.94 | 94.23 | 4.01 | 3.87 | 95.86 | 3.87 | 3.72 | 90.61 | |
T5 | 3.98 | 3.84 | 97.66 | 3.94 | 3.80 | 98.73 | 3.84 | 3.69 | 94.46 | ||
W7-OW | T1 | 4.07 | 3.93 | 93.79 | 4.00 | 3.86 | 95.38 | 3.86 | 3.72 | 90.14 | |
T5 | 3.97 | 3.83 | 97.20 | 3.93 | 3.79 | 98.24 | 3.83 | 3.68 | 93.98 | ||
W22-FW | T1 | 5.30 | 5.07 | 156.25 | 5.27 | 5.03 | 162.48 | 5.09 | 4.84 | 153.65 | |
T5 | 5.24 | 5.00 | 166.23 | 5.18 | 4.94 | 167.84 | 5.04 | 4.80 | 160.26 | ||
W22-OW | T1 | 4.27 | 4.08 | 100.59 | 4.20 | 3.99 | 102.07 | 4.06 | 3.85 | 96.26 | |
T5 | 4.18 | 3.97 | 104.26 | 4.13 | 3.92 | 105.08 | 4.03 | 3.81 | 100.34 | ||
D2 | W0 | T1 | 5.06 | 4.90 | 145.29 | 5.00 | 4.83 | 149.32 | 4.83 | 4.65 | 140.98 |
T5 | 4.98 | 4.81 | 152.91 | 4.92 | 4.75 | 154.30 | 4.79 | 4.61 | 147.30 | ||
W7-FW | T1 | 5.05 | 4.88 | 144.25 | 4.99 | 4.81 | 148.18 | 4.81 | 4.64 | 139.90 | |
T5 | 4.96 | 4.79 | 151.76 | 4.91 | 4.73 | 153.13 | 4.78 | 4.60 | 146.17 | ||
W7-OW | T1 | 5.06 | 4.90 | 144.76 | 5.00 | 4.82 | 148.73 | 4.82 | 4.65 | 140.42 | |
T5 | 5.00 | 4.80 | 152.33 | 4.92 | 4.74 | 153.70 | 4.79 | 4.61 | 146.72 | ||
W22-FW | T1 | 5.80 | 5.57 | 188.31 | 5.88 | 5.62 | 202.92 | 5.70 | 5.44 | 193.22 | |
T5 | 5.88 | 5.63 | 209.82 | 5.82 | 5.56 | 212.07 | 5.66 | 5.40 | 202.40 | ||
W22-OW | T1 | 5.07 | 4.87 | 143.18 | 5.02 | 4.80 | 147.30 | 4.86 | 4.63 | 139.02 | |
T5 | 5.00 | 4.78 | 150.93 | 4.95 | 4.72 | 152.22 | 4.82 | 4.59 | 145.24 | ||
D3 | W0 | T1 | 5.51 | 5.34 | 172.14 | 5.50 | 5.32 | 180.55 | 5.32 | 5.13 | 170.96 |
T5 | 5.49 | 5.30 | 185.7 | 5.43 | 5.24 | 187.44 | 5.29 | 5.09 | 178.93 | ||
W7-FW | T1 | 5.51 | 5.33 | 171.81 | 5.50 | 5.31 | 180.28 | 5.32 | 5.13 | 170.79 | |
T5 | 5.49 | 5.30 | 185.67 | 5.43 | 5.24 | 187.41 | 5.29 | 5.09 | 178.91 | ||
W7-OW | T1 | 5.52 | 5.35 | 172.72 | 5.52 | 5.33 | 181.39 | 5.34 | 5.14 | 171.88 | |
T5 | 5.51 | 5.32 | 186.87 | 5.45 | 5.25 | 188.63 | 5.31 | 5.11 | 180.08 | ||
W22-FW | T1 | 5.92 | 5.70 | 196.67 | 6.04 | 5.79 | 214.67 | 5.87 | 5.61 | 205.16 | |
T5 | 6.07 | 5.81 | 223.35 | 6.01 | 5.74 | 226.15 | 5.85 | 5.58 | 215.77 | ||
W22-OW | T1 | 5.50 | 5.30 | 169.33 | 5.51 | 5.28 | 178.00 | 5.34 | 5.10 | 168.61 | |
T5 | 5.50 | 5.28 | 183.41 | 5.45 | 5.21 | 185.08 | 5.31 | 5.06 | 176.60 |
© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).
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Silva, D.; Rusu, E.; Guedes Soares, C. High-Resolution Wave Energy Assessment in Shallow Water Accounting for Tides. Energies 2016, 9, 761. https://doi.org/10.3390/en9090761
Silva D, Rusu E, Guedes Soares C. High-Resolution Wave Energy Assessment in Shallow Water Accounting for Tides. Energies. 2016; 9(9):761. https://doi.org/10.3390/en9090761
Chicago/Turabian StyleSilva, Dina, Eugen Rusu, and Carlos Guedes Soares. 2016. "High-Resolution Wave Energy Assessment in Shallow Water Accounting for Tides" Energies 9, no. 9: 761. https://doi.org/10.3390/en9090761