Predicting Wind Wave Suppression on Irregular Long Waves
Abstract
:1. Introduction
Incorporation of Wind Wave Suppression into Sin
2. Experimental Set-Up and Data Collection
2.1. Test Facility
2.2. Instrumentation and Data Collection
2.3. Characterizing the Wind Field
3. The Chen and Belcher (2000) Model
3.1. Long Wave-Induced Stress
3.2. Growth Rate of the Long Wave,
4. Methods: Data Analysis
4.1. Experimental Energy Ratio,
4.2. Quantifying the Growth Rate Coefficient and the Atmospheric Pressure Coefficient
5. Results
5.1. CBM Results for the Monochromatic Waves
5.2. CBM Results for Irregular Waves
5.3. The Growth Rate Coefficient and Atmospheric Pressure Coefficient for the Irregular Waves
6. Discussion
6.1. Modifying the CBM for Irregular Long Waves
6.2. Analysis of the Growth Rate Coefficient
7. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Data Statement
Nomenclature
total spectral energy in the wave field | |
wind energy input source term | |
nonlinear interactions source term | |
dissipation source term | |
f | wave frequency |
a | wave amplitude |
aL | long wave amplitude |
k | wavenumber |
kL | long wavenumber |
ak | wave steepness |
aLkL | long wave steepness |
long wave growth rate | |
density of air | |
density of water | |
growth rate coefficient | |
air friction velocity | |
long wave phase speed | |
peak angular frequency | |
long wave angular frequency | |
Total stress in the wind at the water surface | |
long wave-induced stress | |
turbulent stress | |
x | horizontal fetch distance |
g | gravitational acceleration |
wave variance | |
E | energy density |
U | wind speed |
Hs | significant wave height |
γ | JONSWAP gamma |
κ | von Karman constant |
z | vertical elevation above the water surface |
aerodynamic roughness length | |
atmospheric pressure coefficient | |
dimensionless frequency | |
dimensionless fetch | |
long wave spectral density | |
d | water depth |
L | wavelength |
critical layer height | |
matched height (equivalent to ) | |
contribution due to influence of surface shear stress on the inner region due to undulations at water surface | |
contribution due to the influence of surface shear stress on the inner region due to changes in velocity at the water surface | |
contribution due to the variations in pressure in the outer region | |
contribution due to wave-induced surface shear stress due to variations in surface elevation | |
contribution due to wave-induced surface shear stress due to variations in surface velocity | |
hm | height of the middle layer |
li | height of the inner layer |
wind speed at the height of the middle layer | |
wind speed at the height of the inner layer | |
model parameter, | |
n | model coefficient |
relative dependence coefficient | |
energy in wind waves | |
energy in wind waves in the presence of long wave | |
Tp | peak wave period |
fp | peak wave frequency |
ηL | surface elevation record of the long wave |
spectral energy at each frequency, f |
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ID | Hs (m) | Tp (s) | aLkL | U (m/s) |
---|---|---|---|---|
1 | 0.10 | 2.5 | 0.032 | 0, 5.5, 7, 8.5, 10 |
2 | 0.15 | 2.5 | 0.049 | 0, 5.5, 7, 8.5, 10 |
3 | 0.15 | 2.5 | 0.049 | 0, 7, 8.5, 10 |
4 | 0.15 | 2.25 | 0.060 | 0, 5.5, 7, 8.5, 10 |
5 | 0.15 | 2.0 | 0.076 | 0, 5.5, 7, 8.5, 10 |
6 | 0.25 | 2.5 | 0.081 | 0, 7, 8.5, 10 |
7 | 0.15 | 1.75 | 0.099 | 0, 7, 8.5, 10 |
8 | 0.35 | 2.5 | 0.113 | 0, 7, 8.5, 10 |
9 | 0.30 | 2.2 | 0.125 | 0, 7, 8.5, 10 |
10 | 0.40 | 2.5 | 0.130 | 0, 7, 8.5, 10 |
11 | 0.27 | 2.0 | 0.136 | 0, 7, 8.5, 10 |
12M | 0.27 | 2.0 | 0.136 | 0, 5.5, 7, 8.5, 10 |
13M | 0.15 | 2.5 | 0.049 | 0, 5.5, 7, 8.5, 10 |
14M | 0.15 | 1.75 | 0.099 | 0, 5.5, 7, 8.5, 10 |
15M | 0.3 | 1.75 | 0.197 | 0, 5.5, 7, 8.5, 10 |
Wind Only 1 | - | - | - | 5.5 m/s |
Wind Only 2 | - | - | - | 7 m/s |
Wind Only 3 | - | - | - | 8.5 m/s |
Wind Only 4 | - | - | - | 10 m/s |
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Bailey, T.; Ross, L.; Bryant, M.; Bryant, D. Predicting Wind Wave Suppression on Irregular Long Waves. J. Mar. Sci. Eng. 2020, 8, 619. https://doi.org/10.3390/jmse8080619
Bailey T, Ross L, Bryant M, Bryant D. Predicting Wind Wave Suppression on Irregular Long Waves. Journal of Marine Science and Engineering. 2020; 8(8):619. https://doi.org/10.3390/jmse8080619
Chicago/Turabian StyleBailey, Taylor, Lauren Ross, Mary Bryant, and Duncan Bryant. 2020. "Predicting Wind Wave Suppression on Irregular Long Waves" Journal of Marine Science and Engineering 8, no. 8: 619. https://doi.org/10.3390/jmse8080619