Chapter ll-1. Water Wave Mechanics
Introduction
Regular Waves
Definition of wave parameters. - Part-II-Chap10010
Linear wave theory.
Wave celerity, length, and period.
Wave celerity, length, and period. (cont)
Table ll-1-1. Classification of Water Waves
Some useful functions.
EXAMPLE PROBLEM II-1-1
EXAMPLE PROBLEM II-1-1 (cont)
Local fluid velocities and accelerations.
Figure ll-1-2. Local fluid velocities and accelerations
Figure II-1-3. Profiles of particle velocity and acceleration by Airy theory in relation to the surface elevation
EXAMPLE PROBLEM II-1-2
EXAMPLE PROBLEM II-1-2 (cont)
Figure II-1-4. Water particle displacements from mean position for shallow-water and deepwater waves
Water particle displacements.
EXAMPLE PROBLEM II-1-3
EXAMPLE PROBLEM II-1-3 (cont)
Subsurface pressure.
Group velocity.
Figure II-1-5. Variation of wave parameters with d/L0 (Dean and Dalrymple 1991)
EXAMPLE PROBLEM II-1-4
Figure II-1-6. Characteristics of a wave group formed by the addition of sinusoids with different periods
Wave energy and power.
Figure II-1-7. Variation of the ratios of group and phase velocities to deepwater phase speed using linear theory (Sarpkaya and Isaacson 1981)
Wave energy and power. (cont)
Summary of linear wave theory.
Figure II-1-8. Variation of shoaling coefficient with wave steepness (Sakai and Battjes 1980)
Figure II-1-9. Summary of linear (Airy) wave theory - wave characteristics
Stokes finite-amplitude wave theory.
Stokes finite-amplitude wave theory. (cont)
Figure II-1-10. Wave profile shape of different progressive gravity waves
Maximum wave steepness.
Other wave theories.
Cnoidal wave theory.
Cnoidal wave theory. (cont)
Cnoidal wave theory. (cont)
Figure II-1-12. Normalized surface profile of the cnoidal wave for higher values of k2 and X/L (Wiegel 1960)
Figure II-1-13. k2 versus L2H/d3, and k2 versus T%g &d and H/d (Wiegel 1960)
Figure II-1-14. Relationship among L2H/d3 and the square of the elliptic modulus (k2), yc/H, yt/H, and K(k) (Wiegel 1960)
Figure II-1-15. Relationships among T%g &d , L2H/d3, and H/d (Wiegel 1960)
Figure II-1-16. Relationship between cnoidal wave velocity and L2H/d3 (Wiegel 1960)
EXAMPLE PROBLEM II-1-5
EXAMPLE PROBLEM II-1-5 (cont)
EXAMPLE PROBLEM II-1-5 (cont)
Solitary wave theory.
Figure II-1-17. Functions M and N in solitary wave theory (Munk 1949)
Table ll-1-2. Boundary Value Problem of Water Wave Theories (Dean 1968)
Fourier approximation -- Fenton's theory.
Fourier approximation -- Fenton's theory. (cont)
Fourier approximation -- Fenton's theory. (cont) - Part-II-Chap10059
Fourier approximation -- Fenton's theory. (cont) - Part-II-Chap10060
Figure II-1-18. Surface elevation, horizontal velocity, and pressure in 10-m depth (using Fenton's theory in ACES)
Wave breaking.
Figure II-1-19. Influence of a uniform current on the maximum wave height (Dalrymple and Dean 1975)
Figure II-1-20. Ranges of suitability of various wave theories (Le Mhaut 1976)
Irregular Waves
EXAMPLE PROBLEM II-1-6
Figure II-1-22. Radar image of the sea surface in the entrance to San Francisco Bay
Figure II-1-23. Measured sea surface velocity in the entrance to San Francisco Bay
Figure II-1-24. Representations of an ocean wave
Figure II-1-26. Definition of wave parameters for a random sea state
Wave train (wave-by-wave) analysis.
Definition of wave parameters. - Part-II-Chap10072
A similar approach can be used for the wave period.
Significant wave height.
Short-term random sea state parameters.
Probability distributions for a sea state.
Figure II-1-28. The Gaussian probability density and cumulative probability distribution
Probability distributions for a sea state. (cont)
(b) wave periods with theoretical distributions (Chakrabarti 1987)
Wave height distribution.
Wave period distribution.
Joint distribution of wave heights and periods.
Spectral analysis.
Spectral analysis. (cont)
Figure II-1-31. Surface elevation time series of a regular wave and its spectrum (Briggs et al. 1993)
Figure II-1-32. Surface elevation time series of an irregular wave and its spectrum (Briggs et al. 1993)
Figure II-1-33. A schematic for a two-dimensional wave spectrum E(f,θ)
Figure II-1-34. A directional spectrum and its frequency and direction spectrum (Briggs et al 1993)
Description of wave spectral analysis.
Figure II-1-35. Sketches of wave spectral energy and energy density (Chakrabarti 1987)
Figure II-1-36. Definition of one- and two-side wave spectrum (Chakrabarti 1987)
Figure II-1-37. Energy density and frequency relationship (Chakrabarti 1987)
Figure II-1-38. Comparison of the PM and JONSWAP spectra (Chakrabarti 1987)
Relationships among H1/3, Hs, and Hm0 in shallow water.
Parametric spectrum models.
Figure II-1-39. Definition sketch for Ochi-Hubble spectrum (Ochi and Hubble 1976)
Figure II-1-40. Variation of Hs/Hmo as a function of elative depth d and significant steepness (Thompson and Vincent 1985)
Parametric spectrum models. (cont)
Directional spectra.
Directional spectra. (cont)
Wave groups and groupiness factors.
Figure II-1-41. Identification and description of wave groups through ordered statistics (Goda 1976)
Random wave simulation.
Kinematics and dynamics of irregular waves.
References and Bibliography
References and Bibliography (cont)
References and Bibliography (cont) - Part-II-Chap10107
References and Bibliography (cont) - Part-II-Chap10108
References and Bibliography (cont) - Part-II-Chap10109
References and Bibliography (cont) - Part-II-Chap10110
References and Bibliography (cont) - Part-II-Chap10111
References and Bibliography (cont) - Part-II-Chap10112
References and Bibliography (cont) - Part-II-Chap10113
References and Bibliography (cont) - Part-II-Chap10114
References and Bibliography (cont) - Part-II-Chap10115
References and Bibliography (cont) - Part-II-Chap10116
References and Bibliography (cont) - Part-II-Chap10117
References and Bibliography (cont) - Part-II-Chap10118
References and Bibliography (cont) - Part-II-Chap10119
References and Bibliography (cont) - Part-II-Chap10120
References and Bibliography (cont) - Part-II-Chap10121
Definitions of Symbols - Part-II-Chap10122
Definitions of Symbols (cont) - Part-II-Chap10123
Definitions of Symbols (cont) - Part-II-Chap10124
Definitions of Symbols (cont) - Part-II-Chap10125
Definitions of Symbols (cont) - Part-II-Chap10126
Acknowledgments - Part-II-Chap10127
Part-II-Chap1
Introduction
Regular Waves
Definition of wave parameters. - Part-II-Chap10010
Linear wave theory.
Wave celerity, length, and period.
Wave celerity, length, and period. (cont)
Table ll-1-1. Classification of Water Waves
Some useful functions.
EXAMPLE PROBLEM II-1-1
EXAMPLE PROBLEM II-1-1 (cont)
Local fluid velocities and accelerations.
Figure ll-1-2. Local fluid velocities and accelerations
Figure II-1-3. Profiles of particle velocity and acceleration by Airy theory in relation to the surface elevation
EXAMPLE PROBLEM II-1-2
EXAMPLE PROBLEM II-1-2 (cont)
Figure II-1-4. Water particle displacements from mean position for shallow-water and deepwater waves
Water particle displacements.
EXAMPLE PROBLEM II-1-3
EXAMPLE PROBLEM II-1-3 (cont)
Subsurface pressure.
Group velocity.
Figure II-1-5. Variation of wave parameters with d/L0 (Dean and Dalrymple 1991)
EXAMPLE PROBLEM II-1-4
Figure II-1-6. Characteristics of a wave group formed by the addition of sinusoids with different periods
Wave energy and power.
Figure II-1-7. Variation of the ratios of group and phase velocities to deepwater phase speed using linear theory (Sarpkaya and Isaacson 1981)
Wave energy and power. (cont)
Summary of linear wave theory.
Figure II-1-8. Variation of shoaling coefficient with wave steepness (Sakai and Battjes 1980)
Figure II-1-9. Summary of linear (Airy) wave theory - wave characteristics
Stokes finite-amplitude wave theory.
Stokes finite-amplitude wave theory. (cont)
Figure II-1-10. Wave profile shape of different progressive gravity waves
Maximum wave steepness.
Other wave theories.
Cnoidal wave theory.
Cnoidal wave theory. (cont)
Cnoidal wave theory. (cont)
Figure II-1-12. Normalized surface profile of the cnoidal wave for higher values of k2 and X/L (Wiegel 1960)
Figure II-1-13. k2 versus L2H/d3, and k2 versus T%g &d and H/d (Wiegel 1960)
Figure II-1-14. Relationship among L2H/d3 and the square of the elliptic modulus (k2), yc/H, yt/H, and K(k) (Wiegel 1960)
Figure II-1-15. Relationships among T%g &d , L2H/d3, and H/d (Wiegel 1960)
Figure II-1-16. Relationship between cnoidal wave velocity and L2H/d3 (Wiegel 1960)
EXAMPLE PROBLEM II-1-5
EXAMPLE PROBLEM II-1-5 (cont)
EXAMPLE PROBLEM II-1-5 (cont)
Solitary wave theory.
Figure II-1-17. Functions M and N in solitary wave theory (Munk 1949)
Table ll-1-2. Boundary Value Problem of Water Wave Theories (Dean 1968)
Fourier approximation -- Fenton's theory.
Fourier approximation -- Fenton's theory. (cont)
Fourier approximation -- Fenton's theory. (cont) - Part-II-Chap10059
Fourier approximation -- Fenton's theory. (cont) - Part-II-Chap10060
Figure II-1-18. Surface elevation, horizontal velocity, and pressure in 10-m depth (using Fenton's theory in ACES)
Wave breaking.
Figure II-1-19. Influence of a uniform current on the maximum wave height (Dalrymple and Dean 1975)
Figure II-1-20. Ranges of suitability of various wave theories (Le Mhaut 1976)
Irregular Waves
EXAMPLE PROBLEM II-1-6
Figure II-1-22. Radar image of the sea surface in the entrance to San Francisco Bay
Figure II-1-23. Measured sea surface velocity in the entrance to San Francisco Bay
Figure II-1-24. Representations of an ocean wave
Figure II-1-26. Definition of wave parameters for a random sea state
Wave train (wave-by-wave) analysis.
Definition of wave parameters. - Part-II-Chap10072
A similar approach can be used for the wave period.
Significant wave height.
Short-term random sea state parameters.
Probability distributions for a sea state.
Figure II-1-28. The Gaussian probability density and cumulative probability distribution
Probability distributions for a sea state. (cont)
(b) wave periods with theoretical distributions (Chakrabarti 1987)
Wave height distribution.
Wave period distribution.
Joint distribution of wave heights and periods.
Spectral analysis.
Spectral analysis. (cont)
Figure II-1-31. Surface elevation time series of a regular wave and its spectrum (Briggs et al. 1993)
Figure II-1-32. Surface elevation time series of an irregular wave and its spectrum (Briggs et al. 1993)
Figure II-1-33. A schematic for a two-dimensional wave spectrum E(f,θ)
Figure II-1-34. A directional spectrum and its frequency and direction spectrum (Briggs et al 1993)
Description of wave spectral analysis.
Figure II-1-35. Sketches of wave spectral energy and energy density (Chakrabarti 1987)
Figure II-1-36. Definition of one- and two-side wave spectrum (Chakrabarti 1987)
Figure II-1-37. Energy density and frequency relationship (Chakrabarti 1987)
Figure II-1-38. Comparison of the PM and JONSWAP spectra (Chakrabarti 1987)
Relationships among H1/3, Hs, and Hm0 in shallow water.
Parametric spectrum models.
Figure II-1-39. Definition sketch for Ochi-Hubble spectrum (Ochi and Hubble 1976)
Figure II-1-40. Variation of Hs/Hmo as a function of elative depth d and significant steepness (Thompson and Vincent 1985)
Parametric spectrum models. (cont)
Directional spectra.
Directional spectra. (cont)
Wave groups and groupiness factors.
Figure II-1-41. Identification and description of wave groups through ordered statistics (Goda 1976)
Random wave simulation.
Kinematics and dynamics of irregular waves.
References and Bibliography
References and Bibliography (cont)
References and Bibliography (cont) - Part-II-Chap10107
References and Bibliography (cont) - Part-II-Chap10108
References and Bibliography (cont) - Part-II-Chap10109
References and Bibliography (cont) - Part-II-Chap10110
References and Bibliography (cont) - Part-II-Chap10111
References and Bibliography (cont) - Part-II-Chap10112
References and Bibliography (cont) - Part-II-Chap10113
References and Bibliography (cont) - Part-II-Chap10114
References and Bibliography (cont) - Part-II-Chap10115
References and Bibliography (cont) - Part-II-Chap10116
References and Bibliography (cont) - Part-II-Chap10117
References and Bibliography (cont) - Part-II-Chap10118
References and Bibliography (cont) - Part-II-Chap10119
References and Bibliography (cont) - Part-II-Chap10120
References and Bibliography (cont) - Part-II-Chap10121
Definitions of Symbols - Part-II-Chap10122
Definitions of Symbols (cont) - Part-II-Chap10123
Definitions of Symbols (cont) - Part-II-Chap10124
Definitions of Symbols (cont) - Part-II-Chap10125
Definitions of Symbols (cont) - Part-II-Chap10126
Acknowledgments - Part-II-Chap10127
Part-II-Chap1
