1. Chapter 7. Wave Statistics & Spectra
Rayleigh Distribution (Narrow-banded spectrum)
Wave Spectra (P-M & JONSWAP)
FFT & IFFT
Cross Spectra & Directional Wave Spreading
Wave Simulation

2. Ocean (Irregular) Waves Definitions of Zero-Upcrossing & Downcrossing
Root-mean-Square (RMS), Skewness and Kurtosis
Ochi (1998) Ocean Waves

3. Wave Pattern Combining Four Regular Waves
FFT & IFFT – (Inverse) Fast Fourier Transform.
Irregular wave Regular Waves (Frequency Domain Analysis)

4. Ocean Wave Spectra: P-M & JONSWAP Types

5. Pierson-Moskowitz Spectrum
JONSWAP Spectrum

6. JONSWAP Spectra & H1/3 and Tp
Goda (1987)

7. Wave Directionality & Directional Waves
Wave components do not travel in the same direction.
Single Summation Model: Wave components of different freq. travel at different directions but at the same freq., they travel at the same direction.
Double Summation: At the same freq. wave components travel at different directions. (Energy spreading).

8. Actual Versus Design Seas

9. Discretization of a continuous wave spectrum

10. Simulation of Irregular waves
Uni-directional waves (long-crested)

11. Directional wave energy density spectrum

12. Directional Waves:Double Summation Model
The above directional waves may form a partial standing wave pattern and consequently the related resultant wave amplitude at this frequency is no longer uniform in the x-y plane.

13. Directional Waves: Single Summation Model
To avoid non-uniformity, it was suggested that at each discrete frequency the wave component is in one direction although the directions of waves at different frequencies are different. Hence, inner summation be eliminated and the representation of irregular wave elevation reduces to,