Chapter 7. Wave Statistics

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Chapter 7. Wave Statistics Spectra

• Wave Statistics
• Rayleigh Distribution (Narrow-banded spectrum)
• Wave Spectra (P-M JONSWAP)
• FFT IFFT
• Cross Spectra Directional Wave Spreading
• Wave Simulation

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Ocean (Irregular) Waves Definitions of
Zero-Upcrossing Downcrossing
Root-mean-Square (RMS), Skewness and Kurtosis
Ochi (1998) Ocean Waves
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Wave Pattern Combining Four Regular Waves
FFT IFFT (Inverse) Fast Fourier Transform.
Irregular wave Regular Waves
(Frequency Domain Analysis)
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Ocean Wave Spectra P-M JONSWAP Types
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Pierson-Moskowitz Spectrum
JONSWAP Spectrum
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JONSWAP Spectra H1/3 and Tp
Goda (1987)
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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).

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Actual Versus Design Seas
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Discretization of a continuous wave spectrum
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• Simulation of Irregular waves
• Uni-directional waves (long-crested)

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Directional wave energy density spectrum
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Directional WavesDouble 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.
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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,