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Contents

Preface

1 Description of random seas

1.1 Stochastic concept as applied to ocean waves

1.1.1 Introduction

1.1.2 Ocean waves as a Gaussian random process

1.1.3 Random seas

1.2 Mathematical presentation of random waves

1.3 Stochastic prediction of wave characteristics

2 Spectral analysis

2.1 Spectral analysis of random waves

2.1.1 Fundamentals of stochastic processes

2.1.2 Auto-correlation function

2.1.3 Spectral density function (spectrum)

2.1.4 Wiener-Khintchine theorem

2.1.5 Spectral analysis of two wave records

2.1.6 Wave-number spectrum

2.1.7 Wave velocity and acceleration spectra

2.2 Characteristics of wave spectra

2.3 Wave spectral formulations

2.3.1 Pierson-Moskowitz spectrum

2.3.2 Two-parameter spectrum

2.3.3 Spectral formulation as a function of

2.3.4 Six-parameter spectrum

2.3.5 JONSWAP spectrum

2.3.6 TMA spectrum

2.4 Modification of wave spectrum for moving systems

2.5 Higher-order spectral analysis

3 Wave amplitude and height

3.1 Introduction

3.2 Probability distribution of amplitudes with narrow-band spectrum

3.2.1 Derivation of probability density function

3.2.2 Wave envelope process

3.3 Probability distribution of wave maxima with nonnarrow- band spectrum

3.4 Joint distribution of two wave amplitudes

3.5 Probability distribution of peak-to-trough excursions (wave height)

3.6 Significant wave height

3.7 Probability distribution of half-cycle excursions

3.8 Long-term wave height distribution

3.9 Statistical analysis of amplitude and height from wave records

3.9.1 Introduction

3.9.2 Maximum likelihood estimation

3.9.3 Estimation of Rayleigh distribution parameter from a small number of observations

3.9.4 Goodness-of-fit tests

4 Wave height and associated period

4.1 Introduction

4.2 Joint probability distribution of wave height and period

4.3 Joint probability distribution of positive maxima and time interval

4.4 Probability distribution of wave period

4.5 Joint probability distribution of wave height and direction of wave energy travel

5 Sea severity

5.1 Statistical presentation of sea severity

5.1.1 Probability distribution of significant wave height

5.1.2 Joint probability distribution of significant wave height and period

5.1.3 Time series analysis of sea state data

5.2 Hurricane-associated seas

5.2.1 Introduction

5.2.2 Sea severity measured during hurricanes

5.2.3 Wave spectra and wave height in hurricane-generated seas

6 Estimation of extreme wave height and sea state

6.1 Basic concept of extreme values

6.2 Probable and design extreme wave height

6.3 Estimation of extreme wave height and sea state from data

6.4 Extreme wave height in a non-stationary sea state

6.5 Asymptotic distributions of largest waves and sea states

6.5.1 Type I asymptotic extreme value distribution

6.5.2 Type III asymptotic extreme value distribution

7 Directional characteristics of random seas

7.1 Introduction

7.2 Principle of evaluation of directional wave spectra

7.2.1 Wave probe array

7.2.2 Floating buoys

7.2.3 Pressure and current meters

7.3 Analysis of directional energy spreading function

7.4 Estimation of directional energy spreading from data

7.4.1 Maximum likelihood method

7.4.2 Maximum entropy method

7.4.3 Application of a Bayesian method

7.5 Formulation of the wave energy spreading function

8 Special wave events

8.1 Breaking waves

8.1.1 Wave breaking criteria

8.1.2 Probability of occurrence of wave breaking

8.1.3 Energy loss resulting from wave breaking

8.2 Group waves

8.2.1 Introduction

8.2.2 Statistical properties through the envelope process approach

8.2.3 Statistical properties through the Markov chain approach

8.3 Freak waves

9 Non-Gaussian waves (waves in finite water depth)

9.1 Introduction

9.2 Probability distribution of non-Gaussian waves

9.2.1 Gram-Charlier series distribution

9.2.2 Distribution based on Stokes waves

9.2.3 Distribution based on the concept of nonlinear system

9.3 Probability distribution of peaks and troughs

9.4 Transformation from Gaussian to non-Gaussian waves

Appendix A. Fundamentals of probability theory

Appendix B. Fundamentals of stochastic process theory

Appendix C. Fourier transform and Hilbert transform

References

Index