NRCEST

Wave statics

Chang Hsien Kuo

國立交通大學土木工程學系中華民國 102年 3月 28日

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Reference

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methods

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Significant wave representation

Individual wave H1>H2>H3… Brestchneider (1968)

H1/3: 前 1/3 大之個別波波高平均值 (significant wave, 示性波 )T1/3: 相對於大小排序波高之週期平均值Neir et al. (2003)T1/3:T1>T2>T3… 週期仿照示性波高前 1/3 大之平均值週期

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Statistical properties

Rayleigh distribution

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Representative wave height

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Representative wave height

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Statistical theory for irregular waves

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Rayleigh distribution for wave height

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Rayleigh distribution for wave height

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Rayleigh distribution for wave height

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Rayleigh distribution for wave height

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1/Nth Waves for Rayleigh distribution

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1/Nth Waves for Rayleigh distribution

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1/Nth Waves for Rayleigh distribution

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1/Nth Waves for other distributions

表 2.3-1 計算 Weibull 及 Gauss 分布示性波之理論統計公式

分布函數 計算示性波公式

Weibull 分布 )3ln,1

(3

])3[(ln1

Normal 分布

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3

2

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2 p

xx

Erfcep

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Regular wave

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Irregular wave

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Frequency spectrum of irregular waves

Fourier transform (Fast FT)

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Frequency spectrum of irregular waves

Brestchneider (1968)

Goda (1988)

Wallops spectrum by Hwung et al . (1981)

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Frequency spectra of irregular waves

JONSWAP (1973)

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Directional Spectrum of sea waves

G(θ) : directional distribution of energy spectrum

S(f) : energy (power) spectrum

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Directional Spectra of sea waves

Mitsuyasu (1975)

Smax: Spreading parameter

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Directional Spectra of sea waves

Smax=20

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Relationship between spectra and wave height

Zeroth moment of spectrum

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Relationship between spectra and wave height

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Relationship between spectra and wave period

Zeroth and second moments of spectrum

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Spectra of sea waves-Example I

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Example I

Directional spectrum

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Example-I

sample average of sixteen directional spectra

directional spectra of in-site buoy measurements

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Example-I

directional spreading function

Power spectrum

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Example-II

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Example-II

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Example-II