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[Pages:35]Waves

3. Statistics and Irregular Waves

Statistics and Irregular Waves

Real wave fields are not regular Combination of many periods, heights, directions Design and simulation require realistic wave statistics:

probability distribution of heights energy spectrum of frequencies (and directions)

Statistics and Irregular Waves

3. STATISTICS AND IRREGULAR WAVES 3.1 Measures of height and period 3.2 Probability distribution of wave heights 3.3 Wave spectra 3.4 Reconstructing a wave field 3.5 Prediction of wave climate

Measures of Wave Height

max Largest wave height in the sample av Mean wave height

rms Root-mean-square wave height

13 Average of the highest /3 waves 0 Estimate based on the rms surface elevation Significant wave height

max = ma x() 1

av =

rms =

1

2

1 /3 13 = /3

1

0 = 4 2 12 Either 13 or 0

Measures of Wave Period

Significant wave period (average of highest /3 waves)

Peak period (from peak frequency of energy spectrum)

Energy period (period of a regular wave with same significant wave height and power density; used in wave-energy prediction; derived from energy spectrum)

Mean zero up-crossing period

Statistics and Irregular Waves

3. STATISTICS AND IRREGULAR WAVES 3.1 Measures of height and period 3.2 Probability distribution of wave heights 3.3 Wave spectra 3.4 Reconstructing a wave field 3.5 Prediction of wave climate

Probability Distribution of Wave Heights

For a narrow-banded frequency spectrum the Rayleigh probability distribution is appropriate:

height > = exp - (rms)2

Cumulative distribution function: = height <

= 1 - e- rms 2

Probability density function:

d = d

=

2 r2ms

e-

rms

2

Rayleigh Distribution

=

2 r2ms

e-

rms

2

Single parameter: rms

r2ms 2

= 2 d

0

av = d

0

av = 2 rms = 0.886 rms 13 = 1.416 rms 110 = 1.800 rms 1100 = 2.359 rms

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