OCE421 Marine Structure Designs Lecture

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OCE421 Marine Structure DesignsLecture 8
(wave spectrum)
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Reading

• Coastal Engineering Manual Part II, Chapter 1,
  pp. 77-93.

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Spectral Analysis

• Wave-by-wave analysis define individual waves
• Spectral analysis describe the distribution of
  the variance wrt the
• frequency of the signal.

• wave energy spectrum (a discrete function)
• wave power spectral density function (wave
  spectrum)

(psd function is continuous in frequency space)
It tells what frequency ranges have significant
energy content
Particular useful for structural dynamic
design
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Wave Spectral Energy vs. Wave Power Spectral
Density
(continuous density function)
(discrete mass function)
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Wave Spectrum one-sided psd
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Spectral Moments and Hm0
Spectral moments
m0 zeroth moment of the wave spectrum
P-M spectrum and zero up-crossing technique for
wave decomposition
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Pierson-Moskowitz Spectrum
a 0.0081 (Phillips constant) U wind speed
measured at an elevation of 19.5 m
This spectrum is independent of the fetch and
duration of the wind and thus is only for fully
developed sea.
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P-M and JONSWAP Spectra
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JONSWAP Spectrum
peak shape factor
1.6 lt g lt 6 ave. g 3.3
JONSWAP spectrum was developed for fetch limited
condition
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Matlab function spectrum
spectrum Power spectrum estimate of one
or two data sequences. Pspectrum(X,NFFT,NOVE
RLAP,WIND) estimates the Power Spectral Density
of signal vector X using Welch's averaged
periodogram method. The signal X is divided
into overlapping sections, each of which is
detrended and windowed by the WINDOW
parameter, then zero padded to length NFFT. The
magnitude squared of the length NFFT DFTs of
the sections are averaged to form Pxx. P is
a two column matrix P Pxx Pxxc the second
column Pxxc is the 95 confidence interval.
The number of rows of P is NFFT/21 for NFFT
even, (NFFT1)/2 for NFFT odd, or NFFT if the
signal X is comp- lex. If you specify a
scalar for WINDOW, a Hanning window of that
length is used.
The default values for the parameters are NFFT
256 (or length(X), whichever is smaller),
NOVERLAP 0, WINDOW HANNING(NFFT).
(Thorough analysis should be covered in OCE561)
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Matlab Code Wave Spectrum
pspectrum(eta,nfft) psdp(,1) df1/(nfftdt)
f0df(nfft/2)df psdpsd/(nfft/2df) unit
conversion plot(f,psd) areatrapz(psd)df
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SPM deep water wave prediction
Using a parametric model based on JONSWAP
(rather than the SMB method)
(unit sensitive m/s)
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SPM shallow water wave prediction
based on limited data set, should be used with
caution.
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Case Study Shallow water wave growth
d average depth along the path F the
largest distance between lands (across waterway)
UA determined based on wind rose and wind
speed contours
on a map for a given return period
Thoms fastest-mile wind speed (omni-directional
wind)
From wind rose info (a year), NW winds counts 16
Chosen design wind NW winds with TR 100 years
How can we calculate it?
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Determine Directional Design Wind
NW-direction
Omni-direction
U (mph) TR (years)
poe (yearly)
adjusted poe (yearly)
1/ 2 16 1/50 16 1/100 16
0.08 0.0032 0.0016
2 50 100
1/ 2 1/50 1/100
55 90 100
From wind rose info (a year), NW winds counts 16
Plot U vs. adjusted poe on a Fisher-Tippett Type
II paper
From the regression line, determine the
corresponding U with poe0.01 (i.e., TR 100
years)
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Probability Paper
Omni-
NW