404
CHAPTER 7. LABORATORY WAVE GENERATION
approach to irregular wave synthesis. But they also warned that the method
could produce laboratory waves that would be unrealistic in nature.
Mase, Kita, and Iwagaki (1983) employed the SIWEH method to investigate statistical parameters of simulated irregular wave trains having the
same spectral shape but different wave grouping characteristics. They also
examined field data wave grouping in terms of the grouping factor given in
Eqn. 7.192. Mase, et al., reported that sea surface elevations were nearly
Gaussian-distributed for cases with groupiness factors greater than 0.5 and
that phases were uniformly distributed on the average. However, this was
not true for short records with groupiness factors greater than 0.7. Waves
generated in the wave flume using a linear transfer function successfully
maintained the different types of wave grouping for values of deep-water
wave steepness8 less than 0.03. As wave steepness increased beyond 0.03,
the differences in wave grouping gradually disappeared.
8 Wave steepness was defined as Hs/Lp where Hs is significant wave height and Lp is
the wavelength associated with the spectral peak.
7.6.3 First-Order Irregular Wave Generation
In first-order wavemaker theory the wave amplitude (a) is linearly related
to the wave board stroke amplitude (e) by the expression
a = e •
(7.193)
where e = So/"! and So is the wave board stroke. The transfer function,
was given previously by Eqn. 7.134 as
4smhfc/i
....
(1 —coshfc/i)
mi - ~ , a, .----- aw sinhkh + -——----sinh 2kh + 2kh
k(h + Z)
(7.194)
which reduces to the expression for a piston-type wave board when / —> oo
and for a wave board hinged on the bottom when 1 = 0.
If we consider a sea state comprised of a large number of linearly superimposed regular waves, then the amplitude of the component at each
discrete frequency can be transferred into an equivalent wave board amplitude using Eqn. 7.193. By squaring both sides of Eqn. 7.193 and dividing
by two, we get a linear relationship between sea surface spectra and wave
board spectra, viz.,
or
g2
y = T
— (l^ln) SwbÇ^n)
(7.196)
CHAPTER 7. LABORATORY WAVE GENERATION
approach to irregular wave synthesis. But they also warned that the method
could produce laboratory waves that would be unrealistic in nature.
Mase, Kita, and Iwagaki (1983) employed the SIWEH method to investigate statistical parameters of simulated irregular wave trains having the
same spectral shape but different wave grouping characteristics. They also
examined field data wave grouping in terms of the grouping factor given in
Eqn. 7.192. Mase, et al., reported that sea surface elevations were nearly
Gaussian-distributed for cases with groupiness factors greater than 0.5 and
that phases were uniformly distributed on the average. However, this was
not true for short records with groupiness factors greater than 0.7. Waves
generated in the wave flume using a linear transfer function successfully
maintained the different types of wave grouping for values of deep-water
wave steepness8 less than 0.03. As wave steepness increased beyond 0.03,
the differences in wave grouping gradually disappeared.
8 Wave steepness was defined as Hs/Lp where Hs is significant wave height and Lp is
the wavelength associated with the spectral peak.
7.6.3 First-Order Irregular Wave Generation
In first-order wavemaker theory the wave amplitude (a) is linearly related
to the wave board stroke amplitude (e) by the expression
a = e •
(7.193)
where e = So/"! and So is the wave board stroke. The transfer function,
was given previously by Eqn. 7.134 as
4smhfc/i
....
(1 —coshfc/i)
mi - ~ , a, .----- aw sinhkh + -——----sinh 2kh + 2kh
k(h + Z)
(7.194)
which reduces to the expression for a piston-type wave board when / —> oo
and for a wave board hinged on the bottom when 1 = 0.
If we consider a sea state comprised of a large number of linearly superimposed regular waves, then the amplitude of the component at each
discrete frequency can be transferred into an equivalent wave board amplitude using Eqn. 7.193. By squaring both sides of Eqn. 7.193 and dividing
by two, we get a linear relationship between sea surface spectra and wave
board spectra, viz.,
or
g2
y = T
— (l^ln) SwbÇ^n)
(7.196)