398
CHAPTER 7. LABORATORY WAVE GENERATI01
Hudspeth, Nath, and Sollitt 1985) is one commonly used method for syn
thesizing partially deterministic irregular wave time series realizations. Th
DSA model assumes the sea surface fluctuations at a point can be repre
sented by Gaussian white noise given as
TV/2
7/(0 = y + 52 Cn COS(WnZ - n)
(7.186
where once again the discrete radian frequencies,
= 27r/n, are dense!
spaced along the frequency interval 0 < f < oo, and c0/2 is the mean. Th
discrete phases, 0n, are assumed to be uniformly distributed over the rang
0 < 9n < 2tt, and the Fourier amplitudes, cn, are determined as
cn — y/w(wny2ir&f
(7.187
where w(u?n) is a discrete value of the continuous one-sided power spectra
density function.
Application of the DSA synthesis method consists of the following steps
1. Generate a sequence of random numbers uniformly distributed over the interval between zero and one. Multiply these random numbers by 2tt to obtain a sequence
of uniformly distributed random phases over the interval
0 < 0n < 2tt.
2. Specify the values of cn in terms of the discrete values of
the target spectrum, SVJ1, i.e.,
(7.188)
3. Inverse Fourier transform the amplitudes and phases using
an FFT algorithm to obtain a discrete time series realization.
The DSA method is spectrally deterministic because the amplitude spec
trum is specified in terms of the Fourier amplitudes, cn. Therefore, eac]
time series realization constructed with random phases will closely mate]
the target spectrum. This is desirable because it offers easier matching c
the peak spectral frequency and the spectral shape (Funke and Mansan
1987); however, real sea states exhibit variations in spectra between tim
series measurements, so the DSA method is less realistic.
Repeatability can be achieved with the DSA method if a numerics
pseudo-random number generator is used to determine the random phase
CHAPTER 7. LABORATORY WAVE GENERATI01
Hudspeth, Nath, and Sollitt 1985) is one commonly used method for syn
thesizing partially deterministic irregular wave time series realizations. Th
DSA model assumes the sea surface fluctuations at a point can be repre
sented by Gaussian white noise given as
TV/2
7/(0 = y + 52 Cn COS(WnZ - n)
(7.186
where once again the discrete radian frequencies,
= 27r/n, are dense!
spaced along the frequency interval 0 < f < oo, and c0/2 is the mean. Th
discrete phases, 0n, are assumed to be uniformly distributed over the rang
0 < 9n < 2tt, and the Fourier amplitudes, cn, are determined as
cn — y/w(wny2ir&f
(7.187
where w(u?n) is a discrete value of the continuous one-sided power spectra
density function.
Application of the DSA synthesis method consists of the following steps
1. Generate a sequence of random numbers uniformly distributed over the interval between zero and one. Multiply these random numbers by 2tt to obtain a sequence
of uniformly distributed random phases over the interval
0 < 0n < 2tt.
2. Specify the values of cn in terms of the discrete values of
the target spectrum, SVJ1, i.e.,
(7.188)
3. Inverse Fourier transform the amplitudes and phases using
an FFT algorithm to obtain a discrete time series realization.
The DSA method is spectrally deterministic because the amplitude spec
trum is specified in terms of the Fourier amplitudes, cn. Therefore, eac]
time series realization constructed with random phases will closely mate]
the target spectrum. This is desirable because it offers easier matching c
the peak spectral frequency and the spectral shape (Funke and Mansan
1987); however, real sea states exhibit variations in spectra between tim
series measurements, so the DSA method is less realistic.
Repeatability can be achieved with the DSA method if a numerics
pseudo-random number generator is used to determine the random phase