7.6. IRREGULAR (2-D) WAVE GENERATION
399
and if the initial random number generator “seed” is remembered. Synthesized time series record lengths for both the NSA and the DSA methods
will be given as T = N/Af, and the inverse FFT method is preferred when
N > 1000 (Wang and Crouch 1992).
The DSA method time series simulations tend to show slightly less Gaussian statistics compared to the NSA method. However, in theory, the two
methods are equivalent for extremely large values of the summation parameter N (Hudspeth, Nath, and Sollitt 1985) . For finite length simulations
many investigators believe the differences between the NSA and DSA irregular wave synthesis methods are not too great (Funke and Mansard 1987).
Wang and Crough (1993) gave a discussion about the theoretical correctness of the NSA and DSA methods. Digital simulation of nonlinear random
waves was described by Hudspeth and Chen (1979) and Tuah and Hudspeth
(1982), but laboratory reproduction of nonlinear irregular waves was not
discussed.
An alternate method of generating time series realizations is a direct
summation of a specified number of sinusoidal components according to
Eqn. 7.186 with Fourier amplitudes related to the target spectrum by
Eqn. 7.188. This “brute force” method is capable of generating extremely
long time series realizations; but eventually recycling will occur in the time
series record.
Wang and Crouch (1993) examined the accuracy of the first-order technique of summing sinusoidal components in the time domain. They looked
at how well the summation methods modeled theoretical criteria for wave
maxima, wave periods, and spectral bandwidths; and their work established
guidelines for the use of these simple summation models, such as upper and
lower cutoff frequencies and minimum number of spectral components necessary to capture the features of narrow-banded spectra.
Comparison Between NSA and DSA Synthesis Methods. Funke,
Mansard, and Dai (1988) compared numerical and physical model realizations resulting from irregular wave synthesis using the Nondeterministic Spectral Amplitude (NSA) and the Deterministic Spectral Amplitude
(DSA) models. Their study compared the different time series realizations
in terms of 12 critical wave parameters, including three parameters related
to wave groupiness, and the study was an extension of an earlier numerical
comparison.
Two hundred irregular time series realizations were generated using both
the NSA and the DSA methods. Because of the variation that occurs in
the spectrum of time series generated by the NSA method, 200 additional
NSA realizations were rescaled so the spectra had the same variance as the
target spectrum. The time series were transformed into an appropriate wave
399
and if the initial random number generator “seed” is remembered. Synthesized time series record lengths for both the NSA and the DSA methods
will be given as T = N/Af, and the inverse FFT method is preferred when
N > 1000 (Wang and Crouch 1992).
The DSA method time series simulations tend to show slightly less Gaussian statistics compared to the NSA method. However, in theory, the two
methods are equivalent for extremely large values of the summation parameter N (Hudspeth, Nath, and Sollitt 1985) . For finite length simulations
many investigators believe the differences between the NSA and DSA irregular wave synthesis methods are not too great (Funke and Mansard 1987).
Wang and Crough (1993) gave a discussion about the theoretical correctness of the NSA and DSA methods. Digital simulation of nonlinear random
waves was described by Hudspeth and Chen (1979) and Tuah and Hudspeth
(1982), but laboratory reproduction of nonlinear irregular waves was not
discussed.
An alternate method of generating time series realizations is a direct
summation of a specified number of sinusoidal components according to
Eqn. 7.186 with Fourier amplitudes related to the target spectrum by
Eqn. 7.188. This “brute force” method is capable of generating extremely
long time series realizations; but eventually recycling will occur in the time
series record.
Wang and Crouch (1993) examined the accuracy of the first-order technique of summing sinusoidal components in the time domain. They looked
at how well the summation methods modeled theoretical criteria for wave
maxima, wave periods, and spectral bandwidths; and their work established
guidelines for the use of these simple summation models, such as upper and
lower cutoff frequencies and minimum number of spectral components necessary to capture the features of narrow-banded spectra.
Comparison Between NSA and DSA Synthesis Methods. Funke,
Mansard, and Dai (1988) compared numerical and physical model realizations resulting from irregular wave synthesis using the Nondeterministic Spectral Amplitude (NSA) and the Deterministic Spectral Amplitude
(DSA) models. Their study compared the different time series realizations
in terms of 12 critical wave parameters, including three parameters related
to wave groupiness, and the study was an extension of an earlier numerical
comparison.
Two hundred irregular time series realizations were generated using both
the NSA and the DSA methods. Because of the variation that occurs in
the spectrum of time series generated by the NSA method, 200 additional
NSA realizations were rescaled so the spectra had the same variance as the
target spectrum. The time series were transformed into an appropriate wave