7.6. IRREGULAR (2-D) WAVE GENERATION
405
where Snr](wn) is the discrete sea surface energy spectrum component and
Swb^n) is the discrete component of the wave board energy spectrum. This
linear transformation results in a wave board spectrum with an enhanced
shape at the low frequency side and a damped shape at the high frequency
side in comparison with the wave spectrum (Goda 1985). The use of a linear
transfer function between wave spectra and wave board spectra assumes a
linear process, which is a reasonable assumption for many cases (despite
being incorrect in the strictest sense).
Generation of Synthesized Irregular Waves
First-order laboratory generation of irregular waves conforming to a specified spectral shape is easily accomplished by using either the Nondeterministic Spectral Amplitude (NSA) or the Deterministic Spectral Amplitude (DSA) synthesizing method described in the previous sections. (Other
methods may also be used.) In the NSA method, simply replace S^^(u;n)
with Swi(wn)(mln)2 in Eqns. 7.183 and 7.184, and then continue synthesizing the irregular time series for wave board stroke. Likewise, in the DSA
method the same substitution for
is made in Eqn. 7.188. Additional conversions, such as converting the wave board time series into
an appropriate analog voltage, will be required depending on the specific
wavemaker machinery.
Some newer wavemakers have wave gauges or pressure sensors mounted
on the wave board. Waves are generated by specifying a time history of
water level at the board; and through a feedback system, the wave board
motion is adjusted to obtain the specified water level. Active feedback
systems like this eliminate the need for the wave board transfer function,
and they also help to minimize second-order effects that arise when driving
the wave board with a first-order signal.
Design curves based on given spectral shapes were published by Gilbert,
et al. (1971) and Hudspeth and Chen (1981). These curves are useful for
first estimates of irregular wave generating capability for a given water
depth and maximum wave board stroke.
Normally, the wave board signal will have a “ramp-up” to avoid severe
transient effects, and this portion of the measured wave train is usually excluded from analysis. Likewise, if the point of measurement is distant from
the wave board, dispersion will occur among the first waves as the longer
waves start to out-pace the shorter waves. Therefore, wave measurements
should not be started until the initial shorter waves have had time to reach
the wave probe.
Funke and Mansard (1987) pointed out that it is not always possible
to reproduce time-discrete idealized mathematical descriptions of the sea
405
where Snr](wn) is the discrete sea surface energy spectrum component and
Swb^n) is the discrete component of the wave board energy spectrum. This
linear transformation results in a wave board spectrum with an enhanced
shape at the low frequency side and a damped shape at the high frequency
side in comparison with the wave spectrum (Goda 1985). The use of a linear
transfer function between wave spectra and wave board spectra assumes a
linear process, which is a reasonable assumption for many cases (despite
being incorrect in the strictest sense).
Generation of Synthesized Irregular Waves
First-order laboratory generation of irregular waves conforming to a specified spectral shape is easily accomplished by using either the Nondeterministic Spectral Amplitude (NSA) or the Deterministic Spectral Amplitude (DSA) synthesizing method described in the previous sections. (Other
methods may also be used.) In the NSA method, simply replace S^^(u;n)
with Swi(wn)(mln)2 in Eqns. 7.183 and 7.184, and then continue synthesizing the irregular time series for wave board stroke. Likewise, in the DSA
method the same substitution for
is made in Eqn. 7.188. Additional conversions, such as converting the wave board time series into
an appropriate analog voltage, will be required depending on the specific
wavemaker machinery.
Some newer wavemakers have wave gauges or pressure sensors mounted
on the wave board. Waves are generated by specifying a time history of
water level at the board; and through a feedback system, the wave board
motion is adjusted to obtain the specified water level. Active feedback
systems like this eliminate the need for the wave board transfer function,
and they also help to minimize second-order effects that arise when driving
the wave board with a first-order signal.
Design curves based on given spectral shapes were published by Gilbert,
et al. (1971) and Hudspeth and Chen (1981). These curves are useful for
first estimates of irregular wave generating capability for a given water
depth and maximum wave board stroke.
Normally, the wave board signal will have a “ramp-up” to avoid severe
transient effects, and this portion of the measured wave train is usually excluded from analysis. Likewise, if the point of measurement is distant from
the wave board, dispersion will occur among the first waves as the longer
waves start to out-pace the shorter waves. Therefore, wave measurements
should not be started until the initial shorter waves have had time to reach
the wave probe.
Funke and Mansard (1987) pointed out that it is not always possible
to reproduce time-discrete idealized mathematical descriptions of the sea