418
CHAPTER 7. LABORATORY WAVE GENERATION
Other Second-Order Long-Wave Correction Techniques. Klopman and Van Leeuwen (1990) presented an alternative second-order wavemaker theory for generating irregular waves with the correct second-order
bound waves. Their method made the assumption that the sea surface spectrum is narrow-banded, which allowed application of the multiple-scales
perturbation procedure to derive expressions for the second-order wave
board displacement time series. Klopman and Van Leeuwen stated that
calculations with their method require an effort proportional to that of
generating the first-order signal, whereas calculations using the full secondorder equations (given above) require an effort proportional to the square
of the first-order generation effort.
Fittschen and Scheffer (1987) demonstrated that a self-correcting wavemaking system could be used to establish the correct second-order control
signal using an iterative technique. Wave measurements made in the flume
without any highly reflective structures in place were used to develop an
empirical transfer function between the target spectrum and control signal.
The technique was demonstrated for a simple two-component wave group
and for a typical spectrum.
Gotschenberg and Daemrich (1990) also reported that the self-correcting
system was successful in suppressing the unwanted long waves during irregular wave generation. An interesting observation they made was that
commonly used irregular wave height parameters were not influenced significantly by whether or not the unwanted spurious waves were suppressed.
When Second-Order Long-Wave Correction is Important. Studies where long-wave motions are a critical forcing function, such as in harbor seiching and mooring of floating structures, will likely benefit by the
use of the correct second-order irregular wave generation technique. This
was substantiated by Mansard and Pratte (1982) who examined the response of a moored vessel in shallow water to irregular waves generated
in a wide (7.7 m) laboratory wave flume. Tests were conducted with and
without suppression of the spurious long waves. Measured results indicated
greater motions and mooring forces when the long waves were effectively
suppressed.
Barthel, Mansard, and Funke (1983a) studied the effect of group-induced
long waves on wave runup on a concrete plane slope of 1:25. Each of their
test conditions was generated with and without spurious long wave suppression. Their results indicated that maximum runup is greater when the
spurious waves are present, and this difference was more pronounced as
groupiness increased. Presumably, the unwanted spurious long waves cancel the set-down under the wave groups, hence the large waves in the group
can uprush farther. Therefore, correct generation of the second-order bound
CHAPTER 7. LABORATORY WAVE GENERATION
Other Second-Order Long-Wave Correction Techniques. Klopman and Van Leeuwen (1990) presented an alternative second-order wavemaker theory for generating irregular waves with the correct second-order
bound waves. Their method made the assumption that the sea surface spectrum is narrow-banded, which allowed application of the multiple-scales
perturbation procedure to derive expressions for the second-order wave
board displacement time series. Klopman and Van Leeuwen stated that
calculations with their method require an effort proportional to that of
generating the first-order signal, whereas calculations using the full secondorder equations (given above) require an effort proportional to the square
of the first-order generation effort.
Fittschen and Scheffer (1987) demonstrated that a self-correcting wavemaking system could be used to establish the correct second-order control
signal using an iterative technique. Wave measurements made in the flume
without any highly reflective structures in place were used to develop an
empirical transfer function between the target spectrum and control signal.
The technique was demonstrated for a simple two-component wave group
and for a typical spectrum.
Gotschenberg and Daemrich (1990) also reported that the self-correcting
system was successful in suppressing the unwanted long waves during irregular wave generation. An interesting observation they made was that
commonly used irregular wave height parameters were not influenced significantly by whether or not the unwanted spurious waves were suppressed.
When Second-Order Long-Wave Correction is Important. Studies where long-wave motions are a critical forcing function, such as in harbor seiching and mooring of floating structures, will likely benefit by the
use of the correct second-order irregular wave generation technique. This
was substantiated by Mansard and Pratte (1982) who examined the response of a moored vessel in shallow water to irregular waves generated
in a wide (7.7 m) laboratory wave flume. Tests were conducted with and
without suppression of the spurious long waves. Measured results indicated
greater motions and mooring forces when the long waves were effectively
suppressed.
Barthel, Mansard, and Funke (1983a) studied the effect of group-induced
long waves on wave runup on a concrete plane slope of 1:25. Each of their
test conditions was generated with and without spurious long wave suppression. Their results indicated that maximum runup is greater when the
spurious waves are present, and this difference was more pronounced as
groupiness increased. Presumably, the unwanted spurious long waves cancel the set-down under the wave groups, hence the large waves in the group
can uprush farther. Therefore, correct generation of the second-order bound