412
CHAPTER 7. LABORATORY WAVE GENERATION
irregular waves with correctly generated second-order bound long waves.
Sand and Donslund also extended the second-order wavemaker solution
to include the case of a hinged wave board with variable draft, and they
presented a unified set of equations for practical implementation in the
laboratory.
The mathematical development of the correct wave board signal for generating second-order bound long waves is lengthy and somewhat monstrous
in its algebra, so it will not be covered in its entirety here. However, those
who revel in algebraic manipulation should not hesitate consulting the references and performing the derivation on their own! The short summary
below was drawn from the above-cited references.
Consequences of First-Order Irregular Wave Generation. Generation of irregular wave trains in a two-dimensional wave flume using a
first-order wavemaker theory control signal to drive the wave board creates
a number of longer waves not present in the original signal. Bound long
waves occur naturally with the wave groups, and this is the one long wave
we want to occur in the flume.
The first-order theory wave board boundary condition does not meet
the requirements for the second-order bound long wave, and this results in
generation of a free long wave (opposite in amplitude, but smaller), termed
the parasitic long wave. Another long wave, termed the displacement
long wave is caused by finite wave board displacements away from the
mean position. (Of course, the first-order wave board boundary condition
assumed small displacements.) The displacement long wave has a maximum amplitude near the traditional deep water limit. Finally, a local
disturbance long wave, caused by the exponentially decaying summation terms in the first-order wavemaker theory, is generated. Fortunately,
it’s magnitude is so small relative to the other long wave amplitudes that
it is normally neglected.
As mentioned, the bound long wave is the only long wave we want to
occur in the wave flume during wave generation. The other long waves
inherently occur when using first-order wavemaker theory, and they have
such long wavelengths that reflection is assured in most situations. These
unwanted long waves have been termed spurious long waves, and they
are free waves traveling at their own celerity. Sometimes the spurious long
waves act to cancel the bound long wave travelling with a wave group, and
at other times they might enhance the magnitude of the bound long wave.
Obviously, these spurious long waves will contaminate experiments sensitive
to long-wave frequencies. A comprehensive discussion of the spurious long
waves, along with methods for estimating their magnitudes can be found
in Barthel, et al. (1983).
CHAPTER 7. LABORATORY WAVE GENERATION
irregular waves with correctly generated second-order bound long waves.
Sand and Donslund also extended the second-order wavemaker solution
to include the case of a hinged wave board with variable draft, and they
presented a unified set of equations for practical implementation in the
laboratory.
The mathematical development of the correct wave board signal for generating second-order bound long waves is lengthy and somewhat monstrous
in its algebra, so it will not be covered in its entirety here. However, those
who revel in algebraic manipulation should not hesitate consulting the references and performing the derivation on their own! The short summary
below was drawn from the above-cited references.
Consequences of First-Order Irregular Wave Generation. Generation of irregular wave trains in a two-dimensional wave flume using a
first-order wavemaker theory control signal to drive the wave board creates
a number of longer waves not present in the original signal. Bound long
waves occur naturally with the wave groups, and this is the one long wave
we want to occur in the flume.
The first-order theory wave board boundary condition does not meet
the requirements for the second-order bound long wave, and this results in
generation of a free long wave (opposite in amplitude, but smaller), termed
the parasitic long wave. Another long wave, termed the displacement
long wave is caused by finite wave board displacements away from the
mean position. (Of course, the first-order wave board boundary condition
assumed small displacements.) The displacement long wave has a maximum amplitude near the traditional deep water limit. Finally, a local
disturbance long wave, caused by the exponentially decaying summation terms in the first-order wavemaker theory, is generated. Fortunately,
it’s magnitude is so small relative to the other long wave amplitudes that
it is normally neglected.
As mentioned, the bound long wave is the only long wave we want to
occur in the wave flume during wave generation. The other long waves
inherently occur when using first-order wavemaker theory, and they have
such long wavelengths that reflection is assured in most situations. These
unwanted long waves have been termed spurious long waves, and they
are free waves traveling at their own celerity. Sometimes the spurious long
waves act to cancel the bound long wave travelling with a wave group, and
at other times they might enhance the magnitude of the bound long wave.
Obviously, these spurious long waves will contaminate experiments sensitive
to long-wave frequencies. A comprehensive discussion of the spurious long
waves, along with methods for estimating their magnitudes can be found
in Barthel, et al. (1983).