7.4. NONLINEAR WAVE GENERATION
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wave is generated in addition to the secondary Stokes wave, and because
the free wave travels at a slower speed, the wave profile deforms as it propagates. In principle, all of the methods discussed above could be used to
determine the necessary wave board motion to suppress the free secondary
wave; but in practice, Madsen’s (1971) approximate theory is the most convenient, although it is limited to relatively shallow water. An alternative
method for suppressing the secondary free wave was posed by Flick and
Guza (1980). They suggested generating the waves in deep water using a
sinusoidal wave board motion, and then shoaling the waves to shallow water in the wave tank. Although the free secondary waves are still present,
they are diminished in amplitude relative to the amplitude of the Stokes
second-order component.
7.4.2 Solitary and Cnoidal Waves
As water depth decreases and wavelength increases, Stokes second-order
theory become less appropriate for describing waves of permanent form,
and instead we rely on cnoidal and solitary wave theories. Theoretical
studies that invoke these shallow water wave theories benefit by laboratory validation; therefore, generation of reasonable shallow water waves of
permanent form in a wave tank is a vital laboratory capability.
Raichlen (1970) described generation of solitary waves in a study of
tsunami waves generated by the impulsive movement of seafloor. A twodimensional wave facility was outfitted with a piston that was displaced
vertically upward from the bottom of the wave tank. Hammack and Segur
(1974) showed theoretically and experimentally that solitary waves could
be generated by any boundary movement that produced a net positive
displacement of a volume of water. As waves created by this disturbance
propagate away from the source, at least one solitary wave eventually forms
followed by a train of oscillatory waves. The solitary wave moves at a faster
speed, and it ultimately emerges clear of the trailing waves.
This method can be used to generate solitary waves in a laboratory
wave flume provided there is sufficient tank length for the solitary wave to
emerge, and the presence of trailing oscillatory wave train will not disrupt
the experiment. However, there are circumstances that dictate generation
of shallow water waves of permanent form without the trailing wave train,
and this need led to development of a wavemaker theory for generating
either solitary or cnoidal waves in the laboratory.
379
wave is generated in addition to the secondary Stokes wave, and because
the free wave travels at a slower speed, the wave profile deforms as it propagates. In principle, all of the methods discussed above could be used to
determine the necessary wave board motion to suppress the free secondary
wave; but in practice, Madsen’s (1971) approximate theory is the most convenient, although it is limited to relatively shallow water. An alternative
method for suppressing the secondary free wave was posed by Flick and
Guza (1980). They suggested generating the waves in deep water using a
sinusoidal wave board motion, and then shoaling the waves to shallow water in the wave tank. Although the free secondary waves are still present,
they are diminished in amplitude relative to the amplitude of the Stokes
second-order component.
7.4.2 Solitary and Cnoidal Waves
As water depth decreases and wavelength increases, Stokes second-order
theory become less appropriate for describing waves of permanent form,
and instead we rely on cnoidal and solitary wave theories. Theoretical
studies that invoke these shallow water wave theories benefit by laboratory validation; therefore, generation of reasonable shallow water waves of
permanent form in a wave tank is a vital laboratory capability.
Raichlen (1970) described generation of solitary waves in a study of
tsunami waves generated by the impulsive movement of seafloor. A twodimensional wave facility was outfitted with a piston that was displaced
vertically upward from the bottom of the wave tank. Hammack and Segur
(1974) showed theoretically and experimentally that solitary waves could
be generated by any boundary movement that produced a net positive
displacement of a volume of water. As waves created by this disturbance
propagate away from the source, at least one solitary wave eventually forms
followed by a train of oscillatory waves. The solitary wave moves at a faster
speed, and it ultimately emerges clear of the trailing waves.
This method can be used to generate solitary waves in a laboratory
wave flume provided there is sufficient tank length for the solitary wave to
emerge, and the presence of trailing oscillatory wave train will not disrupt
the experiment. However, there are circumstances that dictate generation
of shallow water waves of permanent form without the trailing wave train,
and this need led to development of a wavemaker theory for generating
either solitary or cnoidal waves in the laboratory.