376
CHAPTER 7. LABORATORY WAVE GENERATION
Daugaard (1972) formulated the problem by including the standing wave
summation terms in the first-order functions
and
when substituted
into the wave board boundary condition, but he neglected the summation
terms when solving the set of equations with the inhomogeneous free surface
boundary condition.
Hansen and Svendsen (1974) reported on an experimental investigation
of second-order effects associated with a piston-type wavemaker. Three series of experiments were performed: (1) pure sinusoidal motion of the wave
board as a piston, (2) pure sinusoidal motion comprised of both translation
and rotation, and (3) sinusoidal piston motion combined with the secondorder compensation
Hansen and Svendsen’s measured results were compared to predictions
from the theories of Fontanet (1961), Madsen (1971), and Daugaard (1972).
In the tested range 0.1 < h/L < 0.65 they observed second-order Stokes
waves superimposed with a free secondary harmonic. Considerable scatter
appeared in the data when compared to the theories, however, in some
instances remarkable correspondence existed.
Hansen and Svendsen (1974) were successful in suppressing the free secondary wave amplitude to about 5-10% of second-order Stokes component
when moving the piston-type wave board in a nonsinusoidal motion. However, this level of free wave suppression requires empirical fitting (Svendsen
1985), and successful suppression is limited to Ursell numbers HL2/h3 < 30
(Svendsen 1985). Results obtained from a combined translation and rotation of the wave board were not significantly better despite the fact that
the wave board motion was closer to fitting the water particle motion under
the second-order wave.
Hulsbergen (1974) investigated second-order Stokes waves in an experimental facility, and he noted that free secondary waves could be suppressed
by the passage of a second-order wave over a sill placed on the horizontal
bottom. Wave characteristics, sill dimensions, and distance of the sill from
the wave board appeared to be important design parameters related to
effective suppression of secondary waves.
As previously mentioned, Flick and Guza (1980) formulated the secondorder wavemaker problem for the case of a wave board configured as shown
in Figure 7.1. Their derivation parallels the derivation given in the preceding sections except they retained the standing wave summation terms in
<$1 and r]i when evaluating the set of equations containing the wave board
boundary condition, which “... considerably complicates the algebra at second order and precludes a simple, analytic calculation of the second-order
free wave solution”.
Like Madsen (1971) and Daugaard (1972), Flick and Guza neglected
the standing wave terms when evaluating the set of equations containing
CHAPTER 7. LABORATORY WAVE GENERATION
Daugaard (1972) formulated the problem by including the standing wave
summation terms in the first-order functions
and
when substituted
into the wave board boundary condition, but he neglected the summation
terms when solving the set of equations with the inhomogeneous free surface
boundary condition.
Hansen and Svendsen (1974) reported on an experimental investigation
of second-order effects associated with a piston-type wavemaker. Three series of experiments were performed: (1) pure sinusoidal motion of the wave
board as a piston, (2) pure sinusoidal motion comprised of both translation
and rotation, and (3) sinusoidal piston motion combined with the secondorder compensation
Hansen and Svendsen’s measured results were compared to predictions
from the theories of Fontanet (1961), Madsen (1971), and Daugaard (1972).
In the tested range 0.1 < h/L < 0.65 they observed second-order Stokes
waves superimposed with a free secondary harmonic. Considerable scatter
appeared in the data when compared to the theories, however, in some
instances remarkable correspondence existed.
Hansen and Svendsen (1974) were successful in suppressing the free secondary wave amplitude to about 5-10% of second-order Stokes component
when moving the piston-type wave board in a nonsinusoidal motion. However, this level of free wave suppression requires empirical fitting (Svendsen
1985), and successful suppression is limited to Ursell numbers HL2/h3 < 30
(Svendsen 1985). Results obtained from a combined translation and rotation of the wave board were not significantly better despite the fact that
the wave board motion was closer to fitting the water particle motion under
the second-order wave.
Hulsbergen (1974) investigated second-order Stokes waves in an experimental facility, and he noted that free secondary waves could be suppressed
by the passage of a second-order wave over a sill placed on the horizontal
bottom. Wave characteristics, sill dimensions, and distance of the sill from
the wave board appeared to be important design parameters related to
effective suppression of secondary waves.
As previously mentioned, Flick and Guza (1980) formulated the secondorder wavemaker problem for the case of a wave board configured as shown
in Figure 7.1. Their derivation parallels the derivation given in the preceding sections except they retained the standing wave summation terms in
<$1 and r]i when evaluating the set of equations containing the wave board
boundary condition, which “... considerably complicates the algebra at second order and precludes a simple, analytic calculation of the second-order
free wave solution”.
Like Madsen (1971) and Daugaard (1972), Flick and Guza neglected
the standing wave terms when evaluating the set of equations containing