7.5. TRANSIENT WAVE GENERATION
389
Next, a finite Fourier transform with respect to the horizontal coordinate
(i) was performed resulting in a second-order ordinary differential governing equation and its associated boundary conditions. A solution to the
transformed set of equations was then inverse transformed to obtain the
velocity potential function, and analytical solutions were given for sea surface variation and hydrodynamic forces on the wave board. Lee, et al.
confirmed the theory by applying it to the case of a flap-type wave board
hinged at the bottom of a wave tank. Favorable comparison was shown
between their theory and solutions obtained using a numerical finite element method and an analytic source integral method. No comparisons to
laboratory data were presented.
Joo, et al. (1990) employed small amplitude expansion and a Fourierintegral method to obtain transient solutions to the wavemaker problem.
They applied their solution to wave board velocity functions corresponding
to a ramp, a step, simple harmonic oscillation, and a sum of 72 cosine terms
(irregular transient wave). Surface tension was included in the formulation,
and very close to the wave board it was shown to be important. Further
away from the wave board surface tension was considered less important.
A comparison of theory to laboratory measurements was performed for the
case of irregular transient waves, and good correspondence was shown at
moderate distances from the wavemaker for all times. Comparison was less
favorable at further distances and longer time because nonlinear effects in
the translating wave train had time to accumulate.
The theory of transient waves has progressed to where it is possible to
predict the temporal and spatial sea surface elevation fluctuations for a
specified wave board motion, provided reflected waves are effectively suppressed. However, the above studies did not address the more difficult
inverse problem of determining the required wave board motion needed to
produce a specific transient wave form at a given time and location in the
wave tank.
T.5.3 Generation of Specific Transient Waves
The capability to generate specific transient waves at given location in a
wave tank requires determination of the appropriate wave board displacement as a function of time. Usually, the signal for wave board displacement
bears little resemblance to the desired transient because allowance has to
be made for wave dispersion as the waves propagate. Under the assumptions of linear wave theory, the transient signal can be represented as a
combination of smaller waves of different frequencies which travel at different speeds (except in the case of very shallow water). Therefore, the
generation of the component waves must be timed so they all arrive at the
389
Next, a finite Fourier transform with respect to the horizontal coordinate
(i) was performed resulting in a second-order ordinary differential governing equation and its associated boundary conditions. A solution to the
transformed set of equations was then inverse transformed to obtain the
velocity potential function, and analytical solutions were given for sea surface variation and hydrodynamic forces on the wave board. Lee, et al.
confirmed the theory by applying it to the case of a flap-type wave board
hinged at the bottom of a wave tank. Favorable comparison was shown
between their theory and solutions obtained using a numerical finite element method and an analytic source integral method. No comparisons to
laboratory data were presented.
Joo, et al. (1990) employed small amplitude expansion and a Fourierintegral method to obtain transient solutions to the wavemaker problem.
They applied their solution to wave board velocity functions corresponding
to a ramp, a step, simple harmonic oscillation, and a sum of 72 cosine terms
(irregular transient wave). Surface tension was included in the formulation,
and very close to the wave board it was shown to be important. Further
away from the wave board surface tension was considered less important.
A comparison of theory to laboratory measurements was performed for the
case of irregular transient waves, and good correspondence was shown at
moderate distances from the wavemaker for all times. Comparison was less
favorable at further distances and longer time because nonlinear effects in
the translating wave train had time to accumulate.
The theory of transient waves has progressed to where it is possible to
predict the temporal and spatial sea surface elevation fluctuations for a
specified wave board motion, provided reflected waves are effectively suppressed. However, the above studies did not address the more difficult
inverse problem of determining the required wave board motion needed to
produce a specific transient wave form at a given time and location in the
wave tank.
T.5.3 Generation of Specific Transient Waves
The capability to generate specific transient waves at given location in a
wave tank requires determination of the appropriate wave board displacement as a function of time. Usually, the signal for wave board displacement
bears little resemblance to the desired transient because allowance has to
be made for wave dispersion as the waves propagate. Under the assumptions of linear wave theory, the transient signal can be represented as a
combination of smaller waves of different frequencies which travel at different speeds (except in the case of very shallow water). Therefore, the
generation of the component waves must be timed so they all arrive at the