388
CHAPTER 7. LABORATORY WAVE GENERATION
Madsen (1970) stated that the response arising from the initial wavemaker problem was “analogous to the response of a slightly damped mechanical system”, and he suggested that the first large wave could be eliminated
by slowly increasing the wavemaker stroke at startup until it reached its
steady-state value. With the advent of wavemakers controlled by hydraulic
servo-systems this has become possible, and most laboratory routinely include “ramp-up” and “ramp-down” signals when operating the wavemaker.
7.5.2 Theories for Predicting Transient Waves
A number of studies have looked at the problem of determining the transient waves that evolve for a given wave board motion. Das and Wiegel
(1972) examined Kennard’s linearized equation (Eqn. 7.176) by considering a piston-type wave board and specifying the board velocity as a series
of discrete time steps. This allowed them to represent a range of nonlinear
oscillatory waves and solitary waves. Comparisons between measurements
and the linearized theory agreed quite well
for fairly small values of
wall displacement and velocity,” and from a practical standpoint, the theory proved useful outside the range of its strict theoretical limits (as often
is the case with linear wave theory).
Moraes, et al. (1972) examined waves produced by impulse and steptype motions by a piston-type wave board. Their objective was to determine
whether or not this type of wave generation could be represented as a
linear system where wave board spectra could be related to transient wave
spectra via a transfer function. They discovered that nonlinearities were
always present in the system, particularly for shallower depths and higher
frequencies.
Takayama and Goda (1987) derived a theoretical expression for nonlinear transient waves created by a piston-type wave board having periodic
(sinusoidal) motion. Their two-dimensional derivation employed a moving coordinate system fixed to the wave board, thus finite-amplitude wave
board motions were taken into account. The resulting formulation is linear
when expressed in the moving coordinate system, but becomes nonlinear
when referenced to a stationary coordinate system. Included in the formulation are the free secondary waves and bounded long waves associated
with the nonlinearity of the free surface boundary condition. Takayama
and Goda presented computed results, but no laboratory measurements
were reported.
Lee, et al. (1989) presented a first-order analytic theory for unsteady
waves generated in a finite-length two-dimensional wave channel. Their theoretical development began with the familiar linearized (first-order) wavemaker equations which were then Laplace transformed with respect to time.
CHAPTER 7. LABORATORY WAVE GENERATION
Madsen (1970) stated that the response arising from the initial wavemaker problem was “analogous to the response of a slightly damped mechanical system”, and he suggested that the first large wave could be eliminated
by slowly increasing the wavemaker stroke at startup until it reached its
steady-state value. With the advent of wavemakers controlled by hydraulic
servo-systems this has become possible, and most laboratory routinely include “ramp-up” and “ramp-down” signals when operating the wavemaker.
7.5.2 Theories for Predicting Transient Waves
A number of studies have looked at the problem of determining the transient waves that evolve for a given wave board motion. Das and Wiegel
(1972) examined Kennard’s linearized equation (Eqn. 7.176) by considering a piston-type wave board and specifying the board velocity as a series
of discrete time steps. This allowed them to represent a range of nonlinear
oscillatory waves and solitary waves. Comparisons between measurements
and the linearized theory agreed quite well
for fairly small values of
wall displacement and velocity,” and from a practical standpoint, the theory proved useful outside the range of its strict theoretical limits (as often
is the case with linear wave theory).
Moraes, et al. (1972) examined waves produced by impulse and steptype motions by a piston-type wave board. Their objective was to determine
whether or not this type of wave generation could be represented as a
linear system where wave board spectra could be related to transient wave
spectra via a transfer function. They discovered that nonlinearities were
always present in the system, particularly for shallower depths and higher
frequencies.
Takayama and Goda (1987) derived a theoretical expression for nonlinear transient waves created by a piston-type wave board having periodic
(sinusoidal) motion. Their two-dimensional derivation employed a moving coordinate system fixed to the wave board, thus finite-amplitude wave
board motions were taken into account. The resulting formulation is linear
when expressed in the moving coordinate system, but becomes nonlinear
when referenced to a stationary coordinate system. Included in the formulation are the free secondary waves and bounded long waves associated
with the nonlinearity of the free surface boundary condition. Takayama
and Goda presented computed results, but no laboratory measurements
were reported.
Lee, et al. (1989) presented a first-order analytic theory for unsteady
waves generated in a finite-length two-dimensional wave channel. Their theoretical development began with the familiar linearized (first-order) wavemaker equations which were then Laplace transformed with respect to time.