408
CHAPTER 7. LABORATORY WAVE GENERATION
data can be represented in the physical model by following these steps
(Carvalho 1989):
1. After scaling the measured sea surface elevation time series, Fourier transform the time series using an FFT to get
discrete values of amplitudes (cn) and phases (0n) in the
equation
N
r](x,t) =
cn cos(knx — unt — 6n)
(7.198)
n=0
2. Transform the Fourier amplitude components into wave
board amplitude components using the transfer function
given by Eqn. 7.193, being careful to evaluate mi at each
discrete frequency.
3. Inverse Fourier transform the wave board amplitude components using the original phase angles to get a time series
of wave board displacement.
4. Generate waves using the resulting wave board displacement time series. This method should give a reasonable
reproduction of the desired time series close to the wave
board. Further from the wave board the wave train should
exhibit general characteristics of the measured wave train
because the phases have been retained.
It is also possible to “phase-shift” each wave board component by an
amount knAx from a given location in the wave facility a distance Ax
back to the location of the wave board. Details are given by Carvalho
(1989).
The Method of Lundgren and Sand (1978). Lundgren and Sand
(1978) presented a first-order technique for determining the wave board
displacement necessary to generate a measured (and suitably scaled) wave
train at a given position in the wave tank. Their derivation is given below.
We want to reproduce a specific sea surface elevation time series at a
given location (denoted as xo) in the wave tank. Invoking first-order wave
theory, we can represent the wave train at xo over the finite time interval
—to < t < +t0 by the Fourier series
oo
rç(zo,t) =
[an cos(knxo - unt) + bn sin(knx0 — wnt)]
(7.199)
n=l
CHAPTER 7. LABORATORY WAVE GENERATION
data can be represented in the physical model by following these steps
(Carvalho 1989):
1. After scaling the measured sea surface elevation time series, Fourier transform the time series using an FFT to get
discrete values of amplitudes (cn) and phases (0n) in the
equation
N
r](x,t) =
cn cos(knx — unt — 6n)
(7.198)
n=0
2. Transform the Fourier amplitude components into wave
board amplitude components using the transfer function
given by Eqn. 7.193, being careful to evaluate mi at each
discrete frequency.
3. Inverse Fourier transform the wave board amplitude components using the original phase angles to get a time series
of wave board displacement.
4. Generate waves using the resulting wave board displacement time series. This method should give a reasonable
reproduction of the desired time series close to the wave
board. Further from the wave board the wave train should
exhibit general characteristics of the measured wave train
because the phases have been retained.
It is also possible to “phase-shift” each wave board component by an
amount knAx from a given location in the wave facility a distance Ax
back to the location of the wave board. Details are given by Carvalho
(1989).
The Method of Lundgren and Sand (1978). Lundgren and Sand
(1978) presented a first-order technique for determining the wave board
displacement necessary to generate a measured (and suitably scaled) wave
train at a given position in the wave tank. Their derivation is given below.
We want to reproduce a specific sea surface elevation time series at a
given location (denoted as xo) in the wave tank. Invoking first-order wave
theory, we can represent the wave train at xo over the finite time interval
—to < t < +t0 by the Fourier series
oo
rç(zo,t) =
[an cos(knxo - unt) + bn sin(knx0 — wnt)]
(7.199)
n=l