8.4. WAVE REFLECTION ANALYSIS
511
wavelengths from the structure and even farther away from nonabsorbing
wave boards.
Goda and Suzuki (1976) listed the following factors that may lead to
errors in the estimation technique:
1. Deviation from the linear dispersion relationship due to
nonlinear effects
2. Presence of second-order harmonics in the incident wave
train
3. Generation of nonlinear interactions in the standing wave
field
4. Presence of transverse waves and other disturbances in the
wave flume
5. High levels of signal noise in the measured time series
Several authors (e.g., Mansard and Funke 1980, Tatavarti, et al. 1988,
Hughes 1993) noted that reliable results are obtained only in those frequencies that exhibit high coherency in the cross-correlation between gauge
records. Erroneous estimates (often with reflection coefficients much greater
than unity) will occur at frequencies containing little wave energy because
of low signal-to-noise ratios. Therefore, the coherency function serves as
an indicator of confidence in the estimation of incident and reflected waves
(Mansard and Funke 1980).
The method of Goda and Suzuki (1976) is commonly used in twodimensional laboratory studies, and it provides a valuable technique for
examining wave reflections from beaches and coastal structures. Some laboratories apply the “Goda Method” using three wave gauges with differing
spacing between the gauges. Analysis of different pairs of gauges in the
array extends the effective resolution frequency range by avoiding singularities that occur when gauge spacing is an integer multiple of half the
wavelength. At frequencies where results are obtained for more than one
gauge pair, a simple average can be made.
Mansard and Funke Method. Mansard and Funke (1980) presented
a least-squares method for separating incident and reflected waves from
synoptic time series recorded at three wave gauges with known spacing.
The derivation is a little too lengthy to include here, and interested readers
should examine the original paper.
In the method given by Mansard and Funke, auto- and cross-spectral
analyses of gauge pairs result in estimates of incident and reflected wave
energy and a noise signal. A least-squares procedure is used to minimize the
511
wavelengths from the structure and even farther away from nonabsorbing
wave boards.
Goda and Suzuki (1976) listed the following factors that may lead to
errors in the estimation technique:
1. Deviation from the linear dispersion relationship due to
nonlinear effects
2. Presence of second-order harmonics in the incident wave
train
3. Generation of nonlinear interactions in the standing wave
field
4. Presence of transverse waves and other disturbances in the
wave flume
5. High levels of signal noise in the measured time series
Several authors (e.g., Mansard and Funke 1980, Tatavarti, et al. 1988,
Hughes 1993) noted that reliable results are obtained only in those frequencies that exhibit high coherency in the cross-correlation between gauge
records. Erroneous estimates (often with reflection coefficients much greater
than unity) will occur at frequencies containing little wave energy because
of low signal-to-noise ratios. Therefore, the coherency function serves as
an indicator of confidence in the estimation of incident and reflected waves
(Mansard and Funke 1980).
The method of Goda and Suzuki (1976) is commonly used in twodimensional laboratory studies, and it provides a valuable technique for
examining wave reflections from beaches and coastal structures. Some laboratories apply the “Goda Method” using three wave gauges with differing
spacing between the gauges. Analysis of different pairs of gauges in the
array extends the effective resolution frequency range by avoiding singularities that occur when gauge spacing is an integer multiple of half the
wavelength. At frequencies where results are obtained for more than one
gauge pair, a simple average can be made.
Mansard and Funke Method. Mansard and Funke (1980) presented
a least-squares method for separating incident and reflected waves from
synoptic time series recorded at three wave gauges with known spacing.
The derivation is a little too lengthy to include here, and interested readers
should examine the original paper.
In the method given by Mansard and Funke, auto- and cross-spectral
analyses of gauge pairs result in estimates of incident and reflected wave
energy and a noise signal. A least-squares procedure is used to minimize the