8.4. WAVE REFLECTION ANALYSIS
519
and horizontal current meter) be used if the vertical velocity signal is expected to be weak.
Because the co-located gauge method invokes linear theory to transfer
the velocities to sea surface elevations, it is best to avoid placing the current measuring instrument in the upper portion of the water column where
greater departure from linear theory wave kinematics is known to occur.
However, placing the instrument too deep in the water column will restrict
the analysis to wave frequencies that still produce an appreciable velocity
at that depth.
Hughes (1993) applied the co-located velocities method using a laser
Doppler velocimeter to obtain horizontal and vertical velocity signals at
mid-depth. He validated the method for the case of a completely reflecting
vertical wall, and he reported making reliable estimates using data collected close to the wall where the irregular standing wave pattern would
have invalidated the spatially-separated wave gauge method. A side-byside comparison of the co-located velocities method and the Goda Method
showed similar estimates of incident and reflected spectra for the case of
a mild-sloping plane beach. The same sources of errors listed by Goda
and Suzuki (1976) for the spatially-separated wave gauge method will affect reflection estimates calculated with the vertical array method and the
co-located velocities method.
Previously, warnings have been given regarding application of these firstorder reflection analysis methods at frequencies where low coherence is
observed in the cross-spectra between gauges or when spectral energy is
low. This same warning applies to the co-located velocities method. Hughes
(1993) illustrated how reflection estimates can become unrealistic when
precautions are not taken, with large amounts of “false reflected energy”
being estimated at frequencies that originally contained no energy in the
measured wave train. Automated reflection analysis procedures must be
able to determine the appropriate frequency range for analysis.
8.4.3 Second-Order Reflection Analysis
Mansard, Sand, and Funke (1985) described a technique for nonlinear regular wave reflection analysis. This technique involves a least-squares fit of
sinusoidal waves to the measured time series and estimation of separate reflection coefficients for the first-order frequency and the second-order higher
and lower bound frequencies.
Maoxiang and Zhenquan (1988) presented two methods for estimating
second order long waves in a wave tank. The first method extended Go a
and Suzuki’s (1976) method to three gauges to extract spectra of set-down,
reflected long waves, and parasitic long waves. Recorded data were low pass
519
and horizontal current meter) be used if the vertical velocity signal is expected to be weak.
Because the co-located gauge method invokes linear theory to transfer
the velocities to sea surface elevations, it is best to avoid placing the current measuring instrument in the upper portion of the water column where
greater departure from linear theory wave kinematics is known to occur.
However, placing the instrument too deep in the water column will restrict
the analysis to wave frequencies that still produce an appreciable velocity
at that depth.
Hughes (1993) applied the co-located velocities method using a laser
Doppler velocimeter to obtain horizontal and vertical velocity signals at
mid-depth. He validated the method for the case of a completely reflecting
vertical wall, and he reported making reliable estimates using data collected close to the wall where the irregular standing wave pattern would
have invalidated the spatially-separated wave gauge method. A side-byside comparison of the co-located velocities method and the Goda Method
showed similar estimates of incident and reflected spectra for the case of
a mild-sloping plane beach. The same sources of errors listed by Goda
and Suzuki (1976) for the spatially-separated wave gauge method will affect reflection estimates calculated with the vertical array method and the
co-located velocities method.
Previously, warnings have been given regarding application of these firstorder reflection analysis methods at frequencies where low coherence is
observed in the cross-spectra between gauges or when spectral energy is
low. This same warning applies to the co-located velocities method. Hughes
(1993) illustrated how reflection estimates can become unrealistic when
precautions are not taken, with large amounts of “false reflected energy”
being estimated at frequencies that originally contained no energy in the
measured wave train. Automated reflection analysis procedures must be
able to determine the appropriate frequency range for analysis.
8.4.3 Second-Order Reflection Analysis
Mansard, Sand, and Funke (1985) described a technique for nonlinear regular wave reflection analysis. This technique involves a least-squares fit of
sinusoidal waves to the measured time series and estimation of separate reflection coefficients for the first-order frequency and the second-order higher
and lower bound frequencies.
Maoxiang and Zhenquan (1988) presented two methods for estimating
second order long waves in a wave tank. The first method extended Go a
and Suzuki’s (1976) method to three gauges to extract spectra of set-down,
reflected long waves, and parasitic long waves. Recorded data were low pass