502 CHAPTER 8. LABORATORY MEASUREMENT AND ANALYSIS
• Maximum Likelihood Method (MLM): The principle of the MLM is to minimize the variance of the difference between the estimated and true spectra (Lungren
and Klinting 1987). This method is popular because it
gives better directional resolution than the direct Fourier
transform method and the parametric methods.
• Fourier Vector Method: Sand (1979) and Sand and
Lundgren (1979) proposed this method that computes amplitudes, phases, and directions from measurements of sea
surface elevations and wave orbital velocities.
• Maximum Entropy Method (MEM): The MEM is an
iterative method that maximizes the integral of £)(/, 0) ■
ln[D(f, 0)] over the range of 6 at each frequency, f. The
MEM is reported to give even better directional resolution
than the MLM (Nwogu, et al. 1987).
The goal of simulating directional sea states in the laboratory is to
replicate naturally occurring sea states. However, the wave generation techniques can only reproduce a relatively small number of frequency components, and the directional spreading is predetermined. So it is reasonable
to expect analyzed laboratory directional spectra to be generally smoother
than corresponding field spectra. However, multidirectional wave generation and frequency domain analysis of multi-directional sea states are still
areas of active research, and we should not be surprised if both techniques
are improved in the future.
8.4 Wave Reflection Analysis
Waves in coastal physical models are reflected by beaches, coastal structures, floating or submerged solid bodies, and model boundaries. The reflected waves interact with the incident waves and contribute to the characteristics of the wave field and the flow field beneath the waves. Wave
reflection is correctly reproduced in properly scaled laboratory studies with
the additional complexity of reflected waves being re-reflected at the wave
board unless some active absorption technique is employed.
In many laboratory studies it is desirable to separate the measured wave
train into its incident and reflected wave components so that model response
can be related to parameters of the incident wave field. Analysis methods
have been developed for resolving incident and reflected wave trains in
two-dimensional laboratory wave flumes, and several commonly applied
reflection analysis methods are covered in the following sections.
• Maximum Likelihood Method (MLM): The principle of the MLM is to minimize the variance of the difference between the estimated and true spectra (Lungren
and Klinting 1987). This method is popular because it
gives better directional resolution than the direct Fourier
transform method and the parametric methods.
• Fourier Vector Method: Sand (1979) and Sand and
Lundgren (1979) proposed this method that computes amplitudes, phases, and directions from measurements of sea
surface elevations and wave orbital velocities.
• Maximum Entropy Method (MEM): The MEM is an
iterative method that maximizes the integral of £)(/, 0) ■
ln[D(f, 0)] over the range of 6 at each frequency, f. The
MEM is reported to give even better directional resolution
than the MLM (Nwogu, et al. 1987).
The goal of simulating directional sea states in the laboratory is to
replicate naturally occurring sea states. However, the wave generation techniques can only reproduce a relatively small number of frequency components, and the directional spreading is predetermined. So it is reasonable
to expect analyzed laboratory directional spectra to be generally smoother
than corresponding field spectra. However, multidirectional wave generation and frequency domain analysis of multi-directional sea states are still
areas of active research, and we should not be surprised if both techniques
are improved in the future.
8.4 Wave Reflection Analysis
Waves in coastal physical models are reflected by beaches, coastal structures, floating or submerged solid bodies, and model boundaries. The reflected waves interact with the incident waves and contribute to the characteristics of the wave field and the flow field beneath the waves. Wave
reflection is correctly reproduced in properly scaled laboratory studies with
the additional complexity of reflected waves being re-reflected at the wave
board unless some active absorption technique is employed.
In many laboratory studies it is desirable to separate the measured wave
train into its incident and reflected wave components so that model response
can be related to parameters of the incident wave field. Analysis methods
have been developed for resolving incident and reflected wave trains in
two-dimensional laboratory wave flumes, and several commonly applied
reflection analysis methods are covered in the following sections.