of period equal to that of the wavemaker. 



The simple method for obtaining the reflection coefficient from an 

 experiment, i.e., simply seeking out a node and an antinode, and using 

 equations C121) and (122) appears to be the method used by Wilson (1971) 

 and Keulegan (1973) as discussed in Section II. 3. b. However, this may 

 be a dangerous procedure to use when the reflection coefficient is 

 large and nonlinear effects are pronounced as is often the case in 

 experiments involving relatively long waves. 



To illustrate this, the theoretical variation of the wave amplitude 

 relative to the maximum wave amplitude is found from equation (118) to 

 be 



fW - ^lii^ = (1 . -^ (cos(2k^x . 6) -l))'/2 ^^23) 



max max (1+R) 



Iflien the raw data for the wave height variation along the flume is 

 plotted in this fashion versus x/L, the experimentally observed 

 variation (open circles) in Figure 20 is seen to be somewhat erratic and 

 not resembling the variation predicted by an equation such as equation 

 (123). If one, in spite of this discrepancy between theory and 

 observations, evaluates the reflection coefficient directly from the 

 raw data shown in Figure 20 one finds 0.59 < R < 0.65 with the estimate 

 depending on which node and antinode are chosen. This may not seem to 

 be an alarming variation, but a critical inspection of the surface 

 profile recorded near a node (Fig. 21), reveals that the wave height 

 observed at a node is practically entirely due to a second harmonic 

 motion whose presence manifests itself clearly because of the near 

 vanishing to the first harmonic motion at the nodes. 



Since the theoretically predicted wave amplitude variation along 

 the flume is based on linear theory, it applies only to the fundamental 

 motion which has a period equal to that of the wavemaker. At each 

 station along the flume where the free surface variation with time was 

 recorded, the amplitude of the motion with a period equal to that of the 

 wavemaker was extracted from the wave record by means of a Fourier series 

 analysis. The Fourier series analysis is performed on the Ralph M. 

 Parsons Laboratory Hewlett-Packard computer; the program is presented 

 in Appendix C. 



When plotting the variation of the amplitude of the first harmonic 

 motion with distance along the constant depth part of the flume (full 

 circles in Figure 20), apparent disorder becomes extremely organized 

 and the observed variation of the amplitude of the first harmonic motion 

 is in excellent agreement with the theoretical prediction afforded by 

 equation (123) with R = 0.88. 



The surprising thing to note from the data presented in Figure 20 

 is the drastically different reflection coefficient obtained from the 



65 



