APPENDIX C 



DETERMINATION OF REFLECTION COEFFICIENTS 



During the preliminary experimental runs performed to determine the 

 reflection coefficients of steep, rough slopes it was observed that an 

 appreciable effect of second or higher harmonic motions was present in 

 the wave flume. It was also found that if one sought out the locations 

 along the constant depth part of the flume where the wave height, i.e., 

 distance between crest and trough, was maximum and minimum, respectively, 

 the resulting estimate of the reflection coefficient could vary as much 

 as from 0.45 to 0.75 depending on the choice of maximum and minimum wave 

 height. With the intended use of the experiments such a variation of 

 the experimentally determined reflection coefficient is clearly 

 undesirable. 



The theoretical foundation for using the formula for the experimental 

 determination of the reflection coefficient, 



H - H . 



max min 



is based on an analysis assuming linear waves, i.e., the motion consists 

 of purely sinusoidal waves of one frequency. Hence, the appearance of 

 higher harmonics is an indication of the inapplicability of equation (C-1) 

 for the prediction of reflection coefficients. Furthermore, the physical 

 concept of a reflection coefficient really makes sense only if super- 

 position, i.e., linear waves, may be assumed. 



If the motion in the wave flume was purely sinusoidal, the surface 

 variation should at any point vary sinusoidally with a period, T, equal 

 to that of the wavemaker. Since this was not the case it was decided 

 to extract from the measured surface variation at each station the 

 amplitude of the motion having a period equal to that of the wavemaker. 

 This amplitude of the first harmonic is the one which, according to 

 linear theory, should vary in such a manner that equation (C-l) provides 

 a determination of the reflection coefficient, R. 



The experimental procedure used was the following. For a particular 

 experimental run the wave generator was started from rest. The wave 

 motion in the flume was allowed to reach a quasi-steady state in which 

 the motion at any point along the flume was periodic, i.e., the motion, 

 although not purely sinusoidal, repeated itself with a period equal to 

 that of the wavemaker. It generally took 2 to 3 minutes for this quasi- 

 steady state to be reached in the present experimental setup. As 

 mentioned in Section III of the report it was not possible to attain this 

 quasi-steady state for large amplitude incident waves, which limited the 

 test conditions for which reflection coefficients could be determined. 



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