operated with any type of input boundary data. Their results are presented 

 in Figure 86 (a, b, c) . The surface elevation contours (a) result from 

 H =1.5 meters (T = 10.5 seconds) at the harbor entrance and generate 

 the wave amplification factors K shown in (c) for 10 different positions 

 along the quay (b) . The difference between rms wave heights in the physical 

 and numerical models was small enough to provide an acceptable level of 

 confidence in the accuracy of the models generated by the Boussinesq theory. 

 Figure 46 is a perspective plot of waves in the outer harbor shown in Figure 

 86(a). This is the only published comparison of the two-dimensional numer- 

 ical results with physical experiments found in the literature. 



Comparisons of the two-dimensional computations with other analytical 

 methods are also available. Figure 87 demonstrates a comparison for pure 

 diffraction theory with the classical analytical results of Sommerfield 

 for linear, light waves (Abbott, Petersen, and Skovgaard, 1978). The analy- 

 tical wave orthogonals and fronts shown as dashlines are found to agree 

 with the numerical methods as long as waves with very small amplitude 

 (linearized wave theory) are tested. . 



Hebenstreit and Reid (1978) tested their numerical model against 

 some experimental results for solitary wave reflection from vertical barriers 

 and linear theory (Snell's Law) refraction over a plane beach. The finite- 

 difference algorithm devised by Street, Chan, and Fromm (1970)'' was employed. 

 Figure 88 demonstrates the numerical results (solid line) for wave reflection 

 against the ripple tank measurements of Perroud (1957)^°. The Mach-Stem 

 effect was observed in the numerical work for incident angles between 20° 

 and 45°, as expected. Numerical accuracy was considered quite good since 

 the calculations neglected wall friction, the measured values were quite 

 small, and it was not certain if steady state had been reached in Perroud 's 

 values. 



The wave refraction studies were very revealing. Significant differ- 

 ences in wave crest bending (refraction) and wave shoaling were observed 

 in the model as compared with that predicted by linear wave theory and 

 Snell's Law for refraction. The Boussinesq theory simulations for solitary 



^^HEBENSTREIT, G.T., and REID, R.O., "Reflection and Refraction of Solitary 

 Waves — A Numerical Investigation," Report 78-7-T, Oceanography Department, 

 Texas A&M University, July 1978 (not in bibliography) . 



''''STREET, R.L., CHAN, R.K.C., and FROMM, J.E., "Two Methods for the Computa- 

 tion of the Motion of Long Water Waves — A Review and Applications," Stanford 

 University, Department of Civil Engineering, Technical Report No. 136, 1970 

 (not in bibliography) . 



^^PERROUD, P.H., "The Solitary Wave Reflection Along a Straight Vertical 

 Wall at Oblique Incidence," University of California, Berkeley, Technical 

 Department, Series 99, Issue 3, Berkeley, Calif, (not in bibliography). 



215 



