114 Shallow Water Wave Transformation through External Factors 



parison between observed values and the wave velocity calculated according 

 to the Laplace formula. The observations were grouped to eliminate random 

 observational errors. The agreement is good, notwithstanding a slight tendency 

 of the observed wave velocities to exceed the theoretical ones. However, 

 deviations are small. 



A few good stereophotogrammetric wave pictures made by Eckhardt 

 (1931) for the construction of the harbour of Heligoland, can be used for 

 testing the theoretical results. Those taken on 24 February and 6 November, 

 1911 are particularly remarkable. Figure 50 shows in the first series of pictures 

 a partial section of the wave plane south-west of the western breakwater, 

 where the wave-train is not yet disturbed by the harbour construction. More 

 to the north, there was a rather strong shock surf against the breakwater. 

 From both series of pictures an average wave-train was derived, for an 

 appropriate zone (in the first case over a width of 200 m, in the latter case 

 over a width of 450 m) by drawing longitudinal profiles, if possible per- 

 pendicular to the wave crests and by averaging same. This could be done, 

 in view of the very uniform waves in the area. Small irregularities were thus 

 eliminated and a good wave profile obtained. Figures 51 and 52 give these 



Fig. 51. Average from five wave profiles taken from a stereo photogrammetric picture 

 24 February, 1911 South-west of East Heligoland breakwater. Wind: W.N.W., 17-20 m/sec. 

 When picture was taken mean water level was +3-43 over zero level. Average wave length: 

 114 m± 8 m; average wave height: 3-32 m; wave velocity: 10-12-5 m/sec (height scale 1 :51). 



Fig 52. Average from ten wave profiles on 6 November, 1911, same location as Fig. 51, 

 Wind: W. 18-20 m/sec; Mean water level was +4-35 m over zero level. Average wave length: 

 143± 10 m; Average wave height: 4-5 m; Wave velocity: 10-15 m/sec (height scale 1:5-1). 



typical average waves for both cases, and also all the data necessary for 

 their use. The average wave length and the average wave height were in the 

 first case 114 and 3-32 m, in the latter one 143 and 4-5 m. The graphs show 

 the typical profile of the shallow-water waves with the sharp crests and the 

 wide flat wave troughs; also that in travelling the wave length increases 

 somewhat: in the first case from about 110 to 133 m (except the last wave, 



