Shallow Water Wave Transformation through External Factors 115 



which appears to be disturbed in its length), in the latter case from 136 to 

 153 m. In both cases the depth decreases in the direction of propagation 

 from about 8 to 6 m, and 9 to 7 m respectively, except for a small elevation 

 of the ocean bottom up to a depth of 4 m underneath the second wave trough 

 in the first case, and a larger elevation up to a depth of 6 m beneath the 

 fourth crest in the second case. The profile keeps its form, but during its 

 travel the crest becomes sharper on both sides. The trough is very flat and 

 in many localities the wave trough is practically level over a large surface. 

 This flattening shows particularly well in the median waves in the second 

 case; the last wave has an absolutely flat trough. 



To test the theory, the first four half waves were averaged. These average 

 wave profiles are shown in Fig. 53. To compute the cnoidal wave profiles, 



5 



4 



E 3 



20 



30 40 



X, m 



50 



60 



?0 



Fig. 53. Comparison between observed and cnoidal wave profiles. Upper figure: 6 November, 



1911; lower figure: 24 February, 1911; Average values of four half wave lengths. 



, cnoidal wave profile; , observed wave profile. 



we have the following value: \l = 570, and 71 -5 m respectively, and for 

 2A = 3-32 and 4-67 m respectively; then we take h =9-5 and 12-5 m re- 

 spectively (from below the wave trough), so that in both cases a becomes 11 h°. 

 The computed cnoidal wave profiles have been entered in the figure as dotted 

 lines. They correspond fairly well with the observed wave profile, but in both 

 cases we find the same systematical deviation: in the upper part of the wave 

 slope the computed profile is above, while in the lower part it is below the 

 observed curve. The deviations are not very large, but characteristic. If we 

 vary a, we still have the same deviations. As Fig. 47 shows, the values of a 

 in the crest are larger than 80°, whereas in the wave trough they are about 65° 

 and 60°. The last wave in Fig. 52 fits pretty well a = 88°, but would require 

 for a wave length of 153 m and a wave height of 3-4 m a water depth under- 

 neath the wave trough of 8-75 m. The observed water depth varies between 

 7-7 and 97 m, with an average of 87 m, which corresponds to the theoretical 

 value. 



According to equation (V.3), the velocity of propagation is in the first 

 case c = 10-56 m/sec, in the second case c = 1218 m/sec. The observed 

 values are not accurate and are not comparable to the theoretical values; 

 the values do fit the Laplace equations better than the equations of Lagrange. 



8* 



