Shallow Water Wave Transformation through External Factors 111 



consists almost exclusively of narrow, steep wave crests, separated by a stretch 

 of almost smooth surface. Such degenerated waves have sometimes really 

 been observed in shallow water (for I = 50 m, a wave height of 4 m, and 



0-5 



Fig. 47. Cnoidal wave profiles for several water depths, wave lengths and wave heights 

 (+ values for the normalized four half wave lengths of 24 February and 6 September 1911 



near Heligoland). 



a depth below the wave trough of 4 m, a becomes indeed 89°). Thorade has 

 computed wave profiles for different kinds of shallow water waves, which 

 are reproduced in Fig. 48. It shows that like cnoidal waves, there is a steepen- 



-->- I -<' L. 



Fig. 48. Theoretical profiles of different kind of long waves (Thorade) (Height scale 



doubled). , sinus wave after Laplace-Airy (Stokes's wave); , waves according to 



Stokes-Struik; , cnoidal waves by Korteweg de Vries; , orbit of en waves 



(normal height scale). 



ing of the wave crests and a widening of the wave troughs. The orbit of 

 the en waves is pointed at the top; it remains in this form of the orbits 

 derived by Kohlschuetter from trie wave pictures taken on the "Planet" 

 Expedition (see p. 49), Figs. 29 and 30. The Struik wave shows a pointed 

 crest about the same as the en wave, but a flatter trough. The velocity of 

 propagation of the en waves is given by 



ygh 



i + 



2k 2 h 



'-f 



(V.3) 



