street^ Chan and Fromm 



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T- 43.493 



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V 



Fig. 11. Periodic waves (v contours) 



In Fig. 11, the time history of the v-field is shown. The 

 plot increment for the contours is also 0.025 per line. On the chan- 

 nel floor, V = 0,0. The first contour above the floor has v = +0.0125 

 if it is in front of the wave crest, and v = - 0.0125 if it is at the 

 back. The sparse contours on the right-hand side of the channel at 

 t = 80. 984 and t = 84.233 indicate that when the standing waves 

 reach their peaks the fluid velocity almost becomes zero temporarily. 

 This phenomenon is caused by the interaction of the reflected and 

 incident waves that tend to alternately enhance and cancel each other. 



In Fig. 12 we used a long channel with L| = 60.0. Thus the 

 "progressive" wave patterns can be ancilyzed before the reflection 

 sets in. The wave train is composed of a group of dispersive waves. 

 The amplitude increases from the leading wave to the third wave. 

 It then decreases on the following waves. This observation suggests 

 that the nonlinear response of the fluid system is somewhat out of 

 phase with the forcing function at the surface. Therefore, it appears 

 that pure nondispersive periodic waves cannot be generated by the 

 disturbance described by Eq. (53) unless the amplitude p^ is very 

 small. 



Because of its symmetrical profile, we selected the fourth 

 wave in Fig. 12 and compare it in Fig, 13 with Stokes' second-order 

 and third-order theories [ Wiegel, 1964] . Good agreement with the 



180 



