12 



General Remarks on Waves 



Vertical displacement 

 of water particles 



Distribution of pressure 



Influence of the earth's 

 rotation 



surface. Motion impercep- 

 tible at a depth which equals 

 the wave length. In some 

 types of surface waves the 

 motion is in wide ellipses 



Decreases rapidly with in- 

 creasing distance from the 

 surface and becomes imper- 

 ceptible at a depth which 

 equals the wave length 



Below the depth of percep- 

 tible motion of the water 

 particles the pressure is not 

 influenced by the wave 



Negligible 



and forth in a horizontal 

 plane. Horizontal motion 

 independent of depth 



Decreases linearly from the 

 surface to the bottom 



The wave influences the 

 pressure distribution in the 

 same manner at all depths 



Cannot be neglected if the 

 period of the wave ap- 

 proaches the period of the 

 earth'srotation.The velocity 

 of progress of the wave and 

 the movement of the water 

 particles are modified 



Surface waves and long waves are, of course, to be considered as the two 

 extremes of a continuous series of waves. However, the transition zone is 

 relatively small, so that the separation in "short" and "long" waves is 

 appropriate. From this difference in velocities between long and short waves 

 (see p. 1 8) it results that a group of waves composed of long waves remains 

 undivided, as each wave travels with the same velocity. This is not the case 

 with a group of surface waves, as the long waves travel faster than the shorter 

 ones. The group disintegrates with time. Long waves, consequently, show 

 no dispersion, whereas, in the case of surface waves, dispersion is faster 

 when the difference in the wave lengths becomes greater. 



3. Group Velocity 



In observing nature, we find that in general an ocean wave does not exist 

 by itself, but that in most cases a train of waves is composed of a system 

 of waves of all possible lengths, each wave progressing with the velocity 

 corresponding to its own particular wave length. The free surface, therefore, 

 is subjected to constant changes, and the wave profile shifts constantly. When 

 observing carefully, e.g. a wave train produced by a stone or a single falling 

 drop of water in a deep water basin, we find that the waves appear in groups. 

 Such an isolated group of waves as a whole shows a velocity smaller than 

 that of the individual waves composing it. Following a single wave in such 

 a group, we see it advances through the group, but, at the same time, it 

 gradually loses its height in approaching the front. The place it formerly 



