General Remarks on Waves 



11 



the progressive form of the surface, but also to the oscillatory motion which 

 decreases rapidly with depth, in as much as the base of the cornsticks remain 

 equally at rest. The only difference is that the length of the stems remains 

 constant, whereas the water columns stretch and shrink as the wave passes by. 

 In shallow water where /? is smaller than half a wave length, the orbital 

 motion reaches to the bottom and is of about the same size in all depths. 

 The motion of the individual water particles then corresponds more to 

 a forward and backward shift of whole water columns whereby they become 

 at times wider and thus shrink in vertical extent or at times narrow and 

 thus stretch depending upon whether they are situated in a wave trough 

 or wave crest. Figure 5 shows rectangles of equal size in a position of rest 

 and during the passing of the wave and the resultant wave at the surface. In 

 these deformations the horizontal components of the velocity and acceleration 

 of the particles play the main role, whereas the vertical acceleration can be 

 neglected. With deep water waves (surface waves) on the contrary, the verti- 



i ; ;-- -- + 



Fig. 5. Behaviour of vertical line of particles during passage of a long wave (shallow depth). 



cal component of acceleration must be considered. It is, therefore, quite 

 possible that an ocean is rather shallow relative to the long waves of ocean 

 tides, whereas it must be considered as very deep even for the largest of the 

 ordinary wave trains that can be perceived on its surface. Deep and shallow 

 water, therefore, are only to be considered in relation to the wave length. 

 Waves of tidal periods are the best example of such long waves, which 

 therefore are also called tidal waves; the name long waves is mostly used; 

 Scott Russell called them also primary waves. 



An excellent summary of the most outstanding characteristics of ocean 

 surface and long waves has been given by Sverdrup (1942, p. 521) which 

 we quote here: 



Character of wave 



Velocity of progress 



Movement of water par- 

 ticles in a vertical plane 



Surface waves 



Progressive, standing, 

 forced or free 



Dependent on wave length 

 but independent of depth 



In circles, the radii of which 

 decrease rapidly with in- 

 creasing distance from the 



Long waves 



Progressive, standing 

 forced or free 



Dependent on depth but 

 independent of wave length 



In ellipses which are so flat 

 that practically the water 

 particles are oscillating back 



