120 Shallow Water Wave Transformation through External Factors 



3. Changes in Form of Waves by Exterior Causes 



When the wind increases in force, the wave crests become higher and 

 sharper and the waves will show a tendency to break. We observe the 

 formation of foam on the wave crests and this will occur with a wind force 

 of about 4 Beaufort. This is so constant that the appearance of foam on the 

 ocean is a characteristic for this wind force. If the wave height increases 

 to the limit of the cycloid and above, the motion of the water particles in 

 the wave crest becomes discontinuous, which will lead to the breaking of 

 the wave crest and to the making of foam. But after the explanations of the 

 preceding chapters, this usual explanation is not any longer valid. If wind 

 velocity and wave height are not any longer in equilibrium (unsteady state) 

 then with too great a wind we have the deficiency in pressure in the faster 

 moving air become greater and greater, and the excess pressure on the side 

 of the water in the wave crests is increasing. The displacement upwards of 

 the water particles becomes stormy and unsteady (p. 75). The water is mixed 

 with air and, consequently, we have foam on the wave crests. The first forma- 

 tion of foam on relatively small waves for a wind force of 4 can be attributed 

 to a not yet attained steady state between wind and waves. We have to 

 compare this to the foam which appears, when the larger waves increase 

 their unsymmetric wave profile and the wave crest topples over. This happens 

 either because the wind becomes too strong and forces the wave profile 

 to become asymmetric, or because the water depth decreases and produces 

 the surf. 



With very strong winds, we observe these enormous breakers, which can 

 become highly destructive. We observe very high waves and mighty breakers 

 where a swell runs against a strong current, i.e. in estuaries and in areas 

 with strong ocean currents and tidal currents. In the vicinity of the wave 

 crest, the orbit of the wave motion becomes compressed through the opposing 

 currents, the crests become higher and steeper until they break in the di- 

 rection of the current. Waves change considerably when approaching the 

 shores, especially when the water depth becomes smaller than half the wave 

 length. The character of the wave changes from a short wave in a deep ocean 

 to a long wave in the vicinity of the shore. The wave velocity decreases from 

 the moment that the wave enters shallow water until it breaks, but the wave 

 period remains unchanged. When a wave continues in shallow water, its 

 wave length becomes smaller and, in general, the wave height becomes 

 larger because the wave fronts are compressed. 



Green (1837) has investigated the influence of the reduction of the cross- 

 section of the wave motion and its influence on the wave height. He found 

 that the wave height is inversely proportional to the fourth root of the water 

 depth; the influence of the variation of the cross-section becomes more 

 important if a wave enters a funnel-shaped estuary, and the wave height 

 changes here inversely proportional to the square root of the width of the 



