port speed (w) at the sea surface is expressed 

 by the formula 



IV = WH/LyC (1.7) 



Figure 1.4. — Orbital motion during two wave periods 

 of a water particle in a deep-water wave of mod- 

 erate or great height. In two wave periods the for- 

 ward displacement equals 2wT. 



The speed is appreciable for high, steep 

 waves but is very small for low waves of long 

 period. Mass transport in waves has received 

 little attention in previous work because in 

 most practical applications it is sufficient to 

 consider the water particles as moving in cir- 

 cles regardless of the wave height. In order 

 to understand the growth of waves through 

 wind action, however, it is necessary to take 

 the mass transport speed into account. 



Interference of Waves; Short-crested Waves; 

 White Caps 



When waves of different heights and lengths 

 are present simultaneously the appearance of 

 the free surface becomes very complicated. At 

 some points the waves are opposite in phase 

 and therefore tend to eliminate each other, 

 whereas at other points they coincide in phase 

 and tend to reinforce each other. 



As a simple case consider two trains of waves 

 which have the same height and nearly the 

 same velocity of progress. Owing to interfer- 

 ence, groups of waves are formed with wave 

 heights roughly twice those in the component 

 wave trains, and between the wave groups are 

 regions in which the waves nearly disappear 

 (fig. I.5A) . Analysis shows that these groups 

 advance with a speed which is nearly equal to 

 one-half of the average speed of the two trains. 



As another example, consider the simultan- 

 eous presence of long, low swell and short but 



high wind waves. The resultant pattern is 

 illustrated in figure I.5B from which it is evi- 

 dent that the short, high waves dominate to 

 such an extent that they obscure the presence 

 of the swell. 



So far the discussion has dealt only with 

 long-crested waves, that is, waves with very 

 long, straight crests and troughs. Waves, how- 

 ever, can also have short, irregular crests and 

 troughs. In the presence of such short-crested 

 waves the free surface shows a series of alter- 

 nating "highs" and "lows", as indicated in 

 figure 1.6. This figure illustrates the topogra- 

 phy of the sea surface, "highs" being shown 

 with solid lines and "lows" with dashed lines. 



White caps are formed by the breaking of 

 relatively short waves which often appear as 

 "riders" on longer waves (fig. I.5B). At wind 

 speeds of about Beaufort force 4, such short 

 waves grow so rapidly that their steepness 

 reaches the critical value and they break. If 

 interference occurs, long waves also may attain 

 this steepness and break. 



Figure 1.5. — Wave patterns resulting from interfer- 

 ence. A. Interference of two waves of equal height 

 and nearly equal length, forming wave groups. 

 B. Interference between short wind waves and long 

 swell. 



Figure 1.6. — Short-crested waves. L is the wave-length, 

 L' is the crest length. 



