SECT. 5] 



WIND WAVES 



081 



The changing characters of the waves as they enter shoaling water are 

 summarized in Fig. 8. After an initial small decrease in height the waves begin 

 to grow higher, their speed decreases and the orbits of the water particles 

 gradually lengthen into ellipses so that the forward and backward motion is 

 greater than the wave height. These changes are dependent on the ratio of the 

 depth of water to the wavelength which the waves had where the water was 

 deep. It is worth remarking therefore that in a given depth of water, near the 

 surf zone for example, swell of low frequency will have grown relatively more 

 than the wind waves and will be more obvious there than in the open sea. 



The curves of Fig. 8 apply only to quite low waves passing over gently 

 sloping beaches. They are given by an approximate theory which merely 

 adjusts the wave heights everywhere to make the rate of forward transport of 

 energy the same at all stages in the wave's f)rogress. More recent theoretical 

 treatments have found exact expression for waves striking steep beaches or 

 overhanging cliffs, subject again to the assumption that the actual wave height 

 is always small. A digest of these treatments is given by Stoker (1957, chap. 5). 



7. The Surf Zone 



As waves enter into gently shoaling water, their group velocity decreases 

 and, to maintain the same forward flow of energy, the waves grow higher. 

 They ultimately reach a limiting form in which the crests are ridge-like. Pro- 

 gress into still shallower ground leads to turbulent water being spilled from the 



(a) 



(b) 



^^^y^-^^^y..^^^ 



Fig. 9. A spilling breaker (a) and a plunging one (b). 



crest and thereafter the wave continuously dissipates energy in this way as it 

 advances. This is one style of breaking. It is often followed by a second stage 

 in which the whole wave crest falls forward (Fig. 9). On steeper beaches, the 

 spilling stage may never develop ; the energy is then dissipated very quickly in 

 a single forward plunge. 



The surf zone is a region in which waves tend to be steep and in which non- 

 linear processes become very important. Consequently it is the region least 

 amenable to theoretical treatment. If the beach is sufficiently steep there may 



