SECT. 5] WIND WAVES 667 



When one is able to create artificially a succession of, say, four or five waves on 

 otherwise calm water, it is easy to see how new wave crests continually arise in 

 the rear of the group, travel forward through it and then die away as they 

 move out of it in front. The group itself, that is the region of water where the 

 waves are high, also advances, but at a lower speed. The wave group is the 

 region possessing the wave energy and, unless this energy is dissipated in some 

 way, its progress can be followed over considerable distances and the wave 

 group has a permanence that is not shared by individual wave crests. In- 

 dividual waves at sea usually grow up, travel, and die away in much less than 

 30 sec, and if they attain a white cap it is only for a very few seconds. But 

 the spreading of wave energy from a storm centre, that is the progress of wave 

 groups, has been traced over great distances. 



A train of waves has considerable energy. This comes partly from the water 

 motion (kinetic energy) and partly from the water having been lifted up from 

 the troughs into the crests (potential energy). The average energy per unit 

 area of sea surface is 



where p is the density of water, g the acceleration of gravity and h"^ the mean 

 square elevation (or depression) from the undisturbed sea-level. If the waves 

 form a sinusoidal wave train whose height (crest to trough) is H, the average 

 energy per unit area is 



IpgH^ 



Wavelength, water depth and frequency do not enter into this formula. 



If a group of waves travels over the surface of otherwise undisturbed water, 

 the energy in the w^ave motion is evidently being handed on from one region of 

 water to the next. Even where there is no very clear division of waves into 

 groups the energy may be thought of as advancing through the water at the 

 group velocity. A moderate ocean swell for instance, perhaps 2 m high when in 

 deep water, has an energy of 5 x 10^ ergs/cm^ of sea surface. If the period is 

 10 sec the group velocity in deep water is 7.8 m/sec and energy is transmitted 

 at the rate of 3.9 x 10^ ergs sec~i cm^i of crestline. If the swell reaches a coast 

 this energy is nearly all spent in turbulence in the surf zone. It approximates to 

 40 kilowatts per metre length of shoreline. 



2. The Description of a Complicated Wave Pattern : the Wave Spectrum 



This subject is treated in detail in Chapter 15, but is so fundamental to the 

 study of waves and to the understanding of this section, that it is felt worth- 

 while to include a brief discussion of it here. 



A particular record of natural waves (for example, a record of the height of 

 the water surface at a vertical pole) is complicated and very local in time and 

 space. A record from the same pole at a different time or from another pole 

 some distance away at the same time, will bear no resemblance to it in detail. 

 In fact, the detail in such a record is random in character and unpredictable. 



