Ch. 15] FACTORS INFLUENCING THE PROBLEM 285 



apparent, and the very long "tidal" waves, or tsunamis, of infrequent 

 occurrence. 



The surface waves and swell result from atmospheric disturbances 

 over the ocean and are propagated over long distances with very 

 slowly diminishing intensity. As a general rule these waves are al- 

 ways present on the ocean to a greater or lesser degree, from the days 

 of dead calm when only very long and low remnants of swell from 

 far-distant storms exist, to the days of violence when waves are being 

 generated by a storm on or near the coast. Their action is unceasing 

 and of an almost unbelievable magnitude. It is believed at present 

 that waves derive their energy entirely from the wind systems to which 

 they are subject, and that this energy is dissipated, except for a 

 negligible fraction lost to internal friction, on the shores ultimately 

 attacked by the waves. "Tidal" waves or tsunamis constitute a special 

 case; because of their infrequent occurrence in highly violent form, 

 they will not be discussed here, although they can by no means be neg- 

 lected. 



Theoretical studies, confirmed by laboratory experimentation and 

 some observations in nature, show that surface waves involve motion 

 of the water only to a depth equal to about one-half the length of the 

 wave from crest to crest. The water moves in circular or elliptical 

 orbits or paths which do not quite close ; that is, there is a small excess 

 forward motion associated with the passage of each wave, and this 

 motion has been called the mass transport of the wave. Its mag- 

 nitude is only a few percent of the actual orbital velocities, which range 

 from to a frequently attained maximum in excess of 6 feet per second. 

 The velocity at the bottom varies with the depth of water, the wave 

 length or period, and the wave height; it is the velocity most effective 

 in causing erosion and transportation of material. As a wave moves 

 into shallow water, the bottom velocities due to the wave increase by 

 reason of decreasing depth but the wave energy is not greatly changed. 

 Finally the wave breaks in surf, dissipating most of its energy in a 

 highly turbulent, violently churning area, with the remainder dissipated 

 during the rush of the wave up the beach. It is commonly held that 

 the most active erosion and transportation zone is the area involved 

 in the break of the wave and its uprush on the beach. 



A fair evaluation of the energy available from the waves can be 

 made if knowledge of the wave periods and heights is available, be- 

 cause it is known that the wave energy is proportional to the product of 

 the period squared (T 2 ) and the height squared (H 2 ) : 



E ~ T 2 H 2 



