to the wind speed, but depends upon the stage 

 of development of the wave. The stage of de- 

 velopment, or age of the wave, can be con- 

 veniently expressed by the ratio of the wave 

 speed to the wind speed (C/U), because during 

 the early stages of their formation the waves 

 are short and travel with a speed much less 

 than that of the wind, while at later stages the 

 wave speed may exceed the wind speed. In 

 order to establish the probable relation be- 

 tween wave steepness and wave age, all wave 

 observations were examined which appeared 

 to be consistent with certain basic require- 

 ments and for which values of H, L (or C or T) , 

 and U were recorded. The corresponding val- 

 ues of H/L and C/U were plotted in a diagram 

 (fig. 1.7). The scattering of the values is no 

 greater than would be expected in view of the 



great errors of measurements. There appears 

 to be a definite relationship between the steep- 

 ness and the age of the wave. This relation- 

 ship, shown by the curve in figure 1.7, plays 

 an important part in the theoretical discussion. 



8. Decrease of Height of Swell. — The height 

 of swell decreases as the swell advances. 

 Roughly, the waves lose one-third of their 

 height each time they travel a distance in miles 

 equal to their length in feet. 



9. Increase of Period of Stvell. — Some au- 

 thors claim that the period of the swell remains 

 unaltered when the swell advances from the 

 generating area, whereas others claim that the 

 period increases. The greater amount of evi- 

 dence at the present time indicates that the 

 period of the swell increases as the swell 

 advances. 



GROWTH OF WIND WAVES 



A knowledge of the height, speed, and direc- 

 tion of progress of wind waves is necessary if 

 their arrival as swell at a distant coast is to be 

 predicted. Direct observations of these wind 

 waves are rarely available, but their height and 

 period can be determined from consecutive syn- 

 optic weather maps if the relationship between 

 wind and waves is known. 



In the area of wave formation the highest 

 waves present at any time depend upon the 

 wind speed, the stretch of water over which 

 the wind has blown (the fetch) , the length of 

 time the wind has blown over the fetch (the 

 duration of the wind), and the waves which 

 were present when the wind started blowing 

 (the state of the sea) . These four factors can 

 all be determined if a sequence of weather maps 

 is available showing the meteorological condi- 

 tions over the ocean area in question at inter- 

 vals of, say, 12 or 24 hours. These maps must 

 be based on a sufficient number of ships' obser- 

 vations to make possible the plotting of fairly 

 accurate isobars from which wdnd factors may 

 be determined. In the tropics, wind observa- 

 tions must be available from ships or exposed 

 stations on islands. In middle and higher lati- 

 tudes, direct wind observations on ships will 

 serve as checks on wind estimates from the 

 isobars. 



Thus, with adequate weather maps at one's 

 disposal, an estimate of the significant wind 



waves can be made if accurate relationships 

 between wave height and wind speed, fetch, 

 and duration are known. Such accurate rela- 

 tionships have not been developed in the past 

 because of the inadequacy of observational data 

 on waves, but they can be determined theoreti- 

 cally from a consideration of the wind energy 

 available for wave formation if the funda- 

 mental assumption is made that the speed 

 (period) of a ivave alivays increases with time. 



The area in which waves are formed is called 

 the generating area. In such an area waves 

 receive energy from the wind by two processes : 

 by the push of the wind against the wave crests 

 and by the pull or drag of the wind on the 

 water. 



The energy transfer by push depends upon 

 the difference between wind velocity and wave 

 velocity. If the waves advance with a speed 

 much less than that of the wind, the push is 

 great, but if the two speeds are equal no energy 

 is transferred. If the waves travel faster than 

 the wind they receive no energy but on the 

 contrary meet a resistance comparable to the 

 air resistance against a moving automobile. 

 The effect of the push of the wind or of the 

 air resistance against the waves depends on 

 the form of the wave. There enters, there- 

 fore, a fundamental coefficient which is related 

 to the degree to which the wave is streamlined 

 and which is called the sheltering coefficient. 



