142 WIND CURRENTS AND WIND WAVES 



On the day preceding the gale a heavy swell with a period of 11.4 sec 

 and an average height of about 6 m came from the northwest. The wind, 

 which had blown as a breeze from the southwest, changed during the 

 night to west-northwest and increased in the morning to a strong gale 

 with velocities up to 23 m/sec. The period of the waves increased to 

 13.5 sec, corresponding to a length of 310 m and a velocity of progress 

 of 21 m/sec, while the wave height increased up to 12 m. Accounts of 

 similarly large waves are given in many cases. In a hurricane in the 

 North Atlantic in December, 1922, when the wind velocity probably 

 passed 45 m/sec, one of the officers of the Majestic reported waves that 

 averaged more than 20 m in height and reached a maximum height of 

 up to 30 m. It is probable, however, that the greatest wave heights refer 

 to occasional peaks of water which may shoot up to elevations consider- 

 ably above the general wave height. In the region of the prevailing 

 westerlies of the Antarctic Ocean, wave heights up to 14 or 15 m have 

 been observed relatively frequently, but the average wave height lies 

 much below these values. 



The observations quoted regarding maximum wave heights and wave 

 length all refer to conditions far from land. Near the shore, waves 

 created directly by wind do not reach such heights, but the height will 

 depend upon the stretch of water across which the wind has blown — 

 that is, the fetch of the wind. Stevenson has combined the average data 

 into the simple formula /t = H '\^F, where h is the greatest observed wave 

 height in meters and F is the fetch of the wind in kilometers. This 

 formula is valid for small bodies of water and is also applicable up to a 

 certain distance from the coast when the wind blows away from the 

 coast. If the fetch of the wind is less than about 10 km, a small correc- 

 tion term has to be added. Not only the wave height but also the wave 

 length increases with increasing distance from shore. 



The ratio between the length and the height of the waves appears to 

 vary between 10 and 20 when a fresh wind blows, but, in the case of a 

 swell, may lie between 30 and 100. Results that have been obtained by 

 different observers will be mentioned later (p. 145). 



Relations Between Wind Velocity and Waves 

 In order to explain some of the phenomena thus far discussed, it is 

 necessary to consider the energy of the waves. This energy can be 

 computed by considering that it is present partly as potential energy 

 and partly as kinetic energy. The computation leads to the result that 

 in the case of long-crested waves the energy per unit area of the sea surface 

 is approximately equal to J^ gpa'^, where g is the acceleration of gravity, 

 p is the density of the water, and a is the amplitude of the wave. In the 

 case of short-crested waves the energy per unit area of sea surface is 

 approximately one half of this amount. 



