ratio B./L is plotted against the fetch F for a 

 wind of 40 knots. The curve shows the steady 

 state and the horizontal lines show the stage of 

 development after 10, 20, and 30 hours. 



In the lower curve of figure 1.9 the wave age 

 as expressed by the ratio of wave speed to wind 

 speed, C/TJ, is plotted against fetch. The wave 

 age increases with duration until a steady state 

 appropriate to the particular fetch is reached. 

 Thereafter, any further increase can only take 

 place if the fetch is lengthened. 



If the corresponding values of B./L and C/V 

 are plotted in a graph with wave steepness 

 H/h and wave age C/JJ as coordinates, they 

 fall exactly on the curve in figure 1.7, which 

 represents the empirical data. Actually, this 

 curve has been used for determining the con- 

 stants needed for carrying out all computa- 

 tions. By means of the curves in plates IV to 

 VI it can be ascertained that the empirical re- 

 lationships 1 to 6 are satisfied. 



According to figure 1.9 with a 40-knot wind 

 the wave speed remains lower than the wind 

 speed at fetches up to at least 600 miles. With 

 increasing fetch the wave velocity would ulti- 

 mately exceed the wind velocity and the waves 

 would continue to grow in height but decrease 

 in steepness. 



If the wave speed exceeds the wind speed the 

 waves can no longer receive energy by push 

 but will lose energy because of the air resist- 

 ance they meet. They will, however, continue 

 to receive energy by the pulling force of the 

 wind and will grow in height until this gain is 

 compensated by the loss due to air resistance, 

 which occurs when the ratio C/TJ equals 1.45. 

 The fetch and duration needed for reaching this 

 stage increase rapidly with increasing wind 



velocity as shown in table 1.2. If the fetch and 

 the duration are longer than those listed in the 

 table the highest significant waves will be pres- 

 ent regardless of how much longer the wind 

 blows. 



Table 1.2. — Highest significant waves produced by 

 different wind speeds, and corresponding fetches and 

 durations 



(Ratio of wave speed to wind speed equals 1.45; ratio 

 of wave height to wave length equals 1/45.) 



Waves of the character shown in table 1.2 

 may be present in the trade wind regions and 

 may be approached in the westerlies of the 

 southern oceans. In the middle and higher lat- 

 itudes of the Northern Hemisphere the fetches 

 are so short that with strong winds the wave 

 speed always remains less than the wind speed. 



Plates IV and V show only the significant 

 waves present. These waves have traveled the 

 entire distance from the beginning of the fetch. 

 However, the wind can raise new waves any- 

 where in the fetch, and some of these may grow 

 slowly and reach heights corresponding to the 

 distances they travel, while others may grow 

 rapidly and break. These contribute to the 

 broken appearance of the sea surface which is 

 described as the state of the sea. 



DECAY OF WAVES 



Waves Advancing into Regions of Calm 



When waves spread out from a generating 

 area into a region of calm only half of the 

 wave energy advances with the wave speed. The 

 consequence of this characteristic can be rec- 

 ognized by examining a simple example. As- 

 sume that a series of waves is formed by rhyth- 

 mical strokes of a wave machine which at each 

 stroke adds the energy E/2 in a given locality. 

 The first stroke creates a wave of energy E/2. 



In the time interval between the first and sec- 

 ond strokes one-half of this energy, E/A, ad- 

 vances on wave length and one-half, E/4, is 

 left behind. The second stroke adds E/2 to 

 the part of the energy which was left behind. 

 On completion of the second stroke two waves 

 are present, one close to the wave machine with 

 an energy 3£'/4, and one which has advanced 

 one wave length with energy E/A. By repeat- 

 ing this reasoning, table 1.3 has been prepared. 



11 



