appearances on a wave crest of a well defined 

 patch of foam at a considerable distance from 

 the ship. In order to obtain a reliable value, 

 observations should be made for several min- 

 utes and averaged. 



The ivave length L can be estimated by com- 

 paring the ship's length with the distance be- 

 tween two successive crests. This procedure 

 leads to uncertain results, however, because it 

 is often difficult to locate both crests relative 

 to the ship and because of the disturbance of 

 the water caused by the movement of the ship. 



The speed of the tvave C can be found by 

 recording the time needed for the wave to run 

 a measured distance along the side of the ship 

 and by applying a correction for the ship's 

 speed. 



For more detailed instructions on making 

 wave observations see H. 0. Pub. No. 606-e, 

 Sea and Swell Observations. 



Comparison of Measured and Computed Values 



Theory indicates that the speed, length, and 

 period for deep-water waves are interrelated by 

 the formulae 



UK 



T = -\J27r L/g = 27r C/g 

 With C in knots, L in feet, and T in seconds 



c = 1.34 yl = s.osr (i.s) 



L = 0.555C2 = 5.12^2 (I.9) 



T = 0.422 yZ = 0.33C (I.IO) 



Thus, if one characteristic is measured the 

 other two can be computed, and if two or three 

 are measured the correctness of the theory as 

 applied to ocean waves can be checked. Com- 

 parisons of computed and measured values have 

 given satisfactory results, indicating that wind 

 waves and swell in deep water do have the 

 characteristics described above. In general, 

 the conclusion that the ratio H/L always re- 

 mains less than 1/7 is also confirmed by ob- 

 servations as waves of this or greater steep- 

 ness are very rarely reported. 



Empirical Relationships between Wind and 

 Waves 



Observations of waves have not led to clear- 

 cut conclusions about the empirical relation- 

 ships between wind and waves. The following 

 nine approximate relationships have been pro- 

 posed by various workers : 



1. Maximum wave height and fetch. — For a 

 given wind velocity the wave height becomes 

 greater the longer the stretch of water (fetch) 

 over which the wind has blown. Even with a 

 very strong wind the wave height for a given 

 fetch does not exceed a certain maximum value. 

 For fetches larger than 10 nautical miles it has 

 been observed that 



H„a., = 1.5 ^/F (I.ll) 



where i^max. represents the maximum probable 

 wave height in feet with very strong vdnds 

 and F is the fetch in nautical miles. 



2. Wave Speed and Fetch. — At a given wind 

 speed the wave speed increases with increasing 

 fetch. 



3. Wave Height and Wind Speed. — The 

 height in feet of the greatest waves with high 

 wind speeds has been observed to be about 0.8 

 of the wind speed in knots. If the entire range 

 of wind speeds is considered the observed data 

 conform to 



H = 0.026C72 (1.12) 



where U represents the wind speed in knots. 



4. Wave Speed and Wind Speed. — Although 

 the ratio of wave speed to wind speed has been 

 observed to vary from less than 0.1 to nearly 

 2.0, the average maximum wave speed appar- 

 ently exceeds slightly the wind speed when the 

 latter is less than about 25 knots, and is some- 

 what less than the wind speed at higher wind 

 speeds. 



5. Wave Height and Duration of Wind. — The 

 time required to develop waves of maximum 

 height corresponding to a given wind increases 

 with increasing wind speed. Observations 

 show that with strong winds high waves will 

 develop in less than 12 hours. 



6. Wave Speed and Duration of Wind. — 

 Although observational data are inadequate it 

 is known that for a given fetch and wind speed 

 the wave speed increases rapidly with time. 



7. Wave Steepness. — No well established re- 

 lationship exists between wind speed and wave 

 steepness. This lack is probably due to the 

 fact that wave steepness is not directly related 



