12 



THEORY OF SEAKEEPING 



0.02 004 0.06 0.08 0.10 



Height- Ft 



Fetch Length 6.54 Ft 



0.02 0.04 O.Oe 0.06 aiO O.I2 0.14 O.IG 



Height- Ft 



Fetch Length 20 38 Ft ^o 



0.02 0.04 0.06 008 010 0.12 0.14 0.16 018 0.20 022 



Height-Ft 

 Fetch Length 38.23 Ft 



Fig. 12 Joint frequency distribution of wave period and wave height (U = 42.7 fps) (from Johnson and 



Rice, 1952) 



and took for U the measured wind -velocity at the lieight 

 of 30 m (about 100 ft). In the published works on 

 oceanography heights of (i and 10 ni (19.6 and 3o ft) 

 are mo.st often used. For measurements made on .small 

 waves with small fetches and light winds, Roll (19 19) used 

 U as measured at the height of 1 or 2 m. For small 

 waves in a wind flume Francis (1951) measured (' at z = 

 10 cm (0.:33 ft), while .Johnson and Rice (1952) took the 

 mean air velocity in the wind flume. It should be noted 

 that in a wind flume the air \-elocity first increases with 

 height over the rough-water surface, and then decreases 

 again in approaching the upper wall of the flume. The 

 lack of an established similarity law and a definite con- 

 vention is evident. 



The relationship between wind velocity near a rough 

 surface and the tangential drag r per unit of surface 

 area can be stated by c|Uoting from Francis (1951) : 



"The velocity distribution within a boundary layer 

 gives an indirect method of finding the shear stress ou 

 the boundar3\ and this has been used before to find the 

 stress coefficient from field tests. The case of a turbu- 

 lent flow o\'er a .solid rough surface is well known, and it 

 has been shown that at a height z 



u = 5.75 {T/py'-\ogw(z/zo) (25) 



where zo is a length expressing the effective roughness of 

 the surface .... By plotting u against log z. a straight 

 line results, of which the slope gives the value of 



