305 



Systematic deviations between Cg and clp might be expected since both 

 the effect of surface tension and of finite wave amplitude were not considered 

 in deriving Eq. (3). The correction in ex for surface tension in deep water 

 waves was found to be negligible for the experimental observations. However, 

 the Stokes correction of Cp for gravity waves of finite amplitude (e.g.. 

 Lamb (1932)) could vary from 1 percent to 11 percent (increase) if it is 

 assumed that the amplitude of significant waves is 3.0^ a (e.g., Sibul 

 1955))- Thus, Lilly's equation would give values of c„ somewhat larger on 

 the average than the experimental data. 



The effect of finite amplitudes in the wind waves may be offset partially 

 by the influence of turbulence in the water. Dye traces of the motion in the 

 water indicate that the water flow was turbulent and not laminar. The use 

 of a turbulent velocity profile having a steeper gradient near the surface 

 than the parabolic curve but having the same drift velocity at the surface 

 would result in a smaller correction factor for drift than predicted by 

 Eq. (3). 



These results indicate that the significant wind waves on the water in 

 the channel travel relative to a mean drift approximately as gravity waves 

 of small amplitude . The waves tend to propagate in this way in spite of the 

 steady pushing of the moving air. 



Shearing Stress on the Water 



An important parameter for measuring the action of the wind on the water 

 is the shearing stress on the water surface, t . This is often calculated 

 in terms of the drag coefficient 



% - -^3/ Pa"' • ^""^ 



where p^ is the_density of the air. An average value of the shearing stress 

 at the surface Tg can be estimated for the data of the present study by 

 taking a force balance on the body of air, or the body of water in the chan- 

 nel at a given time. The shearing stress on the (smooth) walls, on the top 

 of the tunnel and on the bottom can be_estimated in well known ways (e.g., 

 Schlicting (1960)). Then the stress Xg can be calculated from differences 

 between the pressure gradient (on the set up of water), and the shear forces 

 on the walls, bottom and the top. This has been done for our data by Goodwin 

 (1965). His results are expressed as the average drag coefficient based on 

 the average air velocity in the tunnel as defined by: 



C = 7 / p U 2 (5) 



s s a avg 



Estimates of C as they vary with Ug^^g are shown for two different depths 

 in Figure 12. For comparison, the daxa of other investigators, Francis 

 (1951), Keulegan (1951), and Fitzgerald (1962) are also indicated. Goodwin's 

 calculations by the force balance technique as applied to the water and the 



