308 



vertical profile where the curvature is greatest. In our measurements, this 

 is poorly defined because the curving portion of U(z') lies too close to the 

 water for accurate measurement with the fixed probe. Thus, the use of Eq.. 

 (6) with Eqs. (7) and (8) can be expected to give only an order of magnitude 

 estimate of Cs ' • 



In addition to the problem of using the experimental data in Eqs. (7-9) > 

 the application of a definition for proper air velocity must be considered. 

 Eqs. (7-9) apply to flow over a solid boundary. When the boundary is moving 

 and waves are superimposed on this motion, the air speed relative to fixed 

 coordinates may be an incorrect estimate for U(z'). Two other systems of 

 velocity coordinates can be used. The air velocity relative to the surface 

 drift may be a better system^ or as Benjamin (1959) has noted, the motion 

 relative to the phase speed c may be better than the fixed system of 

 reference. Introduction o f either one of these reference velocities will 

 affect the definitions of 6* , , 6 , and Cg ' . 



In spite of these difficulties, it is useful as a first approximation 

 to apply Eqs. (7-9) for evaluating Cg'. Calculations of the local drag co- 

 efficients based on the data for U(z') were made, and some typical results 

 for 6* ,e , and Cs' are shown in Table I. These results indicate that 

 Cg' decreases somewhat with fetch, but tends to increase with wind speed. 

 The decrease with fetch is typical of the variation in Cg' in the context 

 of a growing boundary layer over a solid surface. 



TABLE I 



F (meters) Nominal Average 

 Air Speed (mps) 



U (mps) 

 oo 



6 (cm) 6* (cm) 6 (cm) C ' x 10" 



2.14 

 4.58 

 7.03 



5.2 



4.76 

 5.20 

 5.48 



7.12 

 14.0 

 17.8 



2.00 

 2.80 

 4.04 



0.682 3.39 

 1.23 2.65 

 2.08 2.33 



2.14 

 4.58 

 7.03 



7,7 



7.20 

 7.95 

 8.80 



13.7 

 19.6 

 22.8 



97 

 60 

 43 



1.44 

 2.28 

 2.82 



5.66 

 4.32 

 3.31 



2.14 

 4.58 

 7.03 



11.6 



10.8 

 12.1 

 12.8 



12.7 

 19.3 

 21.6 



3.18 

 4.90 

 5.68 



1.40 

 2.35 

 2.74 



5.31 

 3.75 

 2.50 



Using the_nominal average velocity (O.85 Uqq measured at large fetch )_^ 

 estimates of Cg were calculated by averaging each set of three values of Cg' 

 for the ranges of Uqo in Table I. As a comparison to Goodwin's results, the 

 three estimates of TJg by this method are plotted as triangular points in 

 Figure 12. The data for Cg by two different calculations check reasonably 

 well for the 5-1 cm depth of water. 



