was not the case. Lacking a more suitable measured value, the steepness 

 of the waves, i.e., the ratio of wave height to wave length, h/\ , had 

 to serve as a provisional measure for the maximum slope of the wave pro- 

 file. In the case of sine waves, tan a = irh/\ holds. Here too the 

 elevation measurements were corrected according to the average wave 

 height. 



As a result of this work, it was found that there was a definite 

 dependence of roughness upon shear stress velocity in the sense called 

 for by Equation (3). An influence of wave steepness, however, could not 

 be established, or perhaps was obscured by the scatter. 



xn order to cover the average values as often as possible, grouping 

 according to the steepness, h/\ t was discontinued, and only an arrange- 

 ment according to the wind velocities was made. The number of individual 

 runs in the six different wind groups lay somewhere between 20 and 25. 

 The average wind profiles obtained in this manner have been plotted in 

 Figure 1. In this figure a logarithmic scale was selected for the elevations 

 z + h/2. It can be noted that the vertical distributions of wind velocities 

 are represented by straight lines, hence the logarithmic law (1) is 

 satisfied. Figure 2 gives the roughness values, z , as obtained from 

 these profiles (also plotted on a logarithmic scale) as a function of the 

 proper shear stress velocity, u*. This presentation also contains: 



1. The roughness values z as a function of u*, which, according 

 to the formula by v. Karman, would result for flow over a 

 smooth surface. 



2. The roughness values z as a function of u*, which, according 

 to Equation (3) by Motzfeld, would hold for a flow over waves 

 with round crests. Here a sine wave (tan a = tfh/\ ) was 

 assumed which had a steepness h/X = 0.05, which corresponds 

 to the average condition on the sea. 



The measurements show that the roughness values for the sea surface 

 indicate a slight decrease with increasing shear stress velocity (i.e., 

 wind velocity), and are parallel to the curve for smooth surfaces given 

 by v. Karman (shifted toward higher roughness). The numerical values 

 for z lie between 0.006 and 0.002 cm. The values computed from Equation 

 (3) by Motzfeld come remarkably close to the measured ones. Differences 

 could be ascribed to the deviation of the waves from simple sine form, 

 which was used as the basis for computation. The fluctuations in the 

 measured roughness values probably represent the effects of scatter; they 

 are not produced by changes in steepness. The measured values of z 



could be approximated by the relation z = ; hence, the 



° 2.1 u* 

 vertical increase in wind velocity over tidal flats takes on the form 



u = 5.75 u* log 2 ' 1 y "* (z + h/2). (4) 



