For a constant measurement elevation, e.g., z + h/2 = 200, Equation 

 (4) results in a relationship between the wind velocity u„ n for that 

 elevation and the shear stress velocity, u* (Figure 3). This representa- 

 tion reveals that the shear stress velocity is related in a linear manner 

 to the wind velocity. We are now in the position to determine the shear 

 velocity u*, with the help of Figure 3, from a single wind velocity 

 measurement, say for example, at an elevation of 200 cm, and thus ac- 

 cording to Equation (4) to compute the total vertical wind profile. 



Wind profile measurements above the waves of shallow pools at low 

 tide lead to roughness parameters of an order of magnitude equal to 

 that for tidal sea providing that an initial time period of 2 to 3 seconds 

 has elapsed after the change of base. 



The following conclusions have been made from the studies of these 

 measurements over the tidal sea. Wind profile over the tidal sea, at 

 least from the surface to an elevation of 2 m, is not influenced by wave 

 height. The sea surface thus does not possess any constant "roughness" 

 in a real sense. On the contrary, the average field of wind over the 

 sea waves could be satisfactorily represented by equations which are 

 similar to v. Karman* s formula for flow over smooth surfaces, and which 

 are characterized by the inverse proportionality between the roughness 

 z - here purely formally defined - and the shear stress velocity u*. 

 The so-called "roughness" of the water surface thus decreases with in- 

 creasing shear stress velocity (i.e. with increasing wind velocity) in- 

 dependent from wave height. Whether the slight influence of the wave 

 shape (tan a ) as found by Motzfeld in his model experiments actually 

 exists will nave to be left unanswered, as it could not be determined 

 from the measurements, possibly having been obscured by scatter. 



If we now return to the point of departure of our observations, the 

 question of transformation of energy from wind to waves, we would conclude 

 on the basis of our measurements that as indicated by the experiments 

 on models by Motzfeld, the pressure resistance of sea-waves plays a minor 

 role in comparison to the frictional resistance. In wave theory, then, 

 the term describing the dependence upon wind pressure would have to be 

 less than the term describing the tangential force of friction. Above all, 

 it appears that during the generation of initial waves with an approximate 

 wave length of 2 cm, friction is the most important criteria next to 

 surface tension, while during the following transformation and further 

 development of the waves, suction and pressure effects of the field of 

 wind become important factors. Investigations striving for clarification 

 of the question are still in progress. 



REFERENCES 



1. Thomson, W., Phil. Mag. (4) XLI (1871) 



2. Helmholtz, H. v., Sitz. Ber. K. Ak. Wiss. Berlin, 761-780 (1889) 

 Sitz. Ber. K. A. Wiss. Berlin. 853-872 (1890) 



3. Jeffreys, H., Proc. Roy. Soc. London A 107, 189-206 (1925) 



A 110, 241-247 (1926) 



