Because of these technical difficulties in making measurements at 

 sea, the investigations with solid wave models which Motzfeld^ ■ ' employed 

 in a wind channel in order to study the flow over such wavy walls are of much 

 significance. One must keep in mind, however, that the experimental con- 

 ditions deviate essentially from conditions of waves at sea, such as 

 wave progression, yielding of water surface, and orbital motion of water 

 particles. Therefore one cannot expect that the results obtained by 

 Motzfeld with solid wave models would also apply to the sea. 



Before describing the investigations by Motzfeld, a few important 

 basic concepts of the theory of turbulence, which will appear below over 

 and over again, will be briefly explained. In observing flow along a wall 

 we are accustomed to describe the internal bonds caused by turbulence 

 between adjacent stream lines as the effect of tangential shear force, or 

 a tangential shear stress T , (force/unit area). In the air layer close 

 to the ground this shear stress can be considered as a good approximation, 

 independent of height, and thus can be set equal to the shear stress To , 

 acting immediately at the ground, or as the case may be, at the water 

 surface. Still more frequently than T in the theoretical representa- 

 tion of turbulent flow, there appear s the following combination of shear 

 stress To » and air- density, p; Y^o/p . Since the value is essentially 

 determined by the shear stress, and because it has the dimension of a 

 velocity, it is denoted as shear stress velocity u*. It has an order of 

 magnitude of the turbulent fluctuations. Prandtl improved extraordinarily 

 the description of turbulent processes in formulas by introducing the 

 term mixing length. Analogous to the mean free path of molecules in the 

 kinetic theory, the mixing length is defined as the length of the path 

 of an air particle through which it travels in an isolated manner, re- 

 taining its temperature, its impulse, etc., before it again mixes itself 

 with its surroundings. In the layer of air near the ground, this mixing 

 length increases with height in a linear manner. Along a smooth surface 

 it is equal to zero. However, in the case of rough surfaces, the mixing 

 length at the wall, i.e., at the peaks of wall roughnesses, will not 

 vanish, but will be determined by the dimensions of humps, or as the 

 case may be, of concavities. Thus, at a rough wall the minimum value of 

 the mixing length can be expressed by the formulas through a value z , 

 which will be called the roughness, and which in a simple manner is dependent 

 upon the humps or concavities in the wall. However, this obvious meaning 

 of roughness value z Q , when considering the vertical profile of wind 

 velocity (where z Q has an important part), will have to give way to a 

 more formal one. According to Prandtl^6) f the vertical wind velocity 

 profile in the layer of air adjacent to the ground (marked by a shear 

 stress independent of elevation and linear increase in mixing length) 

 can be expressed with sufficient accuracy by the logarithmic formula: 

 -. z + z z + z 



K 

 where: 



In = 5.75 u* log - (1) 



u = the wind velocity, 



z = the elevation above the ground, 



