At a greater distance from the boundary, the effects of turbulent vis- 

 cosity given by (u'w') are many times larger than vBu/Bz, and the 

 viscous term may be neglected. The simplicity of equation (5) can be 

 regained by introducing a microviscosity coefficient, K;,,, to obtain: 



T = p K;;j au/8z . (6) 



Within at least the lowest part of the boundary layer, the stress 

 is sensibly constant and equation (6) may be regarded as a differential 

 equation for the mean fluid velocity profile u(z) . Thus, 



3u _ Uj 



3z " K„ 



(73 



where 



u* = (x/p)'^ (8) 



is called the friction velocity. 



A variety of arguments can be used to show that in the absence of 

 density stratification the integral of equation (7) has the form: 



^ = i Ln (z/zj (9) 



where k is von Karman's constant, generally taken as 0.4, and z^-, is 

 often taken as a measure of the surface roughness. Proofs and alter- 

 native definitions of z^, where needed, are given in most advanced text- 

 books on dynamic meteorology, fluid mechanics, or turbulent flow 

 (e.g., see Hinze, 1959 (ch. 7); Lumley and Panofsky, 1964; or Kraus, 

 1972 (ch. 5)). 



By combining equation (8) with equation (1) it is seen that: 



Cj = u2 ^ 



(10) 



It is clear from equations (7) , (8) , and (9) that u, and therefore 

 Cj, are functions of z, where u^, being a measure of the surface stress, 

 is independent of z. This is often emphasized by writing the_drag coeffi- 

 cient as Cg, where z is the elevation in meters for which u is deter- 

 mined. Ten meters is usually taken as the standard elevation for specifying 

 the wind velocity. Thus, the "reference velocity" in Table 1 is often 

 obtained by using equations (9) and (10) to adjust the observed velocity 

 to an elevation of 10 meters. 



23 



