SECT. 2] SMALL-SCALE INTERACTIONS 



from which, on transposing and integrating, we find 



q,-q^ = {Elpku^)\n[{D + ku^z)ID]. 



81 



(41) 



From (40), (41) and (39), neglecting D in comparison with ku^z, the evapora 

 tion is given by 



pku^{qs-qz) 



^ {kXvlD) + ln{ku^zlD) 

 and comparison with (31) shows that this is equivalent to 



rsiz) = [{kXvlD)+\n{ku^zlD)]-K 



(42) 



(43) 



Curves of the relationship (43) are given in Fig. 17 for two values of the 

 parameter A that have been proposed : 11.5 by von Karman and 7.8 by Mont- 

 gomery (see Montgomery, 1940, for discussion). The value of D, here and 

 later, is taken as 0.24 cm^ sec-i. 



0.1 

 r£(8m) 



0.05 



c _ 



20 30 40 



u,, cm/sec 



I I I 



50 



60 



14 



Ug, m/sec 



Fig. 17. Theoretical values of the humidity coefficient, Fg (8 m), plotted against friction 

 velocity, u^, and [via (22)] wind speed, wg- 



(a) A = 7.8, (b) A =11.5, (c) A = 27.5 in Sverdrup's (1937) theory; (d) Sheppard's 

 theory; (e) A = 7.8, (f) A= 11.5 in Montgomery's theory for a smooth surface. 



L. Aerodynamically Rough Flow 



Several different theories have been proposed for the case of aerodynamically 

 rough flow. Two of these, due to Sverdrup and Sheppard respectively, are now 

 to be discussed. 



In the theory of Sverdrup (1937), it is assumed that there is a layer of 

 molecular transfer of vapour with diffusivity, D, through a surface air film of 

 thickness, 8, given by (39). In contradistinction, the shearing stress is, of course, 

 transmitted by pressure forces against the surface irregularities, rather than 

 by molecular viscosity. In the region above this layer, turbulent transfer is 

 assumed with the same transfer coefficient as for momentum, i.e. 



Ke = Km = ku^{z + zo). 



4 — s. I. 



