80 DEACON AND WEBB [CHAP. 3 



Information on the behaviour of the temperature-profile is even more 

 limited. The eddy-correlation measurements have given values of KhJKm 

 around 0.7 over the range from near-neutral lapse to i?t = 0.08, the strongest 

 stability investigated. Further work on the effects of stable stratification is 

 clearly needed. 



J . Theoretical Approaches to Bulk Relationships 



Several theoretical approaches have been made to the relating of evapora- 

 tion to measured bulk quantities, as in formula (8). No rigorous approach is 

 possible owing to lack of complete knowledge of the transfer characteristics in 

 the lowest layer of air near the water surface ; and the respective theories are 

 based on differing assumptions as to the nature of these characteristics. The 

 subject, as it stood in 1950, has been reviewed by Anderson et al. (1950) and by 

 Sverdrup (1951). 



Of the various theories which have been proposed, we mention below those 

 which appear to be acceptable by comparison with the observational data 

 available at present. Details of the other theories may be found in the reviews 

 quoted above. In the discussion below, the cases of flow over aerodynamically 

 smooth and aerodynamically rough surfaces are considered separately. 



K. Aerodynamically Smooth Flow 



In the case of aerodynamically smooth flow, the treatment proposed by 

 Montgomery (1940) has been adopted by later writers and no alternative has 

 been proposed. His approach proceeds as follows. 



Over a smooth surface, the shearing stress is transmitted through a thin 

 layer of laminar flow (of the order of a millimetre thick) in the air immediately 

 adjacent to the water surface. On dimensional grounds, the thickness, 8. of the 

 laminar layer is related to the friction velocity, u^, and the kinematic viscosity, 

 ^^ by 



u^hjv = A, (39) 



where A is a constant. 



In the laminar layer, the transfer coefficient for water vapour is the molecular 

 diffusivity, D, so that the evaporation is given by 



E = Dp{qs-q,)jh, 

 i.e. 



qs-q, = ESjDp, (40) 



where subscripts s and 8 refer to the water surface and height respectively. In 

 the turbulent region, reckoning height, z, to be measured from the top of the 

 laminar layer, the transfer coefficient is D + ku^^z, and thus the evaporation is 

 given by 



E = - p{D + ku^z) dqjdz, 



