SECT. 2] LARGE-SCALE INTERACTIONS 107 



see, the premises used in deriving the transfer formulas are best appHcable to 

 the very regions in which we are most interested, namely, the tropics, sub- 

 tropics and, secondarily, the western portions of middle-latitude ocean basins, 

 where air-sea transfer is largest and dynamically most important. 



The basic premise underlying the development is that turbulent exchange is 

 the dominant mechanism affecting the vertical distribution of property from 

 the interface to several tens of meters above it, so that the fluxes obey equations 

 analogous to the heat-transfer equation of classical physics, namely, 



F,= -k/£. (9) 



where Fp is the flux of the property p involved (unit property per cm^ per sec), 

 dpidz is the vertical gradient of the property, and Kp is the so-called "eddy 

 transfer coefficient" (units g cm~i sec^i), many orders of magnitude larger than 

 the corresponding molecular transfer coefficient. 



Starting with equations of the form (9) for momentum, water-vapor and 

 sensible heat flux, and introducing several assumptions as to the nature of the 

 turbulence, we can derive equations relating each flux at the boundary to a wind 

 speed u at "anemometer level" (usually 5-10 m) and the difference between the 

 property in question at that level and at the sea surface. 



The momentum flux formulation is basic to the other two ; in order for an 

 equation of the form (9) to govern vertical transport of horizontal momentum, 

 or shearing stress r, the vertical variations of other forces acting on the air 

 parcels must be negligible in comparison to that of the turbulent frictional 

 forces. In some regions, it has been demonstrated observationally (Sheppard, 

 Charnock and Francis, 1952) that the vertical variation of horizontal pressure 

 forces (thermal wind) is significant even in the lowest few meters ; however, the 

 lower trade-wind air is nearly "barotropic", that is to say the pressure forces 

 are nearly constant in the vertical, so that this difficulty is minimal. 



Equation (9) predicts the distribution of a property above the sea, if enough 

 can be said about Fp and Kp in order to integrate it in the vertical. In the case 

 of momentum, Fp is constant with height in a steady state if the barotropic 

 condition is met ; for heat and water vapor, Fp is constant in the vertical 

 through a thin boundary layer in which heat and vapor are not accumulating. 

 Furthermore, the classical turbulence work of Prandtl (1932) and von Karman 

 (1935) may be drawn on to argue that, in cases of neutral static stability, Kp 

 should increase linearly upward. Upon integrating (9), we then derive 



p{z)(x: In z, (10) 



the famous logarithmic profiles upon which the transfer formulas are based. 



In recent years, over-extension of the "eddy exchange coefficient" concept 

 and attempts to apply equations of the form (9) to situations where the basic 

 premises are far from realized have led to an unfortunate discrediting in 

 meteorology of the entire approach. Actually the low-level profiles of the 



