194 MALKTTS [chap. 4 



of the trade-wind belts where the meridional temperature gradient is directed 

 poleward. The geostrophic wind is strongest at the ground and decreases 

 throughout the trade-wind layer. On account of ground friction, however, the 

 maximum actual wind is situated at some distance above the ground, and the 

 vertical profile assumes the shape depicted in Fig. 31a. Thus the conclusions 

 drawn cannot be readily applied to tropical regions in their entirety. A separate 

 assessment of the role of the heat source must be made, as we saw, for those 

 regions such as the equatorial trough where the instability extends through a 

 deep layer, and to those parts of the trades where easterlies do not decrease, 

 but perhaps even increase with height (Riehl, 1951). Nevertheless, in the some- 

 what less complex region studied here, we may deduce some of these important 

 features as the consequences of a simplified dynamic model. 



b. A dynamic model of the lower trades 



The features of the low-level trade-wind section are sufficiently remarkable 

 to offer hope that we may have here a simple enough geophysical heat engine 

 to handle theoretically, perhaps even to provide a prototype for more complex 

 planetary thermal circulations. Fig. 31 and the natural co-ordinate system 

 serve as the framework of the study. Taking the two-dimensionality and the 

 layered stability structure as given, we shall attempt to relate the heating and 

 the overall sinking motion via the steady-state hydrodynamic equations. Thus 

 we investigate the interaction between the physically important scales of 

 motion, namely convective turbulence and the large-scale trade flow, under 

 prescribed constraints. 



It will be assumed that a uniform wind, u, enters our section at the upstream 

 end and that u'{s, z) is the increment within the section. The other hydro- 

 dynamic variables are similarly divided into barred quantities, referring to the 

 observationally given properties of the current at the entrance end, and primed 

 quantities denoting changes produced within ; these latter are the dependent 

 variables to be solved for. The vertical velocity is of the magnitude of a primed 

 quantity, being related to u' via the continuity equation ; both u' and w' are 

 independent of the n co-ordinate. Since changes within the section are small 

 compared to entrance values of the variables, this separation permits linear 

 mathematics, which may be shown not essential to the physical results (Stern, 

 1956). 



Under these conditions, the basic equations become 



_ du' 1 dj)' 1 Btsz . , . 



w^= -=^ + =:^' 33b 



OS p CS p cz 



1 dr>' p' 

 -^-f = ^g' (37) 



p dz p 



du' dw' 

 ^s dz 

 p' T 



-s^-z='^ (^^^ 



(39) 

 P T 



