SECT. 2] LARGE-SCALE INTERACTIONS 197 



where P <G and D^d. When reahstic boundary conditions and values of B^ 

 are substituted, the lo' and divergence fields derived from the solution are in 

 excellent agreement with the observations (Fig. 46). The first exponential is 

 now readily related to the heating function of Fig. 31b. 



An independent test of the results is provided by comparing (42b) and (42) 

 to try the relation 



-^' = ^^-^^^' (45) 



pu dz^ 



which is now integrated twice with respect to z to obtain the friction force 

 (1/p) dTszjdz and tsz under the assumed boundary conditions that tsz— 1 dyne 

 cm~2 at the surface and vanishes at the level of wind maximum. The height 

 derivative of the shearing stress has a distribution similar to Fig. 45 and to 

 that described by Sheppard (1954). It falls off with height in a manner con- 

 sistent with the hypothesis that the frictional drag is brought about by the 

 same processes which distribute the heating. Due to the small (~1%) con- 

 tribution of u 8u' Ids in equation (33b), the downstream pressure drop is for all 

 practical purposes proportional to drszldz. It decays exponentially and has 

 nearly vanished at 3 km (Fig. 47) ; its magnitude is now correctly related to the 

 divergence and the heating function. 



Although the model says nothing explicitly about the cross-stream pressure 

 gradient (which is given by the n equation of motion), the disappearance of 

 the large downstream pressure gradient toward the top of the section means 

 that the isobars are rotating with height into parallel orientation with the 

 trajectory, as observed. This conclusion has been reached without any a priori 

 assumptions concerning the pressure field or of any simple relation between it 

 and the wind. The trade-wind maximum at cloud base is also predicted by the 

 model. Recalling that the u = u + u' and du'jds profiles have a similar shape, 

 we solve (42b) for — d^w' jdz^ = {d ldz){du' I ds), namely, 



d^w' d (du'\ Ti, V -r,„ , , . 



= xbr =nz) + B^w', (42c) 



dz"^ dz\ds J 



where F{z) > and B^ is proportional to S^, the static stability. In the sub-cloud 

 layer, S^'^O and so du'jds increases rapidly upward. At the base of the cloud 

 layer, positive stability sets in suddenly. Since w' is negative, the sign of the 

 right-hand term is rapidly changed to negative. The divergence and wind then 

 begin to decrease with height, giving rise to the physically important "knee" 

 in their profiles. In laterally broad, wind-driven ocean currents, a similar 

 approach might be applied to explain the rapid decrease of current speed 

 through the thermocline. Also of consequence to oceanography is the reliabihty 

 of the trade-wind flow, of which this model permits a rudimentary treatment. 



c. The steadiness of the lower trades 



The pronounced steadiness of the flow has been emphasized as a significant 

 feature of the trades. The overall dynamic stability of a Hadley-type meridional 



