SECT. 2] LARGE-SCALE INTERACTIONS 193 



(^930 mb, see Fig. 31a). The trades are thus transferring easterly momentum 

 downward to the ocean and upward to the high troposphere, or as commonly said 

 in meteorology, the trades receive westerly momentum from both above and 

 below. The Woods Hole expeditions have related the stresses mechanistically 

 to turbulent elements (50-150 m dimensions) in the sub-cloud layer and with 

 the cumuli themselves, and their associated eddying in the cloud layer. 



The important result of Fig. 45 is that in the momentum budget the advec- 

 tive terms are of no importance. Essentially we have a balance involving only 

 pressure and frictional forces. For example, in the lowest layer, the pressure 

 production force is 2.7 units, while the turbulent drag, the difference between 

 stress through top and bottom, is —2.8 units. The pressure drop along the 

 trajectory accelerates the air toward west-southwest, and this acceleration is 

 counteracted by friction, so that for many purposes in illustrating basic force- 

 momentum relations the tangential equation of motion (33) may be written : 



The balance of forces in the cross-stream, n, equation may be shown to be 

 approximately that between the earth's rotation (Coriolis) force directed to 

 the right (Northern Hemisphere) looking downstream and the normal pressure 

 gradient force, —{llp)dpldn, directed to the left, with lateral stresses con- 

 tributing not more than 20% of the two major terms. Thus while we have a 

 balance of forces in the lower trade, it is quite different from the quasi- 

 geostrophic or gradient balance often hypothesized for the free atmosphere in 

 mid-latitudes, or from the Ekman friction layer discussed by oceanographers, 

 where the current vector rotates with depth. Here in the lower tropical atmos- 

 phere, the current is two-dimensional and the isobars rotate counterclockwise 

 with height (Fig. 31c) becoming nearly parallel to the flow at the top of the 

 moist layer. Fig. 45 brings out the important further result that, along with 

 the downstream pressure head, turbulent friction also vanishes at the same 

 level. Thus at the top of the convective layer, the balance of forces is similar to 

 that found farther poleward in broad currents with little acceleration; the 

 wind is nearly parallel to the isobars and thus is quasi-geostrophic. Aloft, only 

 the mecKanism of travelling synoptic disturbances is available to provide 

 momentum transports and stresses, so that it is small wonder that the flow 

 steadiness breaks down. 



Therefore, the oceanic heat source plays a dual role in the loiver trades: produc- 

 tion of downstream warming and maintenance of vertical turbulence in a layer of 

 limited thickness. The coincident requirements on the balance of forces and the 

 mass distribution arising from this dual role are such as to permit direct utilization 

 of the heat gained to maintain the trades. 



The preceding deductions depend specifically on two characteristics of the 

 region studied : existence of a trade inversion, and a vertical wind-profile with 

 a curvature in the convective layer such that the turbulence must act to retard 

 the flow (cf. Fig. 31a). This kind of profile "knee" is typical of those portions 



