SECT. 2] LAKGE -SCALE INTERACTIONS 199 



right-hand terms both upon one another and upon external influences, only 

 one illustrative calculation is presented here. 



Rainfall in the trade stream is the least reliable of its properties. Even casual 

 observers have noted that a skyful of trade cumuli on some days produces 

 plentiful showers from clouds of all sizes, while on other days with apparently 

 similar cloud conditions no drop of rain appears. We try the hypothesis that 

 due to deficient rainfall the amplitude of the heating function is cut by 10% 

 without altering its height dependence or the d^Tsz/dz'^ term in (42). The 

 solution now gives the dotted curves in Figs. 46 and 47. The boundary condition 

 that the stress vanishes at the wind maximum and internal consistency with 

 the wind field requires a surface stress of 2.2 dynes/cm^. 



The new situation is in all respects an extreme of observed configurations 

 in the trades (Charnock, Francis and Sheppard, 1956). It does, however, con- 

 tain restoring influences. Fig. 46a shows that sinking has been replaced by 

 mean ascent up to 1 km, and that subsidence is much weaker than normal 

 throughout the cloud layer. Weakening the descent in the cloud layer favors 

 increased cloudiness and precipitation, while ascent in the sub-cloud layer aids 

 upward transport of sensible heat, both directly and by destabilizing the 

 already near-neutral lapse rate. Observational studies (Malkus, 1955, 1958) 

 suggest that processes in the tropical sub-cloud layer are critically sensitive to 

 shght amounts of subsidence or its removal. In view of this, it seems likely 

 that the system would usually restore its heating and return toward normal 

 even before departing so far as the conditions of the dotted curves in Figs. 46 

 and 47. 



Kraus (1959) has broadened the basis of inquiry into the relationship 

 between sea-air exchange and the stability of tropical flows. The form of the 

 transfer formulas suggest that the local heat-energy input from sea to air 

 iQs + Qe) is proportional to a lower power of the wind speed than is the momen- 

 tum loss. The rate of kinetic energy dissipation is still more wind-sensitive, 

 being proportional to the stress times the wind speed. Following this up with 

 an extensive statistical analysis, Kraus showed, in fact, that when an integra- 

 tion over the whole tropical ocean area from 30°S to 30°N is made, the energy 

 input depends upon the first power of the area-median wind speed, while the 

 frictional dissipation is approximately proportional to its cube! Thus if the 

 fraction of Qe + Qs converted into pressure head or the efficiency of the thermal 

 engine is specified, there is one and only one mean equilibrium wind speed at 

 which input and dissipation are balanced. Below that speed the trades will 

 accelerate, and above it they will run down. 



Under a fixed efficiency, the situation of the dotted curves in Figs. 46 and 47, 

 which show an abnormally large stress and small heating, probably could not 

 maintain long as a steady state ; we have perhaps described the mechanism by 

 which the system goes back to normal. In considering efficiency, we should 

 recall that the heating function in equation (42) is the net residual of sensible 

 heat sources minus sinks, namely H = Qs + LP + Ra. It will be larger for a 

 given Qe + Qsy the greater the fraction of Qe converted into LP by condensation 



