216 MALKUS [chap. 4 



hemispheric caps. Considerable success has been achieved in modelhng the 

 discrete phase (Levine, 1959; Malkus and Witt, 1959; Ludlam, 1958). These 

 elements turn themselves slowly inside out as they rise. Experiments and 

 observational tests suggest that they entrain and shed roughly one -half their 

 own mass per cycle. What is important is that the rate of turning inside out is 

 inversely related to size and is completed in about two diameters ascent. 

 Dilution, supposed proportional to the rate of exposure of surface area (per 

 unit mass flux) to the dry surroundings, is thus much greater for the small 

 bubbles than the large ones. An ordinary trade-cumulus element of 500 m dia- 

 meter turns inside out once per kilometer rise and is diluted in this distance by 

 the incorporation of an amount of outside air equal to about half its own mass. 

 A 5-km cumulonimbus element, in contrast, rises through nearly the whole 

 troposphere before doing this. If protected by a cloud body for the critical first 

 few kilometers,! such large elements may reach 30-40,000 ft or even to the 

 tropopause with little or no diminution of their original heat content (Malkus, 

 1960). 



The predictions of this model have been tested against photographic measure- 

 ments in several contexts, particularly that of the hurricane. The important 

 question of how the large elements are formed, and the relationship between 

 synoptic-scale convergence and their occurrence, is just beginning to be 

 studied. It is becoming uncomfortably clear, however, that even in the "steady" 

 trades, we shall have to examine the "abnormal" situation to comprehend the 

 normal. This means a closer examination of fluctuations in the air-sea system 

 and its exchanges. 



B. Exchange Fluctuations in the Tropics 



The interface layers in the tropics constitute the primary energy-regulating 

 valve for the planetary fluids of ocean and atmosphere. Since the sea is both 

 more uniform and much slower to respond to change than is the air, we have 

 implied throughout this chapter that it is mainly variations in air structure 

 which close down or open up this valve. Simplifying to bare essentials, we may 

 say that the exchange valve is opened as the air-sea temperature and humidity 

 difference is enhanced and/or the wind speed strengthened, and is closed as 

 these diminish. Thus we must seek to examine fluctuations in terms of the 

 processes and scales of motion which produce alterations in these property 

 differences : that is to say, primarily those which change the temperature, 

 humidity and wind speed in the air overlying the ocean surface. 



We may now interpret the seasonal marches of Qs, Qe and momentum ex- 

 change in this light (Figs. 18, 19, 29, 39, 40, 42, 43). In winter, the subtropical 

 high pressure cells are strongest and in their most equatorward positions. 



1 The argument of p. 175 shows that above 4-5 km the saturation specific humidity is 

 very small due to low temperature. Thus the difference between in-cloud and ambient 

 moisture content diminishes with elevation and the drying of a cloud by entrainment 

 becomes ineffective in the upper atinosphere. 



