SECT. 2] LARGE-SCALE INTERACTIONS 249 



from about 0.5 to 3.0^C accounts for only a factor of six ; the remainder is 

 therefore due to the high wind speed. The latent heat pick-up of 2420 cal/cm^ 

 per day is an enhancement by a factor of seven over the trades, and is practi- 

 cally entirely due to high wind, since qo-Qa is little altered from normal 

 (compare Tables II, XVI and XXI). Altogether, Qs + Qe, or the heat energy 

 abstracted from unit sea surface, is about 3000 cal/cm^ per day or up by an 

 order of magnitude in the moderate hurricane. Since the surface stress times 

 wind speed, a measure of kinetic energy dissipation, is up by three orders of 

 magnitude, it is suggested that in the hurricane the atmosphere has created an 

 abnormally efficient heat engine. This point was pursued further in the original 

 paper by Malkus and Riehl (1960). 



In ordinary tropical disturbances, we also noted (Table XVI) that heat 

 exchange is enhanced above normal, and that the increase in Qs was per- 

 centually larger. However, the increase of To — Ta in this type of situation was 

 related to evaporation of falling rain and thunderstorm downdrafts rather 

 than to adiabatic expansion during horizontal motion toward lower pressure. 

 These mechanisms for lowering the air temperature need not be discounted in 

 hurricane circulations, especially in the outskirts and formation stage, since all 

 hurricanes form from pre-existing disturbances of the kinds described pre- 

 viously. Clearly, however, the foregoing has demonstrated that, although the 

 enhanced boundary input is essential, it is not the difficult constraint to meet 

 in deepening a tropical storm to the moderate hurricane stage ; the critical 

 restriction must be sought in the concentrated release of the latent heat in the 

 middle and high troposphere. Nor can the enhanced pick-up be regarded as 

 the cause of hurricane development, since it is largely the result of the high 

 winds ; it is merely a vital part of the machinery. 



(vi) Maximum kinetic energy production, the Bowen ratio, and conditions for 

 extreme storms 



We may use the hurricane as a prototype example of a geophysical thermal 

 circulation by examining some of its vital relationships in the framework of 

 the new theoretical approach to convection by W. V. R. Malkus and Veronis 

 (1958). These authors showed that when a hierarchy of solutions exists to the 

 hydrodynamic equations of motion, that one will be realized by the system 

 which, under the operating constraints, maximizes the release of potential 

 energy or the production of kinetic energy. This so-called "relative stability 

 criterion" has been worked out entirely formally in simple examples of convec- 

 tion, where it has also been tested by corresponding precise laboratory experi- 

 ments. A crude application of this approach by Malkus and Riehl (1960) 

 suggests strongly that the hurricane is aware of this principle and is a fruitful 

 ground for creating the bridge between idealized cases, which can be treated 

 rigorously, and the vast complexity of real geophysical, thermally-maintained 

 flows. 



The solutions to the dynamic equations for the hurricane inflow layer contain 

 a parameter C{r) = — Ci>/sin ^ hz, variations in which gave rise to an infinite 



