SECT. 2] LARGE-SCALE INTERACTIONS 237 



even reasonable? Must the exchange demand per unit sea surface be ten, one 

 hundred or one milhon times as rapid as that in the normal trade? 



These questions cannot be answered quantitatively without some knowledge 

 of the dynamic relations in the hurricane core. We need to know the radial 

 pressure distribution to tie the pressure ordinate of Fig. 69 to radial distance ; 

 we also need to know the inflow paths, the speed the air moves along them, 

 and the rate at which it is being exposed to the sea surface. True, there are 

 almost enough data available to set up these computations purely observa- 

 tionally ; however, one loses then any predictive relationships. Secondly, 

 analytic formulation of any part of the foregoing model permits both its 

 testing from existing observations and the possibility of going beyond these to 

 suggest new ones and even extensions of the approach to other problems. 

 Since this is one of the few atmospheric circulations where a flow-dependent 

 exchange has been explicitly connected into a dynamic model, the hurricane 

 menace may have the beneficial facet of serving as a prototype for studying 

 even more complex geophysical flows. 



{in ) A dynamic model of the loiv-level rain area 



The inflow into a hurricane is confined mainly to low levels. Sub-cloud air is 

 accelerated inward along spiral-shaped trajectories ; acceleration results from 

 excess work done by pressure-gradient forces over frictional retardation. We 

 shall consider the dynamics of the inflow layer in a natural co-ordinate frame- 

 work (Fig. 66) as we did in the model of the trades (Section 6-C, pages 194-201). 

 As already clear, this heat-engine model of the hurricane has much in common 

 procedurally and philosophically with the trade- wind model. W^e consider as 

 basic the hydrostatic pressure gradients along the trajectories and inquire how 

 the smaller scales of motion, namely turbulent exchange and convection, 

 produce these ; the dynamic part of the model relates the studied scale of 

 motion to its energy sources in a steady state via the pressure field. Thus the 

 hurricane model has the same limitations as did the trade model. The trajec- 

 tories are assumed given ; how they got that w^ay, and the life-cycle aspect of 

 the phenomenon, cannot as yet be treated. 



For the steady-state, stationary (or slow-moving) hurricane inflow layer, the 

 tangential and normal equations of motion are as follows : 



du 8u \ dp I 8tsz 1 cp . - 1 drsz ,_,, 



-Tf- ^ u— = --^ + --^ ^ - —sm^ + -^ (52) 



at cs p cs p cz p cr p cz 



and 



^+/„=_i|P=l|?lco.^. (53) 



R p en p cr 



The natural co-ordinate system is oriented as shown in Fig. 66, superimposed 

 on a standard polar co-ordinate system, where the radial distance, r, increases 

 outward. R is the radius of curvature of the trajectories ; ^ is the "inflow angle" 



