provided that x » L . This is the concentration along the axis of the plume 

 (i.e., the x axis). In contrast with Eq. (2), Sutton (p. 276-7) indicates that 

 the empirical resvilts of smoke plume experiments indicates that the concentration 

 is inversely proportional to the wind speed to the first power and also drops in- 

 versely as X " instead of as x ' , for a uniform line source. The formula 

 based upon the Fickian diffusion therefore gives an upper limit of possible con- 

 centration at a given distance x and also overestimates the concentration in 

 the presence of a moderate or strong current. 



As numerical example , consider the following conditions : 



137 

 Q^ = 100 curies per year for Cs 



D = 30 meters 



2 

 K = 1cm /sec ( for stable stratification with 



weak currents ) 



U = 10 cm/sec (approx. 5 n. mi/day) . 



Then 



(C ) = O.2I/-7-X (3) 



1 max ' — 



q 



where (C.) is in ixc/m"^ and x is in kilometers . The estimate of 



i'max ^ 



K given above is really applicable for vertical mixing. Measmrements of hori- 



3 2 

 zontal diffusion in the surface layers indicate values of K in excess of 10 cm /sec 



(Ketchum and Ford, 1952 and Moon, et.al. , 1957). Thus the values of concentration 



indicated by (3) are probably overestimated by at least one order of magnitude . 



However , since we know very little about the horizontal mixing near the sea bed , 



the very low value of K is taken as a factor of safety. Values of C. as obtained 



from (3) for different distances from the center of the source are listed in Table I. 



