numbered rectangles within Pj, Ptf etc. represent uniform distri- 

 bution of the contaminant in the bay at low tide. 



At high water. Figure 8B, some of the particles 1 , which were in 

 volume Pj at the previous low water, would still be expected to be 

 found near the entrance boundary of the bay. Similarly at high water 

 some of the particles 4 in Figure 8A would be expected to be found 

 at an excursion length farther into the bay as in Figure 8B. The 

 maximum span of the contaminant on the flooding tide is thus twice 

 that of the particle excursion distance. Thus, the contaminant in 

 Pi becomes distributed in the volume Pi + P = 2P. The volume 

 of water containing contaminant which is lost during the next ebb 

 tide is equal to P, and therefore the exchange ratio for volume Pj 

 is r 1 = 1/2. 



Figure 8C shows what the situation would be at low tide if an adjust- 

 ment of the remaining contaminant did not now occur because of 

 diffusion. Since the volumes being considered are small, we assume 

 that the process of diffusion is complete before the next flood tide 

 begins. The effect of diffusion is to disperse the remaining contaminant 

 uniformly (Fig. 8D). Now the total contaminant remaining in Pi at 

 the end of the first ebb tide is P^ (1-ri). If P is taken equal to unity, 

 then, since r^^ = 1/2, the contaminant remaining in Pj is r^. On this 

 basis the contaminant in P^' Figure 8C, is 2ri, giving for the adjusted 

 value in each of the volumes Pj and Pt the amounts ^= 3/4. The con- 

 taminant lost from P2 is thus 1/4 = r^^^. This is the exchange ratio 

 for volume P2. Similarly, the contaminant in P^ and P^ is now 2rj^ 

 + 3 -i , and for each of the volumes P2 and P3 this becomes 1/2 

 (2ri +3^) = 7/8. Hence, the exchange ratio for P3 is r^ . In general 

 we can write for the exchange ratio of the nth segment P , 



Now suppose that the bay volume at high water is equal to 



nP = Pi + Pt + P . 



1 ii n 



The remaining contaminant near the head of the bay after 



1 \" 



tidal cycles is approximately i 



* Where e = is base of natural logarithm. 



11 



