380
C;. T. CSANADY
the intensity of deposition at any instant is given by
where Q is the number of alewives rekased. On substituting into Eq. (4) we
find the total deposit D :
This result shows the nondimensional deposit DhU/Qv, to be mainly a
function of the nondimensional distance variable
(8 1
t = Kx/UhZ
The exponential term in Eq. (7) is only signilkant for values of ( between
about 0.05 and 1.0. At such values of 5, the other nondimensional variable
on the right of Eq. (7), o,x/Uh may be large:
(9)
I ; . x / U ~ = (ta h/K)t
The combination us h/K already appeared in Eq. (9, and was supposed
sufficiently large. Given c’, = 0.1 to 1.0 cm sec-’, K = lo3 cmz sec- I , and a
release spot of h = 1 to 5 km from shore, the range of this combination is
t$h/K = 10 to 500. The bracketed expression in Eq. (7). (1 + 2v,x/Uh)- I ,
then becomes ( I + l ) - ’ to (1 + l a ) - ’ . For some of this range one may
neglect 1 in comparison with 20, xlUh and write Eq. (7) in a simplified form
(10)
DUh2/QK = in-1’2<-’ exp( - l/4<) (u,h/k large)
This relationship is illustrated in Fig. 7.
1
I
I
1
0.25
OfQ
0
10
K r / U h 2
Flu. 7. Beach deposition of floating objects, released as a point source at a distance h from
shore inlo il current of speed L’.