294
8 Transport in the Oceans and Coastal Zone
..c: 0.0
....
water su ace
c.
~ -0.1
[)
.... -0.2
C<:I
~
Cil -0.3
I:
0 -0.4
.;;;
I:
S
:.a -0.6
I
I:
0
Z -0.7
-0.8
-0.9
-1.0
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Flow velocity (mls)
Fig. 8.16: Vertical distribution of the normalized flow velocity
Let us now determine the vertical distribution of salinity, S, for small river
discharge. We assume both the diffusion, K z , and gradient, oS/ox, to be
constant as a function of depth. Thus, Eq. (8.30) simplifies as follows (Officer,
1976):
At the sea bottom, the vertical salt flux vanishes, i. e.:
oS
K z -
= 0 at z = -h.
oz
Substituting Eq. (8.108) into Eq. (8.110) and integrating we obtain:
u1 h 2 oS [1 (Z)2 3 (Z)4 2 (Z)5 ]
S(z) = -
- - - - - - - - - + C
Kz ox 2 h
4 h
5 h
'
in which:
(8.110)
(8.111)
(8.112)
(8.113)