274
8 Transport in the Oceans and Coastal Zone
full saturation
- /- - - --"------=---~::::=--2
W
~
W W 100 lW 1~ lW lW ~ m ~ ~
Time t (s)
Fig. 8.7: Evolution in time of concentration of substance at particular distances
from release point
For the values used in Fig. 8.7, the concentration of full saturation equals
5 kg/m.
Steady Release of a Substance on a Plane in a Steady Uniform Flow.
We now consider the case when a contaminant is introduced steadily at one
point on the sea surface. The plume of contaminant moves downstream (current
velocity u is constant) and spreads out at the sea surface as well as below.
Ozmidov (1986) suggests using the following variant of the basic advectiondiffusion equation (8.30):
ac
a 2 c
a 2 c
u ax = KYax2 + K Zaz2 '
(8.65)
The contaminant is introduced at point x = y = z = 0 at the rate of Q (kg/s).
A solution of Eq. (8.65) becomes (Ozmidov, 1986):
c(x,y,z) =
exp - - - - - - .
_
2Q
(u y2 uz 2 )
47rxJKyK z
4Kyx 4Kzx
(8.66)
In particular at the sea surface (z = 0), Eq. (8.66) becomes:
_
2Q
(u y2 )
c(x,y,O) =
~exp - - - .
47rx y K yK z
4Kyx
(8.67)