260
8 Transport in the Oceans and Coastal Zone
c
G
H
D 1""-------''------('
~
,
:B
.... 1- __
--------- F
z
~~
A
Ax
E
y
r D (dc/dz)z~o Axllyllt
0
x
Fig. 8.2: Fick's equation and three-dimensional volume of fluid
or:
oe
2
-+V(ue)=DVe,
ot
(8.18)
in which V is the nabla operator defined by Eq. (C.lO). In particular for
diffusion of particles in an (x, y) plane with uniform water flow along the x
axis, Eq. (8.17) becomes:
(8.19)
The terms on the left side of this equation describe the rate of change due to
advective mechanisms which carry particles with the current, while the terms
on the right side describe processes due to the molecular nature of the diffusion
which spreads the particles. These two processes are shown schematically in
Fig. 8.3. At time t = 0, some initial distribution of particles is given (stage a).
Due to current with velocity u, this distribution is advected along the x axis
(stage b). At the same time molecular diffusion is acting and particles are
spread further (stage c). A combination of advection and diffusion results in
'cloud' of particles being widely distributed and at the same time, shifted along
the x axis (stage d).
The proportion by which the two mechanisms of advection and diffusion contribute to the final particle transport can be measured by the ratio of advection
8 Transport in the Oceans and Coastal Zone
c
G
H
D 1""-------''------('
~
,
:B
.... 1- __
--------- F
z
~~
A
Ax
E
y
r D (dc/dz)z~o Axllyllt
0
x
Fig. 8.2: Fick's equation and three-dimensional volume of fluid
or:
oe
2
-+V(ue)=DVe,
ot
(8.18)
in which V is the nabla operator defined by Eq. (C.lO). In particular for
diffusion of particles in an (x, y) plane with uniform water flow along the x
axis, Eq. (8.17) becomes:
(8.19)
The terms on the left side of this equation describe the rate of change due to
advective mechanisms which carry particles with the current, while the terms
on the right side describe processes due to the molecular nature of the diffusion
which spreads the particles. These two processes are shown schematically in
Fig. 8.3. At time t = 0, some initial distribution of particles is given (stage a).
Due to current with velocity u, this distribution is advected along the x axis
(stage b). At the same time molecular diffusion is acting and particles are
spread further (stage c). A combination of advection and diffusion results in
'cloud' of particles being widely distributed and at the same time, shifted along
the x axis (stage d).
The proportion by which the two mechanisms of advection and diffusion contribute to the final particle transport can be measured by the ratio of advection