The basic convection - diffusion equation is presented in Ariathurai, MacArthur, and

Krone (l977),

∂C

∂C

∂C ∂ ⎛

∂C ⎞ ∂ ⎛

∂C ⎞

∂y ⎟ α 1

⎟ + * C *+α 2

⎟ + ⎜ Dy

= ⎜ Dx

+*u*

+*v*

∂x ⎠ ∂y ⎜

∂t

∂x

∂y ∂x ⎝

⎝

⎠

where

concentration, kg/m3

=

=

time, sec

=

flow velocity in x - direction, m/sec

=

primary flow direction, m

=

flow velocity in y - direction, m/sec

=

direction perpendicular to x , m

effective diffusion coefficient in x - direction, m2/sec

=

effective diffusion coefficient in y - direction, m2/sec

=

α1

=

a coefficient for the source term, 1/sec

α2

=

the equilibrium concentration portion of the source term,

kg/m3/sec = - α1Ceq

The bed shear stress is needed to evaluate the bed source-sink terms in the governing

equation. Several options are available for computing bed shear stresses using

(u )

2

*

τb = ρ

where

ρ

=

water density

u*

=

shear velocity

⎞

⎛

*

⎜ 3.32 u D ⎟

= 5.75 log

ν ⎟

⎜

*

⎠

⎝

which is applicable to the lower 15 percent of the boundary layer when

8

Title

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