This term can be called an advective Courant number, using the advective velocity

rather than the wave celerity. This is a measure of the fraction of the element over

which a parcel of water is transported within a single time step.

For the three basic groupings of dimensional parameters (storage, advection and

diffusion), there are only three unique ratios to be defined (ignoring the inverses of

each ratio). When two of the three ratios are known then the other ratio is defined

from the other two.

⎛ *C *o ⎞ ⎛ *D*r∆*t *⎞ * C *n

⎛ *C*oDr ⎞

⎟=⎜

⎟=

⎜

⎜

⎟

⎝ ∆*t *⎠ ⎝ * L*

⎝* L*

⎠

⎠

This term could be called a non-dimensional diffusion coefficient or simply the ratio

of the advective Courant number and the Peclet number.

The SED2D model's response to various ranges of these non-dimensional

parameters can best be evaluated experimentally.

The bed source-sink terms will now be addressed separately. There are four basic

cases to be considered. These are: sand deposition, sand erosion, clay deposition

and clay erosion.

The sand deposition terms were developed earlier.

⎛ *C * oVs ⎞ (*C *'-*G * p ' )*V*s '

α1C + α 2 = -⎜

⎜*L H*⎟

⎟

⎝ de ⎠

This dimensional grouping can now be ratioed to the other terms in the equation.

⎞

⎛ *C *o ⎞ ⎛ *V*s∆*t*

⎛ *C *oV s ⎞

⎟ = *C*v

⎟=⎜

⎜

⎜*L H *⎟

⎜

⎟

⎟

⎝ ∆ *t *⎠ ⎜ *L * de H

⎝ de

⎠

⎠

⎝

The term Lde ,already dimensionless, so that this non-dimensional term can be

viewed as a vertical advective Courant number.

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