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 ⎞ ⎛ Dr∆t ⎞ C n
⎛ CoDr ⎞
⎝ ∆t ⎠ ⎝ 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.
Transform The Bed Source-Sink Terms
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 ' )Vs '
α1C + α 2 = -⎜
⎝ de ⎠
This dimensional grouping can now be ratioed to the other terms in the equation.
(sand deposition/storage). The sand deposition to storage ratio is
⎛ C o ⎞ ⎛ Vs∆t
⎛ C oV s ⎞
⎟ = Cv
⎜L H ⎟
⎝ ∆ t ⎠ ⎜ L de H
The term Lde ,already dimensionless, so that this non-dimensional term can be
viewed as a vertical advective Courant number.
(sand deposition/convection). The ratio of sand deposition to convection is
46 Advanced Techniques
Users Guide To SED2D-WES