D-R-A-F-T
⎞
⎛ E o ⎞ E0 ' ⎛ τ
⎜ - 1⎟
α 1C + α 2 = - ⎜
⎟
⎟
⎝ H ⎠ D' ⎜ τ e
⎠
⎝
(clay particle erosion/storage). The clay particle erosion to storage ratio is
Equation 53
⎞⎛ V s ∆t ⎞
⎛ E o ⎞ ⎛ C o ⎞ ⎛ E o ∆t ⎞ ⎛ E o
⎟⎜
⎜C H ⎟=⎜C V
⎟=⎜
⎟⎝ H ⎟ = Pd C v
⎟ ⎜
⎜
⎝ H ⎠ ⎝ ∆t ⎠ ⎝ o ⎟ ⎜ o s
⎠
⎠
⎠ ⎝
This ratio reflects the relative speed at which the entrainment of sediment from the
bed causes the concentration in the water column to change. It is the product of the
vertical advective Courant number and a non-dimensional term, Pd, which can be
viewed as a particle Peclet number (Teeter, 1984).
(clay particle erosion/convection). The ratio of clay particle erosion to
convection is
Equation 54
⎞⎛ Vs L ⎞ ⎛ C v ⎞
⎞ ⎛ Eo
⎛ E o ⎞ ⎛ C oV ⎞ ⎛ E o L
⎟ VH ⎟ = ⎜ C ⎟ Pd
⎟⎜
⎟=⎜
⎟=⎜
⎟ ⎜
⎜
⎟
⎜
⎟ ⎜C V
⎝ H ⎠ ⎝ L ⎠ ⎜ C oVH
⎠ ⎝ n⎠
⎝
⎠
⎠ ⎝ o s
⎝
(clay particle erosion/diffusion). The ratio of clay particle erosion to
diffusion is
Equation 55
⎛ E o ⎞ ⎛ C o Dr ⎞ ⎛ E o L
⎞ ⎛ Eo
⎞⎛ Vs L2
⎞ C ve
2
⎟ ⎜ 2 ⎟=⎜
⎟=⎜
⎟⎜
⎟=
⎜
⎟ C Pe Pd
⎟ ⎜C V
⎟⎜ D H
⎝ H ⎠ ⎝ L ⎠ ⎜ C o Dr H
⎠ ⎝ o s
⎠⎝ r
⎝
⎠
n
Clay Mass Erosion
When the bottom shear stress is greater than the shear strength of the clay layer the
entire layer is entrained into suspension during the model time step. The relationship
is encoded as
Equation 56
ρ Lδ L
S=
Dt c
where:
the density of the layer, kg/m3
ρL
=
δL
=
the thickness of the layer, m
=
characteristic time of response, sec
tc
50 Advanced Techniques
Users Guide To SED2D-WES
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