A Semi-Implicit, Three-Dimensional Model for Estuarine ... - USGS

176 A Semi-Implicit, Three-Dimensional Model for Estuarine Circulation
Because the eddy viscosities are needed in the momentum equations at the layer interfaces lying vertically between the u- and
v-points, these are determined by horizontal interpolation as follows:
n
AV n
AV + , jk , – 1⁄ 2
i 1⁄ 2
ij , + 1⁄ 2 , k – 1⁄ 2
1 n
n
= -- ( A
2 Vi,
j, k– 1 + A
⁄ 2 Vi
+ 1,
j, k– 1⁄ )
2
1 n
n
= -- ( A
2 Vi,
j, k– 1 + A
⁄ 2 Vi,
j+ 1,
k – 1⁄ )
2
.
To avoid model instabilities, the eddy viscosity within the interior of the water column is not permitted to take a value below some
preassigned minimum, usually about 1 cm 2 /s.
The eddy diffusivity is computed from equation 2.36 as
n
DV i, j, k – 1⁄ 2
The Munk-Anderson coefficients in this case are β 2
( AV0) n n
( 1 + β
i, j, k – 1⁄ 2Rii, j, k – 1⁄ )
2
2
α2 = . (E.4)
= 3.33 and α2 = – 1.5 .