Geoscience Reference
In-Depth Information
6.3 DEPTH-AVERAGED 2-D SIMULATION OF FLOW
AND SEDIMENT TRANSPORT IN CURVED
AND MEANDERING CHANNELS
As described in Section 2.4.1, in the derivation of the depth-integrated momentum
and suspended-load transport equations, dispersion terms arise from the split of
three-dimensional quantities into their depth-averaged values and the remainders. For
nearly straight channels, the dispersion terms can be combined with the turbulent
stress/flux terms. However, for curved channels, the dispersion terms are of great
significance, due to the presence of helical flow (Flokstra, 1977). Thus, among the
depth-averaged flow and sediment transport equations introduced in Sections 6.1 and
6.2, the depth-integrated momentum equations (6.2) and (6.3) and suspended-load
transport equation (6.53) are replaced by
hU
x
)
∂
∂(
hU
x
)
+
∂(
+
∂(
hU
y
U
x
)
gh
∂
z
s
1
ρ
∂
[
h
(
T
xx
+
D
xx
)
]
=−
x
+
∂
t
x
∂
y
∂
∂
x
1
ρ
∂
[
h
(
T
xy
+
D
xy
)
]
−
τ
bx
ρ
+
(6.75)
∂
y
hU
y
)
∂
+
∂(
∂(
hU
y
)
+
∂(
hU
x
U
y
)
gh
∂
∂
[
h
(
T
yx
+
D
yx
)
]
z
s
1
ρ
=−
+
∂
t
∂
x
y
∂
y
∂
x
−
τ
by
ρ
1
ρ
∂
[
h
(
T
yy
+
D
yy
)
]
+
(6.76)
∂
y
h
D
sxk
∂(
hC
k
/β
sk
)
∂
+
∂(
hU
x
C
k
)
∂
+
∂(
hU
y
C
k
)
∂
=
∂
∂
s
∂
C
k
∂
ε
+
t
x
y
x
x
h
D
syk
+
∂
∂
s
∂
C
k
∂
ε
+
y
y
+
αω
(
C
−
C
k
)
(6.77)
sk
∗
k
where
D
ij
and
D
sik
(
=
)
are the dispersion momentum transports and sediment
fluxes defined in Eqs. (2.82), (2.83), and (2.86). Note that the wind driving and
Coriolis forces are omitted in Eqs. (6.75) and (6.76), for simplicity.
The helical flow also affects the bed-load transport. Introduced in this section are
the methods used to evaluate the dispersion fluxes in Eqs. (6.75)-(6.77) and account
for the effect of helical flow on the bed load.
i
,
j
x
,
y
6.3.1 Flow properties in curved channels
As shown in Fig. 6.12, the major secondary flow observed in the cross-section of
a channel bend is the helical flow, which exists due to the difference between the
centrifugal forces in the upper and lower flow layers, and points to the outer bank
in the upper layer and to the inner bank in the lower layer. Other secondary flow
cells may also exist. For example, one often appears in the upper corner along the
outer bank due to anisotropic turbulence, and more may exist in trapezoidal and
