Geoscience Reference
In-Depth Information
3-D numerical models
Flows in curved and braided channels and near in-stream structures usually exhibit
complex three-dimensional features that significantly affect sediment transport and
morphological evolution processes. Realistically simulating these complex near-field
phenomena must rely on 3-D models rather than 1-D or 2-D models. Introduced in
this chapter are 3-D modeling approaches for open-channel flows, sediment transport
in general situations, local scour near in-stream structures, and headcut migration.
7.1 FULL 3-D HYDRODYNAMIC MODEL
7.1.1 Governing equations
As described in Section 2.2.3, the influence of sediment transport on the flow field is
assumed to be negligible in the case of low sediment concentration. However, the bed
sediment affects the flow by forming bed roughness elements, such as particles, ripples,
and dunes. This will be accounted for through bed boundary conditions in the 3-D
model. Therefore, the flow field is determined by the Reynolds-averaged continuity
and Navier-Stokes equations (2.42) and (2.43), which are written in the Cartesian
coordinate system shown in Fig. 2.6 as follows:
∂
u
i
x
i
=
0
(7.1)
∂
t
+
∂(
u
i
u
j
)
∂
∂τ
ij
∂
∂
u
i
∂
1
ρ
∂
p
1
ρ
=
F
i
−
x
i
+
(7.2)
∂
x
j
x
j
where
u
i
are the components of mean flow velocity;
F
i
are the components
of external forces, such as gravity and Coriolis force, per unit volume;
p
is the mean
pressure; and
(
i
=
1, 2, 3
)
τ
ij
are the stresses, including both viscous and turbulent effects. If
Boussinesq's eddy viscosity concept is adopted, the stresses are determined by
∂
x
j
+
∂
u
j
u
i
2
3
ρ
τ
=
ρ(ν
+
ν
)
−
k
δ
(7.3)
ij
t
ij
∂
∂
x
i
t
can be determined by the parabolic model, mixing length
model, or linear (standard, non-equilibrium, and RNG)
k
-
The eddy viscosity
ν
ε
turbulence models.
