Geoscience Reference
In-Depth Information
near-bed suspended-load concentration that is related to local flow features. This is
also true for the bed-load transport capacities at the interfaces between 1-D, 2-D, and
3-D subdomains. Therefore, conservative correction is often made to satisfy conditions
(8.15) and (8.16).
Bed change
The bed changes at the interfaces satisfy
B
B
∂
A
b
,1
d
∂
0
∂
z
b
,2
d
∂
0
∂
z
b
,3
d
∂
=
dy
=
dy
(8.18)
t
t
t
where
∂
A
b
,1
d
/∂
t
is the rate of change in bed area calculated in the 1-D subdomain;
and
t
are the rates of change in bed elevation calculated in the
2-D and 3-D subdomains, respectively.
At the interface between the 1-D and 2-D subdomains, bed change equations (5.36)
and (6.61) show that if the actual discharges and transport capacities of sediment sat-
isfy conditions (8.13)-(8.16) and if the adaptation length has the same value in the
1-D and 2-D domains, the bed changes automatically satisfy condition (8.18) at the
interface. However, to maintain the same cross-sectional geometry at the interface,
the redistribution of the 1-D bed area change along the channel width should result
in the same bed elevation change as that calculated in the 2-D subdomain.
However, because the adapatation length
L
and coefficient
∂
z
b
,2
d
/∂
t
and
∂
z
b
,3
d
/∂
are often treated as
calibrated parameters (as discussed in Sections 2.5 and 2.6) and different methods
are used to calculate the 2-D and 3-D bed-load and suspended-load transport capac-
ities, difficulties exist in satisfying condition (8.18) at the interface between 2-D and
3-D subdomains. The simplest way to solve this problem is to correct one of the bed
changes calculated in the adjoining two subdomains to make sure both have the same
value at the interface.
α
Bed-material gradation
The bed-material gradations at the interfaces satisfy
B
B
Bp
bk
,1
d
=
p
bk
,2
d
dy
=
p
bk
,3
d
dy
(8.19)
0
0
where
p
bk
,1
d
,
p
bk
,2
d
, and
p
bk
,3
d
represent the bed-material gradations calculated in the
1-D, 2-D, and 3-D subdomains, respectively.
It is found from Eqs. (5.32) and (6.57) that if the mixing layer thickness has the
same value in two neighboring subdomains, satisfaction of condition (8.18) for all
size classes will guarantee satisfaction of condition (8.19).
Among all the above connection conditions, conditions (8.9), (8.10), (8.13), and
(8.14) are more essential because they are internal boundary conditions and guarantee
the continuity of flow and sediment transport between subdomains, while the other
conditions affect only locally and can be satisfied by correction. However, there is
a problem in the use of conditions (8.9), (8.10), (8.13), and (8.14). It is straightfor-
ward to convert the calculated water level, flow velocity, bed-load transport rate, and
