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Faculty of Geosciences
River and delta morphodynamics
Critical dependence of morphodynamic
models on transverse slope effects
Anne Baar
Marcio Boechat Albernaz, Wout van Dijk, Maarten Kleinhans
gravity
Secondary flow
Transverse slope effect
2
Transverse slope effect
Major influence large-scale morphology
Flow direction
default value
strong
(physically correct)
(Baar et al, 2018 WRR)
weak
?
X 100
3
tan ψ =
1
Ash θ
𝛿𝑧
𝛿𝑦
qn = qs αbn
θ 𝑐
θ
𝛿𝑧
𝛿𝑦
Slope effect in Delft3D
Ikeda (Bagnold) Koch & Flokstra
ψ
4
tan ψ =
1
Ash θ
𝛿𝑧
𝛿𝑦
qn = qs αbn
θ 𝑐
θ
𝛿𝑧
𝛿𝑦
Slope effect in Delft3D
αbn
Ash
Ikeda (Bagnold) Koch & Flokstra
ψ
5
Different effect on morphology
Ikeda (αbn) Koch & Flokstra (Ash)
X 15
Engelund-
Hansen
Van Rijn
X 100
6
Calibrating with slope parameter
➢ Sediment transport predictor determines
tendency to incise
➢ Slope parameterization influences bar/channel
stability
7
Incision vs transverse slope effect
What controls severe incision in models with
default slope effect?
flow
Sediment transport
W
decaytransverse sediment transport
8
growth
Incision vs transverse slope effect
What controls severe incision in models with
default slope effect?
flow
Sediment transport
W
transverse sediment transport
9
Van Rijn 2004
Growth of perturbation
➢ W/h = 21
➢ Default slope effects
(abn = 1.5)
Straight channel of 5 grid cells
Engelund-Hansen
Initial channel
10
Van Rijn 2004
Growth of perturbation
➢ W/h = 21
➢ Increased slope
effects (abn = 30)
Straight channel of 5 grid cells
Engelund-Hansen
Initial channel
11
Suspended sediment
Slope effect only acts on bedload
Van Rijn
Van Rijn, suspended load treated as bedload
12
Grid size-dependent incision
αbn= 1.5
Engelund-
Hansen
13
Grid size-dependent incision
Engelund-
Hansen
αbn= 3
αbn= 1.5
14
Grid size-dependent incision
Engelund-
Hansen
αbn= 100
αbn= 3
αbn= 25Van Rijn
15
Incision vs transverse slope effect
Rate of incision determined by:
 Transport predictor
 Amount of suspended sediment
 Grid size
Determines magnitude slope effect
16
Role of environment
Large-scale morphology
Erosive Balance Depositional
Van Rijn
Engelund-Hansen
Van Rijn
EH
X 15
17
Literature?
18
time
Van Rijn EHVan Rijn EH
αbn= 5
αbn= 15
αbn= 1
Channel migration
19
A B
A B
A B
αbn= 5
αbn= 15
αbn= 1
Channel migration
Van Rijn, αbn=3 EH, αbn=3
20
Channel migration
Van Rijn, αbn=3 EH, αbn=3
Location of channel centers
time
αbn= 25
21
Large-scale morphology
Channels can migrate when incision is balanced
by increasing slope effect
Environment / objective determines if this is
necessary
22
Implications calibrated models
Calibrating on sediment transport: different
morphology
Calibrating on morphology: sediment transport?
23
24
Western Scheldt estuary
Ikeda (αbn = 30) Koch & Flokstra (Ash= 0.05)
(Van Dijk et al., under review)
sea sea
land land
Western Scheldt estuary
Difference in sediment transport vector
~ 1 million m3/year difference in dredged volume
25
Optimizing model design
Combination depends on research objective
Good Bad
Dynamic/erosional
Sediment transport
Depositional
αI αK αI αKαI αK αI αK
Morphology
VR EH
Sediment transport Channel dynamics
VR EH
Bed slopesSediment transport Bar/bend shape Network
26
Conclusions
Default slope parameters physically correct,
but leads to severe incision
Incision:
Grid size
Suspended sediment > diffusion?
Channel migrate when incision is balanced by
increasing slope effect
Calibrating with slope effects:
Either sediment fluxes or bed slopes calibrated
→ Change morphology & time scales 27

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