1
3-D Modeling of the Lower Mississippi River
UNO FORUM 2014
Alex McCorquodale, Ph.D., PE
Contributors: Joao Pereira, Ehab Meselhe, Ioannis Georgiou, Mead Allison, Ehab Meselhe, John
Lopez, Ahmed Gaweesh
U.S. Army Corps of Engineers
Louisiana Coastal Area: Science & Technology Office
Louisiana Optical Network Initiative
Lake Pontchartrain Basin Foundation
NSF-NG/CHC
The Water Institute of the Gulf
CPRA
2
Acknowledgements
2
Presentation Outline
1) Introduction
2) Objectives
3) 3-D Numerical Modeling
4) Modeling Domain
5) Model Development and Testing
6) Examples of 3-D Modeling Results
7) Summary
3
Introduction River Resources
4 Resources:
Flow
Sediment
Energy
Nutrients
The goal is to optimize the allocation of
these resources for different uses, e.g.: Coastal Restoration
Navigation
Flood Management
Water Supply
4
Introduction River Response Issues
Changes in:
existing flows to distributaries due to
diversions,
energy and energy gradients due to
diversions,
sediment transport in the River due to
diversions,
diverted sand loads due to diversions,
River morphology due the diversions.
Effect of subsidence/ESLR?
5
Introduction Questions???
Does an optimum sediment diversion scheme exist?
If so, what should be optimized?
How should diversions be operated to maximize their benefits?
Can a combination of pass closures and new diversions help sustain the delta?
How do the River responses change with ESLR and Subsidence?
6
Objectives
Main Objective Develop a 3-D hydrodynamic and non-cohesive
sediment transport model for the Lower Mississippi River
Specific Objectives Determine suspended sand distribution for the Lower MR
under existing conditions and with new diversions
Develop a 3-D model for sand transport in the Lower MR
Quantify the impact of diversions in Flow, Energy and Sediment available in the system
7
MOTIVATION
Land loss (up to 30 square miles per year)
Subsidence
Eustatic Sea Level Rise (ESLR)
Salt water intrusion
Other anthorprogenic factors.
Role of the River in offsetting Subsidence,
ESLR and salinity changes.
MODEL FRAMEWORK
0
50
100
150
200
250
300
350
400
450
0 1 2 3 4 5 6
t
Qb
m
0
50
100
150
200
250
300
350
400
450
0 1 2 3 4 5 6
t
Q
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 1 2 3 4 5 6
t
Stag
e
Grain size
Distribution
of Bed MOBILE
BOUNDARY
Van Rijn 1984
Exner Eq.
UNSTEADY WATER SURFACE
Continuity and Momentum Eqs
DISCHARGE
SEDIMENT LOAD or
CONCENTRATION
STAGE
3-D Numerical Modeling:
12
Why use it?
To obtained 3-D flow structure at bends,
diversions and inflows, e.g. secondary
flow.
To get the vertical and lateral distribution
of the suspended sand.
To model sand capture at diversions.
To model salt water intrusion.
To model wind shear.
Some Options for 3-D Numerical
Modeling:
13
ECOMSED (Public)
Delft3d (Public)
TELEMAC (Public)
MIKE3 (Proprietary)
H3D (Restricted)
CH3D (Public)
FLOW3D (Proprietary)
FVCOM (Restricted)
Numerical Model ECOMSED Description
3-D Hydrodynamics and Sediment Transport
Estuarine Model
Finite-Volume Model
Public Domain
Developed by HydroQual (2002)
Unsteady Flow
Hydrostatic assumption
Structured Curvilinear Grid + sigma vertical grid.
Serial Code
No GUI
14
Numerical Model Delft3d Description
3-D Hydrodynamics and Sediment Transport
Estuarine Model
Finite-Volume Model
Public Domain
Developed by Deltares (2011)
Unsteady Flow
Hydrostatic
Structured Curvilinear Grid+sigma or z-vertical grids.
Serial or parallel code
GUI available for pre- and post processing
15
Model Variables in this Study
Calibrated DELFT3d and ECOMSED
(hydrostatic assumption)
STATE VARIABLES:
Stage
3-D velocities
Sand classes (VF, F, M) for this study.
16
FULL GRID FOR Delft3d
Discharge
Stage
2004 x 117 nodes
10 vertical sigma layers
5 bed sediment layers
3 sand classes
Sigma Coordinate System
20
Numerical Model ECOMSED &
Delft3d
The sigma coordinate system (Source: HydroQual 2002)
MODEL TESTING
Grid dependency
Sensitivity to model parameters
Stability and selection of time step
Calibration
Validation
Model Development and Testing [Pereira 2011]
22
Grid Dependency Test
Sand Load Results
Longitudinal Sand Load Profile Comparison
0
50000
100000
150000
200000
250000
51 53 55 57 59 61 63
River Mile
Qs S
an
d (
ton
ne
s/d
ay
)
25x25 50x25 50x50 100x50
Cross-Sectional Profile - September 23, 2009
RM 31 (Empire)
Vertical Profile - May 1, 2009
RM 47 (Magnolia)
Velocity Profiles
Cross-Sectional and Vertical
r : 0.84
RMSE: 8%
r : 0.97
RMSE:
22%
Delft3d
ADCP
Allison (2011)
Figure 24. Velocity Pattern from Allison (2011) from ADCP April 16, 2010.
Recirculating Eddy
0
2
4
6
8
10
12
14
16
18
0 20 40 60 80 100 120 140
Sta
ge
ft
NA
DV
88
RM Miles
Q = 900,000 cfs
Obs Raw ft
Obs Corrected ft
Model ft
Stage Calibration – April 2010
[Teran 2014] Delft3d
Sediment Transport
Vertical Concentration Profiles
Myrtle Grove (RM 61) Magnolia (RM 47)
[Teran 2014] Delft3d
DIVERSION IMPACTS
Scenaroios:
Small diversion (near Myrtle Grove) 30,000
cfs
Large diversion (Belair near White Ditch)
200,000 cfs
3-D Modeling (ECOMSED & Delft3d)
External Boundary Conditions
U/S Boundary: Q and Csand
D/S and Outflow Boundaries: Gulf Stage
32
3-D Model [Pereira 2011]
Existing Outflows vs Existing vs Belair Water Discharge
Peak Flows
5000
10000
15000
20000
25000
30000
35000
0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0
River Mile
Q (
m3/s
)
Existing Belair Myrtle Grove
33
Main Channel Flows for Different Scenarios
Peak Flow (1.2x106 cfs or 35,000 m3/s)
Myrtle Belair
3-D Modeling
36
Total Energy of the Flow (m) {N-m/N}
Existing vs Belair vs Myrtle Grove
Peak Flows
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0
River Mile
To
tal E
nerg
y (
m)
Belair Myrtle Grove Existing
E
3-D Modeling
Peak Flows
0.00
200.00
400.00
600.00
800.00
1000.00
1200.00
1400.00
0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0
River Mile
To
tal
En
erg
y F
lux (
MW
)
Myrtle Grove Existing Belair
37
Total Energy of the Flow (MW) gQE
Existing vs Myrtle Grove vs Belair
Peak Flows
0
50
100
150
200
0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0
River Mile
Cs S
an
d (
mg
/L)
Belair Myrtle Existing
3-D Modeling [Pereira 2011]
38
Main Channel Cs Suspended Sand
Myrtle Belair
Outflows Cs Suspended Sand 3-D Modeling
39
Existing vs Myrtle Grove vs Belair Sand Concentration
Peak Flows (Q ~1.2x106 cfs) - April 2008
0
40
80
120
160
200
Belair (
RM
65)
Myr
tle G
rove
(RM
59)
W.P
Hac
he (R
M 4
9)
Bohe
mia
Spillw
ay (R
M 3
9)
Bayou
Lam
oque
(RM
33)
Fort S
t Phlip
(RM
20)
Baptis
te C
olle
tte (R
M 1
2)
Gra
nd Pas
s + T
iger
Pas
s (R
M 1
0)
Mai
n Pas
s (R
M 4
)
Outflow (River Mile)
Cs
Sa
nd
(m
g/L
)
Existing Myrtle Grove Belair
McCorquodale and Pereira (2011) Report to LPBF
Summary
40
3-D Modeling Scenarios: Existing Outflows
Myrtle Grove Diversion + Existing Outflows
Belair Diversion + Existing Outflows
Myrtle Grove diversion (30,000 cfs) showed mild
impacts
Diversion captures sand at close to the main stem
concentrations, SWR ~ 1
Sand Concentrations at the existing diversions
and distributaries were not dramatically changed;
< 10% decrease in Concentration.
Summary
41
Belair diversion (200,000 cfs) showed strong
impacts:
Increase in Energy gradient upstream and
decrease downstream of the diversion;
Decrease in Energy available for sand transport in
in the River and downstream diversions;
Increase in bed erosion at and upstream of the
diversion with possible head-cutting;
Decrease in stream power downstream of the
diversion leading to shoaling;
Significant decrease in sand concentrations
downstream of the diversion in both the main
stem and the existing passes and outflows.
Decrease of up to 60% in the sand concentrations
in the existing passes.
The Results support the concept that there
are three inter-related resources that must be
considered in optimizing the beneficial use of
the Mississippi River:
Discharge
Energy
Sediment
Nutrients
Summary
42
Governing Equations
Water Continuity
Reynolds-Averaged Navier-Stokes (RANS)
Momentum Equations
45
0
y
VD
x
UD
t
Numerical Model ECOMSED
00
00
2
2
xM Fd
x
DgDd
x
gDU
D
K
xgDfVD
U
y
UVD
x
DU
t
UD
00
00
2
2
yM Fd
y
DgDd
y
gDV
D
K
xgDfUD
V
y
DV
x
UVD
t
VD
Numerical Model ECOMSED
Non-cohesive Sediment Formulation
Suspended Sand by van Rijn (1984)
47
as FzuCq 12
*,
2
* crbedu
uT
3.0
*
5.1015.0
aD
TDC k
a f
f *
'ku
WZZ s
'2.11
'
2.1'
Zh
a
h
a
h
a
FZ
Z
T = transport parameter; F = vertical distribution function;
u*,crbed = critical bed shear velocity for initiation of motion
Ca = concentration at a reference height a; Z = function of fall velocity;
z = depth of lowest layer; qs = sediment flux per unit area for the lowest layer
2/1
50*, 1 crscrbed gDSu