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Introdu tion
Physi al models
Comparison between H and N-H models
Modeling Sediment
Internal solitary wave
Con lusions
Hydrodynami s of Lakes and e osystems
Jair REYES
Institut Jean le Rond d'Alembert - UPMC
Do toral Advisor: Mauri e ROSSI
November 12, 2014
Jair REYES Presentation
Introdu tion
Physi al models
Comparison between H and N-H models
Modeling Sediment
Internal solitary wave
Con lusions
Introdu tion
The role of hydrodynami s on the dynami s of algae populations in
lakes.
What are the determining fa tors in the explosive growth of
ertain algae ?
This thesis is divided into two parts
Analysis of the �uid dynami s in lakes (Presented here).
Coupling biology models with hydrodynami s models
Jair REYES Presentation
Introdu tion
Physi al models
Comparison between H and N-H models
Modeling Sediment
Internal solitary wave
Con lusions
Content
1.- Comparison Hydrostati and Nonhydrostati model
2.- Sediment resuspension using GERRIS ode.
2.a The model and its validations
2.b Example of sediment resuspension due to urrents
2. Example of sediment resuspension due to Internal Solitary
Waves breaking
Jair REYES Presentation
Introdu tion
Physi al models
Comparison between H and N-H models
Modeling Sediment
Internal solitary wave
Con lusions
Equations and Boundary Conditions
Hydrodynami s of Lakes
Physi al Models
Hydrostati model (FORTRAN Code):
Model widely used in marine s ien e
Verti al momentum equation repla ed by the hydrostati
approximation.
Verti al velo ity al ulated from the ontinuity equation.
Primitive equations solved by using sigma oordinates
Is the hydrostati model orre t near boundaries?
Jair REYES Presentation
Introdu tion
Physi al models
Comparison between H and N-H models
Modeling Sediment
Internal solitary wave
Con lusions
Equations and Boundary Conditions
Hydrodynami s of Lakes
Physi al Models
Nonhydrostati model (GERRIS Code):
Navier-Stokes equations
E�e tive vis osity
Surfa e: Rigid-Lid Approximation
We have ompared the hydrostati and nonhydrostati model.
Jair REYES Presentation
Introdu tion
Physi al models
Comparison between H and N-H models
Modeling Sediment
Internal solitary wave
Con lusions
Equations and Boundary Conditions
Hydrodynami s of Lakes
Di�erent simpli�ed topographies: �at and paraboli basins.
We are interested in
Stru ture of urrents
Shear on the bottom
Surfa e:
(
µ∂u∂z,w
)
= (τs
, 0)
W
a
l
l
s
:
S
l
i
p
o
n
d
i
t
i
o
n
Bottom: No-slip ondition
Jair REYES Presentation
Introdu tion
Physi al models
Comparison between H and N-H models
Modeling Sediment
Internal solitary wave
Con lusions
Di�erent ases
Di�erents Reynolds numbers: Re = ρ[U][L]µ
= ρτs
H
2
µ2.
H [m℄ µ [
kg
ms
℄ U
wind
[
km
h
℄ Re Re
max
10 1
3.2 100 24.0
6.4 400 88.7
10.3 1 000 198.5
17.8 3 000 493.6
32.5 10 000 1213.3
With Re
max
as a Reynolds number based in the highest
horizontal velo ity u
max
.
Jair REYES Presentation
Introdu tion
Physi al models
Comparison between H and N-H models
Modeling Sediment
Internal solitary wave
Con lusions
Unsteady �ow
-1-0.8-0.6-0.4-0.2
0
-4 -3 -2 -1 0 1 2 3 4
y
x
Velocity field Re=10 000, t = 1240
-1
0
1
2
3Vorticity
Video Re = 10000
Jair REYES Presentation
Introdu tion
Physi al models
Comparison between H and N-H models
Modeling Sediment
Internal solitary wave
Con lusions
Steady velo ity �eld
Steady velo ity �eld orresponding to paraboli lake of Re = 10
3
-1-0.8-0.6-0.4-0.2
0
-4 -3 -2 -1 0 1 2 3 4
y
x
0 0.04 0.08 0.12 0.16 0.2
Velocity Norm
t = 100
-1-0.8-0.6-0.4-0.2
0
-4 -3 -2 -1 0 1 2 3 4
y
x
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18
Velocity Norm
NH-M
H-M
Jair REYES Presentation
Introdu tion
Physi al models
Comparison between H and N-H models
Modeling Sediment
Internal solitary wave
Con lusions
Steady velo ity �eld
Steady velo ity �eld orresponding to re tangular lake of
Re = 4 · 102
-1-0.8-0.6-0.4-0.2
0
-4 -3 -2 -1 0 1 2 3 4
y
x
0 0.04 0.08 0.12 0.16 0.2 0.24 0.28
Velocity Norm
-1-0.8-0.6-0.4-0.2
0
-4 -3 -2 -1 0 1 2 3 4
y
x
0 0.05 0.1 0.15 0.2 0.25
Velocity Norm
-1
-0.9
-0.8
-0.7
-0.6
-0.5
3.8 3.85 3.9 3.95 4y
x
0
0.005
0.01
0.015
0.02
0.025
NH-M
H-M
Zoom H-M
Jair REYES Presentation
Introdu tion
Physi al models
Comparison between H and N-H models
Modeling Sediment
Internal solitary wave
Con lusions
Upwelling and downwelling regions
NH model H model
P
R
-1-0.8-0.6-0.4-0.2
0 0.2 0.4 0.6 0.8
-4 -3 -2 -1 0 1 2 3 4
UD
W(x
)
x
Re = 102
4·102
103
3·103
104
Lx = 8
-1-0.8-0.6-0.4-0.2
0 0.2 0.4
-4 -3 -2 -1 0 1 2 3 4
UD
W(x
)
x
Re = 102
4·102
103
3·103
104
Lx = 8
-1-0.8-0.6-0.4-0.2
0 0.2 0.4 0.6
-4 -3 -2 -1 0 1 2 3 4
UD
W(x
)
x
Re = 102
4·102
103
-1-0.8-0.6-0.4-0.2
0 0.2 0.4
-4 -3 -2 -1 0 1 2 3 4
UD
W(x
)x
Re = 102
4·102
103
Upwelling and Downwelling Fun tion
w̄(x) = 1
top−bottom
∫
z=topz=bottom w(x , z) dz .
Jair REYES Presentation
Introdu tion
Physi al models
Comparison between H and N-H models
Modeling Sediment
Internal solitary wave
Con lusions
Validation of sediment al ulation
Erosion of sediment in the lake
Modeling Sediment
Dimensionless sediment equation
φt
+ u ·∇φ =1
S Re
∆φ, (1)
with S = νDφ
Dimensionless boundary onditions:
Surfa e and walls:
∂φ∂n
= 0
Bottom: Suspension and deposition depending on shear.
∂φ∂n
= −[Eb
(τb
) + D
b
(τb
)φ].
where τb
is the shear stress on the bottom
Jair REYES Presentation
Introdu tion
Physi al models
Comparison between H and N-H models
Modeling Sediment
Internal solitary wave
Con lusions
Validation of sediment al ulation
Erosion of sediment in the lake
Modeling Sediment
Bottom boundary ondition
Erosion of Sediment:
E
b
=
0 |τb
| < τ e
e
b
(
|τb
|τ e
− 1
)
|τb
| ≥ τ e
,
Deposition of Sediment:
D
b
=
0 |τb
| > τ d
d
b
n · ez
(
1− ‖τb
‖τ d
)
|τb
| ≤ τ d
,
Jair REYES Presentation
Introdu tion
Physi al models
Comparison between H and N-H models
Modeling Sediment
Internal solitary wave
Con lusions
Validation of sediment al ulation
Erosion of sediment in the lake
Validation: Two dimensional In lined Couette Flow
Di�erents angles θ = 0,10, 20
Jair REYES Presentation
Introdu tion
Physi al models
Comparison between H and N-H models
Modeling Sediment
Internal solitary wave
Con lusions
Validation of sediment al ulation
Erosion of sediment in the lake
2D Couette Flow
Sediment omputation
Sediment mass in the total volume
Φ =∫
φ dV = τs
t.
0
0.5
1
1.5
2
2.5
3
0 2 4 6 8 10
Φ
t
Analytical solution Numerical solution, Run 1
23
Jair REYES Presentation
Introdu tion
Physi al models
Comparison between H and N-H models
Modeling Sediment
Internal solitary wave
Con lusions
Validation of sediment al ulation
Erosion of sediment in the lake
2D Couette Flow
θ = 20, Re�ne=2
6
θ = 20, Re�ne=2
8
PDF of relative error in shear omputation:
η =τs
analiti
−τs
numeri
τs
analiti
0
50
100
150
200
250
300
-0.04 -0.03 -0.02 -0.01 0 0.01 0.02
P.D
.F.
Run 123
Refine = 26
0
50
100
150
200
250
300
350
400
-0.04 -0.03 -0.02 -0.01 0 0.01 0.02
P.D
.F.
η
Run 123
Refine = 28
0
0.2
0.4
0.6
0.8
1
-0.04 -0.02 0 0.02
C.F
.D.
η 0
0.2
0.4
0.6
0.8
1
-0.04 -0.02 0 0.02
C.F
.D.
η
0
0.2
0.4
0.6
0.8
1
-0.04 -0.02 0 0.02
C.F
.D.
η
Jair REYES Presentation
Introdu tion
Physi al models
Comparison between H and N-H models
Modeling Sediment
Internal solitary wave
Con lusions
Validation of sediment al ulation
Erosion of sediment in the lake
3D Poiseuille Flow
θ ≈ 0, Re�ne=2
8
θ ≈ 40, Re�ne=2
8
0
5
10
15
20
25
30
-0.1 -0.05 0 0.05 0.1
P.D
.F.
η
Run 123
0 0.2 0.4 0.6 0.8
1
-0.05 0 0.05
C.D
.F.
η
Errors lo ated at the MPI boundaries
Jair REYES Presentation
Introdu tion
Physi al models
Comparison between H and N-H models
Modeling Sediment
Internal solitary wave
Con lusions
Validation of sediment al ulation
Erosion of sediment in the lake
Erosion of sediment in the lake
Video Re = 10
5
Jair REYES Presentation
Introdu tion
Physi al models
Comparison between H and N-H models
Modeling Sediment
Internal solitary wave
Con lusions
ISW Breaking
Internal solitary wave (ISW) modeling
1
Momentum equation with Boussinesq approximation
2
Adve tion-di�usion equation for temperature
Boundary onditions
Surfa e:
(
v , ∂u∂x, ∂ρ∂y
)
= (0, 0, 0);
Right wall:
(
u, ∂v∂y
, ∂ρ∂x
)
= (0, 0, 0);
Bottom:
(
u, v ,∂ρ∂n
)
= (0, 0, 0).
G. Ri kard,J. Callaghan, S. Popinet, OMJ (2009).
Jair REYES Presentation
Introdu tion
Physi al models
Comparison between H and N-H models
Modeling Sediment
Internal solitary wave
Con lusions
ISW Breaking
ISW Breaking
Suspension of sediment du to ISW breaking and run-up
Video suspension
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 5 10 15 20 25
Φ=∫
φdV
t
Sediment concentration evolutionRun 1 Run 2 Run 3
Sediment
Φ =∫
φdV
Jair REYES Presentation
Introdu tion
Physi al models
Comparison between H and N-H models
Modeling Sediment
Internal solitary wave
Con lusions
Con lusion
Comparison of the Hydrostati and Nonhydrostati Models
Sediment resuspension du to urrents in the lake.
Sediment resuspension du to ISW breaking and run-up.
Jair REYES Presentation