a deterministic view of modeling of the gulf of mexico guillaume vernieres (samsi/unc)
DESCRIPTION
Motivations Why do we care?TRANSCRIPT
![Page 1: A Deterministic View of Modeling of the Gulf of Mexico Guillaume Vernieres (SAMSI/UNC)](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b547f8b9ab0599a8e1a/html5/thumbnails/1.jpg)
A Deterministic View of Modeling of the Gulf of Mexico
Guillaume Vernieres (SAMSI/UNC)
![Page 2: A Deterministic View of Modeling of the Gulf of Mexico Guillaume Vernieres (SAMSI/UNC)](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b547f8b9ab0599a8e1a/html5/thumbnails/2.jpg)
Outline
• Motivations• Some physical background• Mathematical formulation of the problem• Results• …That’s it …
![Page 3: A Deterministic View of Modeling of the Gulf of Mexico Guillaume Vernieres (SAMSI/UNC)](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b547f8b9ab0599a8e1a/html5/thumbnails/3.jpg)
Motivations
• Why do we care?
http://www.camex4.com/photos/Ivan.A2004258.1635.2km.jpg
![Page 4: A Deterministic View of Modeling of the Gulf of Mexico Guillaume Vernieres (SAMSI/UNC)](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b547f8b9ab0599a8e1a/html5/thumbnails/4.jpg)
Motivations
• Why do we care?
HURRICANE TRACK PREDICTION !!!!!!!!!
![Page 5: A Deterministic View of Modeling of the Gulf of Mexico Guillaume Vernieres (SAMSI/UNC)](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b547f8b9ab0599a8e1a/html5/thumbnails/5.jpg)
Motivations
• Why do we care?
Test bed for modeling methods
![Page 6: A Deterministic View of Modeling of the Gulf of Mexico Guillaume Vernieres (SAMSI/UNC)](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b547f8b9ab0599a8e1a/html5/thumbnails/6.jpg)
Physical background
• Ocean currents
http://www.waterencyclopedia.com/images/wsci_03_img0381.jpg
![Page 7: A Deterministic View of Modeling of the Gulf of Mexico Guillaume Vernieres (SAMSI/UNC)](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b547f8b9ab0599a8e1a/html5/thumbnails/7.jpg)
Physical background
• Global Wind
http://research.utep.edu/Portals/72/weather%20NOAA/global%20wind.gif
![Page 8: A Deterministic View of Modeling of the Gulf of Mexico Guillaume Vernieres (SAMSI/UNC)](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b547f8b9ab0599a8e1a/html5/thumbnails/8.jpg)
Physical background
• The Gulf Stream
![Page 9: A Deterministic View of Modeling of the Gulf of Mexico Guillaume Vernieres (SAMSI/UNC)](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b547f8b9ab0599a8e1a/html5/thumbnails/9.jpg)
Physical background
• The Gulf of Mexico: Shedding of eddies
Sea Surface Height in cm
![Page 10: A Deterministic View of Modeling of the Gulf of Mexico Guillaume Vernieres (SAMSI/UNC)](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b547f8b9ab0599a8e1a/html5/thumbnails/10.jpg)
Physical background
• The Gulf of Mexico: Shedding of eddies
Sea Surface Temperature
![Page 11: A Deterministic View of Modeling of the Gulf of Mexico Guillaume Vernieres (SAMSI/UNC)](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b547f8b9ab0599a8e1a/html5/thumbnails/11.jpg)
Mathematical formulation of the problem
![Page 12: A Deterministic View of Modeling of the Gulf of Mexico Guillaume Vernieres (SAMSI/UNC)](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b547f8b9ab0599a8e1a/html5/thumbnails/12.jpg)
Mathematical formulation of the problem
![Page 13: A Deterministic View of Modeling of the Gulf of Mexico Guillaume Vernieres (SAMSI/UNC)](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b547f8b9ab0599a8e1a/html5/thumbnails/13.jpg)
Mathematical formulation of the problem
![Page 14: A Deterministic View of Modeling of the Gulf of Mexico Guillaume Vernieres (SAMSI/UNC)](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b547f8b9ab0599a8e1a/html5/thumbnails/14.jpg)
Mathematical formulation of the problem
Simple conservation laws:
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Mathematical formulation of the problem
Simple conservation laws:• Conservation of mass
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Mathematical formulation of the problem
Simple conservation laws:• Conservation of mass
=
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Mathematical formulation of the problem
Simple conservation laws:• Conservation of mass• Conservation of momentum
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Mathematical formulation of the problem
Simple conservation laws:• Conservation of mass• Conservation of momentum• Rotating frame!! (yes the earth is turning!)
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Mathematical formulation of the problem
Simple conservation laws:• Conservation of mass• Conservation of momentum• Rotating frame!! (yes the earth is turning!)• Hydrostatic pressure
![Page 20: A Deterministic View of Modeling of the Gulf of Mexico Guillaume Vernieres (SAMSI/UNC)](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b547f8b9ab0599a8e1a/html5/thumbnails/20.jpg)
Mathematical formulation of the problem
Simple conservation laws:• Conservation of mass• Conservation of momentum• Rotating frame!! (yes the earth is turning!)• Hydrostatic pressure• Neglect thermodynamics
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Mathematical formulation of the problem
Simple conservation laws:• Conservation of mass• Conservation of momentum• Rotating frame!! (yes the earth is turning!)• Hydrostatic pressure• Neglect thermodynamics• L>>D
![Page 22: A Deterministic View of Modeling of the Gulf of Mexico Guillaume Vernieres (SAMSI/UNC)](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b547f8b9ab0599a8e1a/html5/thumbnails/22.jpg)
Mathematical formulation of the problem
Simple conservation laws:• Conservation of mass• Conservation of momentum• Rotating frame!! (yes the earth is turning!)• Hydrostatic pressure• Neglect thermodynamics• L>>D
Similar to the Navier-Sokes equations
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Mathematical formulation of the problem
0
0
u
gz
M
uMukfz
uwuut
uHH
HHH
H
x & y momentum
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Mathematical formulation of the problem
0
0
u
gz
M
uMukfz
uwuut
uHH
HHH
H
Hydrostatic assumption
![Page 25: A Deterministic View of Modeling of the Gulf of Mexico Guillaume Vernieres (SAMSI/UNC)](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b547f8b9ab0599a8e1a/html5/thumbnails/25.jpg)
Mathematical formulation of the problem
0
0
u
gz
M
uMukfz
uwuut
uHH
HHH
H
Continuity equation(conservation of mass)
![Page 26: A Deterministic View of Modeling of the Gulf of Mexico Guillaume Vernieres (SAMSI/UNC)](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b547f8b9ab0599a8e1a/html5/thumbnails/26.jpg)
Mathematical formulation of the problem
0
0
u
gz
M
uMukfz
uwuut
uHH
HHH
H
)),,,(),,,,(),,,,(()),,,(),,,,((
tzyxwtzyxvtzyxuutzyxvtzyxuuH
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Mathematical formulation of the problem
0
0
u
gz
M
uMukfz
uwuut
uHH
HHH
H
Can be further simplified !!
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Mathematical formulation of the problem
z
∞
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Mathematical formulation of the problem
z
u1=u1(x,y,t) ρ1=cst
u2=u2(x,y,t) ρ2=cst>ρ1
∞
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Mathematical formulation of the problem
),,(,...,1 )),,(),,,((
0)(
tyxhhNntyxvtyxuu
hut
h
uMukfdtud
nn
nnn
nnn
nnnn
Shallow water equations
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),,(,...,1 )),,(),,,((
0)(
tyxhhNntyxvtyxuu
hut
h
uMukfdtud
nn
nnn
nnn
nnnn
•Discretized in space using FiniteDifference
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ζ
η
x(ζ, η)=?y(ζ, η)=?
![Page 34: A Deterministic View of Modeling of the Gulf of Mexico Guillaume Vernieres (SAMSI/UNC)](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b547f8b9ab0599a8e1a/html5/thumbnails/34.jpg)
),,(,...,1 )),,(),,,((
0)(
tyxhhNntyxvtyxuu
hut
h
uMukfdtud
nn
nnn
nnn
nnnn
•Discretized in space using FiniteDifference•Discretized in time using Adams-Bashforth 2nd order
![Page 35: A Deterministic View of Modeling of the Gulf of Mexico Guillaume Vernieres (SAMSI/UNC)](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b547f8b9ab0599a8e1a/html5/thumbnails/35.jpg)
22500 grid points x
3 layersx
3 state variables (u,v,h)/layer=
202500 ODE’s
![Page 36: A Deterministic View of Modeling of the Gulf of Mexico Guillaume Vernieres (SAMSI/UNC)](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b547f8b9ab0599a8e1a/html5/thumbnails/36.jpg)
Some Results:
![Page 37: A Deterministic View of Modeling of the Gulf of Mexico Guillaume Vernieres (SAMSI/UNC)](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b547f8b9ab0599a8e1a/html5/thumbnails/37.jpg)
Eulerian and Lagrangian results
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![Page 39: A Deterministic View of Modeling of the Gulf of Mexico Guillaume Vernieres (SAMSI/UNC)](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b547f8b9ab0599a8e1a/html5/thumbnails/39.jpg)
Can real drifter location be used to forecast the state of the GoM ?
![Page 40: A Deterministic View of Modeling of the Gulf of Mexico Guillaume Vernieres (SAMSI/UNC)](https://reader034.vdocuments.mx/reader034/viewer/2022052607/5a4d1b547f8b9ab0599a8e1a/html5/thumbnails/40.jpg)
How much information is contained in one single drifter ?
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Higher Re
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“Influence of a drifter on the state of the GoM”
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“Influence of a drifter on the state of the GoM”