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