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A Deterministic View of Modeling of the Gulf of Mexico

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.

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A Deterministic View of Modeling of the Gulf of Mexico

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  1. A Deterministic View of Modeling of the Gulf of Mexico Guillaume Vernieres (SAMSI/UNC)

  2. Outline • Motivations • Some physical background • Mathematical formulation of the problem • Results • …That’s it …

  3. Motivations • Why do we care? http://www.camex4.com/photos/Ivan.A2004258.1635.2km.jpg

  4. Motivations • Why do we care? HURRICANE TRACK PREDICTION !!!!!!!!!

  5. Motivations • Why do we care? Test bed for modeling methods

  6. Physical background • Ocean currents http://www.waterencyclopedia.com/images/wsci_03_img0381.jpg

  7. Physical background • Global Wind http://research.utep.edu/Portals/72/weather%20NOAA/global%20wind.gif

  8. Physical background • The Gulf Stream

  9. Physical background • The Gulf of Mexico: Shedding of eddies Sea Surface Height in cm

  10. Physical background • The Gulf of Mexico: Shedding of eddies Sea Surface Temperature

  11. Mathematical formulation of the problem

  12. Mathematical formulation of the problem

  13. Mathematical formulation of the problem

  14. Mathematical formulation of the problem Simple conservation laws:

  15. Mathematical formulation of the problem Simple conservation laws: • Conservation of mass

  16. Mathematical formulation of the problem Simple conservation laws: • Conservation of mass =

  17. Mathematical formulation of the problem Simple conservation laws: • Conservation of mass • Conservation of momentum

  18. Mathematical formulation of the problem Simple conservation laws: • Conservation of mass • Conservation of momentum • Rotating frame!! (yes the earth is turning!)

  19. Mathematical formulation of the problem Simple conservation laws: • Conservation of mass • Conservation of momentum • Rotating frame!! (yes the earth is turning!) • Hydrostatic pressure

  20. 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

  21. 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

  22. 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

  23. Mathematical formulation of the problem x & y momentum

  24. Mathematical formulation of the problem Hydrostatic assumption

  25. Mathematical formulation of the problem Continuity equation (conservation of mass)

  26. Mathematical formulation of the problem

  27. Mathematical formulation of the problem Can be further simplified !!

  28. Mathematical formulation of the problem z ∞

  29. Mathematical formulation of the problem z u1=u1(x,y,t) ρ1=cst u2=u2(x,y,t) ρ2=cst>ρ1 ∞

  30. Mathematical formulation of the problem Shallow water equations

  31. Discretized in space using FiniteDifference

  32. η x(ζ, η)=? y(ζ, η)=? ζ

  33. Discretized in space using FiniteDifference • Discretized in time using Adams-Bashforth • 2nd order

  34. 22500 grid points x 3 layers x 3 state variables (u,v,h)/layer = 202500 ODE’s

  35. Some Results:

  36. Eulerian and Lagrangian results

  37. Can real drifter location be used to forecast the state of the GoM ?

  38. How much information is contained in one single drifter ?

  39. Higher Re

  40. “Influence of a drifter on the state of the GoM”

  41. “Influence of a drifter on the state of the GoM”

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