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

14. 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. Can be further simplified !!

28. Mathematical formulation of the problem z ∞

29. z u 1 =u 1 (x,y,t) ρ 1 =cst u 2 =u 2 (x,y,t) ρ 2 =cst>ρ 1 ∞

30. Mathematical formulation of the problem Shallow water equations

31. Discretized in space using FiniteDifference

33. ζ η x(ζ, η)=? y(ζ, η)=?

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

35. 22500 grid points x 3 layers x 3 state variables (u,v,h)/layer = 202500 ODE’s

36. Some Results:

37. Eulerian and Lagrangian results

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

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

41. Higher Re

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