About Lecture
List of slides
  1. Breifing
  2. Introduction
  3. Schedule of Lectures
  4. The classical examples : Arakawa's Jacobian(1966)
  5. Why is it important to maintain these conservations laws?
  6. How does the Arakawa Jacobian work?
  7. What does this have to do with the Arakawa Jacobian?
  8. 2nd-order Arakawa Jacobian
  9. REVIEW OF POISSON BRACKETS
  10. Examples : the shallow water equations(SWE) (1)
  11. Examples : the shallow water equations(SWE) (2)
  12. Arakawa + Lamb (1981)
  13. Hamiltonian approach: EXAMPLE one-dimentional SWE
  14. CONSERVATION LAWS IN HAMILTONIAN SYSTEMS
  15. A 1d SWE scheme that DOES conserve potential enstrophy
  16. GENERAL 2-DIMENTIONAL BRACKET(1)
  17. GENERAL 2-DIMENTIONAL BRACKET(2)
  18. Arakawa + Lamb (1981) scheme
  19. Find all the conservative algorithms that correspond to this stencil:
  20. How are the coefficients actually determined?
  21. C-grid schemes(1)
  22. C-grid schemes(2)
  23. The potential vorticity field
  24. Why do this?
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