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Solutions stationnaires des équations de Navier-Stokes en domaines extérieurs

Solutions stationnaires des équations de Navier-Stokes en domaines extérieurs. Peter Wittwer Département de Physique Théorique Université de Genève. reading : R. P. Feynman, Vol. II G. K. Batchelor, An Introduction to Fluid Mechanics L. Landau, E. Lifchitz, Mécanique des fluides

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Solutions stationnaires des équations de Navier-Stokes en domaines extérieurs

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  1. Solutions stationnaires des équations de Navier-Stokes en domaines extérieurs Peter Wittwer Département de Physique Théorique Université de Genève

  2. reading: R. P. Feynman, Vol. II G. K. Batchelor, An Introduction to Fluid Mechanics L. Landau, E. Lifchitz, Mécanique des fluides M. Van Dyke, An Album of Fluid Motion collaborations: Guillaume Van Baalen Frédéric Haldi Sebastian Bönisch Vincent Heuveline

  3. Introduction to the problem • Asymptotic analysis • Applications

  4. Exterior Flows

  5. Navier-Stokes

  6. Re=0.16

  7. Re=1.54

  8. Re=56.5

  9. Re=118

  10. Re=7000

  11. Case of finite volume

  12. Case of infinite volume, I

  13. Case of infinite volume, II

  14. Asymptotic analysis

  15. Results (d=2)

  16. Interpretation:

  17. Results (d=3)

  18. Two steps: • construct downstream asymptotics • dynamical system • invariant manifold theory • renormalization group • universality • determines asymptotics everywhere

  19. Vorticity:

  20. Vorticity equation

  21. Fourier transform

  22. Diagonalize

  23. Stable and unstable modes

  24. use contraction mapping principle

  25. Large time asymptotics:

  26. Two steps: • construct downstream asymptotics • dynamical system • invariant manifold theory • renormalization group • universality • determines asymptotics everywhere

  27. Determines asymptotics everywhere:

  28. Applications in collaboration with: Sebastian Bönisch Rolf Rannacher Vincent Heuveline Heidelberg & Karlsruhe

  29. Adaptive boundary conditions

  30. To second order:

  31. Comparison with Experiment:

  32. Cloud Microphysics and Climate M. B. Baker, SCIENCE, Vol. 276, 1997

  33. Work in progress: • d=2 case with lift (numerical) • d=2 second order asymptotics (theory) • d=3 (numerical) • d=2, 3: free fall problem (numerical) • d=3 case with rotation at infinity (theory; see P. Galdi • (2005) for recent results) • Other research groups: • d=2 time periodic (theory)

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