1. Universality in low Reynolds number flows: theory and applications 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

8. Re=0.16

9. Re=1.54

10. Re=56.5

11. Re=118

12. Re=7000

15. Case of finite volume

16. Case of infinite volume, I

17. Case of infinite volume, II

18. Asymptotic analysis

19. Results (d=2)

21. Interpretation:

23. Results (d=3)

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

27. Vorticity:

28. Vorticity equation

30. Fourier transform

31. Diagonalize

32. Stable and unstable modes

34. use contraction mapping principle

35. Large time asymptotics:

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

37. Determines asymptotics everywhere:

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

39. Adaptive boundary conditions

43. To second order:

44. Comparison with Experiment:

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

46. 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)