1 / 27

Symmetries of Turbulent State: Understanding Inverse Cascades in Turbulence through Conformal Invariance

Explore the symmetries of turbulent state with Gregory Falkovich and collaborators. From Euler equation in 2D to Charney-Hasegawa-Mima model, uncover the electrostatic analogy and its implications on geodesics in Riemannian manifold. Investigate the role of inverse cascades in turbulence, including Kraichnan’s double cascade and Q-cascade picture. Discover the connection between vorticity clusters and Schramm-Loewner Evolution (SLE) in different systems. Delve into critical phenomena, random walks, and chaotic systems linked to SLE and turbulent inverse cascades. Find out how conformal invariance manifests in isolines of advected quantities in turbulent cascades. Unravel the scale invariance mystery within experimental accuracy.

yahto
Download Presentation

Symmetries of Turbulent State: Understanding Inverse Cascades in Turbulence through Conformal Invariance

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Symmetries of turbulent state Gregory Falkovich Weizmann Institute of Science D. Bernard, A. Celani, G. Boffetta, S. Musacchio Rutgers, May 10, 2009

  2. Euler equation in 2d describes transport of vorticity

  3. Family of transport-type equations m=2 Navier-Stokes m=1 Surface quasi-geostrophic model, m=-2 Charney-Hasegawa-Mima model Electrostatic analogy: Coulomb law in d=4-m dimensions

  4. This system describes geodesics on an infinitely-dimensional Riemannian manifold of the area-preserving diffeomorfisms. On a torus,

  5. Add force and dissipation to provide for turbulence (*) lhs of (*) conserves

  6. Kraichnan’s double cascade picture Q P k pumping

  7. Inverse Q-cascade

  8. Small-scale forcing – inverse cascades

  9. Locality + scale invariance → conformal invariance ? Polyakov 1993

  10. _____________ =

  11. Boundary • Frontier • Cut points perimeter P Bernard, Boffetta, Celani &GF, Nature Physics 2006, PRL2007

  12. Vorticity clusters

  13. Schramm-Loewner Evolution (SLE)

  14. What it has to do with turbulence?

  15. C=ξ(t)

  16. m

  17. Different systems producing SLE • Critical phenomena with local Hamiltonians • Random walks, non necessarily local • Inverse cascades in turbulence • Nodal lines of wave functions in chaotic systems • Spin glasses • Rocky coastlines

  18. Conclusion Inverse cascades seems to be scale invariant. Within experimental accuracy, isolines of advected quantities are conformal invariant (SLE) in turbulent inverse cascades. Why?

More Related