1 / 21

Conformal Invariance in 2D Turbulence

Explore the simplicity and fundamental symmetries of physical laws in 2D turbulence, focusing on the concept of conformal invariance. Discuss the double cascade scenario and the potential for conformally invariant statistics in turbulent problems.

susanlindsey
Download Presentation

Conformal Invariance in 2D Turbulence

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. G. Falkovich Conformal invariance in 2d turbulence February 2006

  2. Simplicity of fundamental physical laws manifests itself in fundamental symmetries. Strong fluctuations - infinitely many strongly interacting degrees of freedom → scale invariance. Locality + scale invariance → conformal invariance

  3. Conformal transformation rescale non-uniformly but preserve angles z

  4. 2d Navier-Stokes equations a In fully developed turbulence limit, Re=UL/n -> ∞ (i.e. n->0): (because dZ/dt≤0 and Z(t) ≤Z(0))

  5. kF The double cascade Kraichnan 1967 • Two inertial range of scales: • energy inertial range 1/L<k<kF • (with constant e) • enstrophy inertial range kF<k<kd • (with constant z) Two power-law self similar spectra in the inertial ranges. The double cascade scenario is typical of 2d flows, e.g. plasmas and geophysical flows.

  6. _____________ =

  7. Boundary • Frontier • Cut points P

  8. Schramm-Loewner Evolution (SLE)

  9. C=ξ(t)

  10. Vorticity clusters

  11. Phase randomized Original

  12. Possible generalizations Ultimate Norway

  13. Conclusion Within experimental acuracy, zero-vorticity lines in the 2d inverse cascade have conformally invariant statistics equivalent to that of critical percolation. Isolines in other turbulent problems may be conformally invariant as well.

More Related