Download presentation
Presentation is loading. Please wait.
1
G. Falkovich February 2006 Conformal invariance in 2d turbulence
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
5
2d Navier-Stokes equations In fully developed turbulence limit, Re=UL -> ∞ (i.e. ->0): (because dZ/dt≤0 and Z(t) ≤Z(0))
6
The double cascade Kraichnan 1967 The double cascade scenario is typical of 2d flows, e.g. plasmas and geophysical flows. kFkF Two inertial range of scales: energy inertial range 1/L<k<k F (with constant ) enstrophy inertial range k F <k<k d (with constant ) Two power-law self similar spectra in the inertial ranges.
9
_____________ =
10
P Boundary Frontier Cut points Boundary Frontier Cut points
11
Schramm-Loewner Evolution (SLE)
14
C=ξ(t)
16
Vorticity clusters
17
Phase randomizedOriginal
20
Possible generalizations Ultimate Norway
21
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.
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.