Stochastic geometry of turbulence. Gregory Falkovich Weizmann Institute. D. Bernard , G. Boffetta, Celani, S . Musacchio , K. Turitsyn,M . Vucelja. APS meeting, 28 February 2012. Fractals, multi-fractals and God knows what. depends neither on q nor on r - fractal.
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D. Bernard, G. Boffetta,
Celani, S. Musacchio,
K. Turitsyn,M. Vucelja
APS meeting, 28 February 2012
depends neither on q nor on r - fractal
depends on q – multi-fractal
depends on r - God knows what
deviated far from equilibrium. It is irregular both in time and in space.
Energy cascade and Kolmogorov scaling
Transported scalar (Lagrangian invariant)
What about a single isoline?
Random Gaussian Surfaces
m=1 Surface quasi-geostrophic model,
m=-2 Charney-Hasegawa-Mima model
Electrostatic analogy: Coulomb law in d=4-m dimensions
This system describes geodesics on an infinitely-dimensional Riemannian manifold of the area-preserving diffeomorfisms. On a torus,
lhs of (*) conserves
Bernard, Boffetta, Celani &GF, Nature Physics 2006, PRL2007
Fractal iso-contours of passive scalar in two-dimensional smooth random flows.
J Stat Phys 147 : 424–435 (2012)
Within experimental accuracy, isolines of advected quantities
are conformal invariant (SLE) in turbulent inverse cascades. Why?
Vorticity isolines in the direct cascade are multi-fractal.
Isolines of passive scalar in the Batchelor regime continue to change on a time scale vastly exceeding the saturation time of the bulk scalar field.