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Updated: Jul 16, 2026

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
Published on: February 27, 2016
Inverse turbulent cascades and conformally invariant curves
D Bernard1, G Boffetta, A Celani
1LPT-ENS, 24 Rue Lhomond, 75231 Paris Cedex 05, France.
Abstract:
We offer a new example of conformal invariance (local scale invariance) far from equilibrium-the inverse cascade of surface quasigeostrophic (SQG) turbulence. We show that temperature isolines are statistically equivalent to curves that can be mapped into a one-dimensional Brownian walk (called Schramm-Loewner evolution or SLEkappa). The diffusivity is close to kappa=4, that is, isotemperature curves belong to the same universality class as domain walls in the O(2) spin model. Several statistics of temperature clusters and isolines are shown to agree with the theoretical expectations for such a spin system at criticality. We also show that the direct cascade in two-dimensional Navier-Stokes turbulence is not conformal invariant. The emerging picture is that conformal invariance may be expected for inverse turbulent cascades of strongly interacting systems.
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