Inverse turbulent cascades and conformally invariant curves
- Others:
- Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] (LPTENS) ; Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS) ; École normale supérieure - Paris (ENS-PSL) ; Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL) ; Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)
- Dipartimento di Fisica Generale [Torino] ; Università degli studi di Torino = University of Turin (UNITO)
- Institut Non Linéaire de Nice Sophia-Antipolis (INLN) ; Université Nice Sophia Antipolis (1965 - 2019) (UNS) ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)
- Physics of Complex systems ; Weizmann Institute of Science [Rehovot, Israël]
- ANR-06-BLAN-0058,SLE,Outils probabilistes et invariance conforme en theorie des champs: SLE et autres processus de croissance.(2006)
Description
We offer a new example of conformal invariance far from equilibrium -- the inverse cascade of Surface Quasi-Geostrophic (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 SLE$_\kappa$). The diffusivity is close to $\kappa=4$, that is iso-temperature curves belong to the same universality class as domain walls in the O(2) spin model. Several statistics of temperature clusters and isolines are measured and shown to be consistent 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.
Abstract
4 pages, 6 figures
Additional details
- URL
- https://hal.archives-ouvertes.fr/hal-00283889
- URN
- urn:oai:HAL:hal-00283889v1
- Origin repository
- UNICA