Inverse turbulent cascades and conformally invariant curves

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.Comment: 4 pages, 6 figure

The large-scale structure of passive scalar turbulence

We investigate the large-scale statistics of a passive scalar transported by a turbulent velocity field. At scales larger than the characteristic lengthscale of scalar injection, yet smaller than the correlation length of the velocity, the advected field displays persistent long-range correlations due to the underlying turbulent velocity. These induce significant deviations from equilibrium statistics for high-order scalar correlations, despite the absence of scalar flux.Comment: 4 pages, 6 figure

Three-point correlation function of a scalar mixed by an almost smooth random velocity field

We demonstrate that if the exponent $\gamma$ that measures non-smoothness of the velocity field is small then the isotropic zero modes of the scalar's triple correlation function have the scaling exponents proportional to $\sqrt{\gamma}$. Therefore, zero modes are subleading with respect to the forced solution that has normal scaling with the exponent $\gamma$.Comment: 13 pages, RevTeX 3.