379 research outputs found
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). The diffusivity is close to , 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 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
. Therefore, zero modes are subleading with respect to the
forced solution that has normal scaling with the exponent .Comment: 13 pages, RevTeX 3.
- …