96 research outputs found
Strong effect of weak diffusion on scalar turbulence at large scales
Passive scalar turbulence forced steadily is characterized by the velocity
correlation scale, , injection scale, , and diffusive scale, . The
scales are well separated if the diffusivity is small, , and one
normally says that effects of diffusion are confined to smaller scales, . However, if the velocity is single scale one finds that a weak dependence
of the scalar correlations on the molecular diffusivity persists to even larger
scales, e.g. \cite{95BCKL}. We consider the case of
and report a counter-intuitive result -- the emergence of a new range of large
scales, , where the diffusivity shows a strong effect on
scalar correlations.Comment: 4 pages, 1 figure, submitted to Physics of Fluid
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.
Anomalous scaling in two and three dimensions for a passive vector field advected by a turbulent flow
A model of the passive vector field advected by the uncorrelated in time
Gaussian velocity with power-like covariance is studied by means of the
renormalization group and the operator product expansion. The structure
functions of the admixture demonstrate essential power-like dependence on the
external scale in the inertial range (the case of an anomalous scaling). The
method of finding of independent tensor invariants in the cases of two and
three dimensions is proposed to eliminate linear dependencies between the
operators entering into the operator product expansions of the structure
functions. The constructed operator bases, which include the powers of the
dissipation operator and the enstrophy operator, provide the possibility to
calculate the exponents of the anomalous scaling.Comment: 9 pages, LaTeX2e(iopart.sty), submitted to J. Phys. A: Math. Ge
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
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