75 research outputs found
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
Passive scalar turbulence in high dimensions
Exploiting a Lagrangian strategy we present a numerical study for both
perturbative and nonperturbative regions of the Kraichnan advection model. The
major result is the numerical assessment of the first-order -expansion by
M. Chertkov, G. Falkovich, I. Kolokolov and V. Lebedev ({\it Phys. Rev. E},
{\bf 52}, 4924 (1995)) for the fourth-order scalar structure function in the
limit of high dimensions 's. %Two values of the velocity scaling exponent
have been considered: % and . In the first case, the
perturbative regime %takes place at , while in the second at , %in agreement with the fact that the relevant small parameter %of the
theory is . In addition to the perturbative results, the
behavior of the anomaly for the sixth-order structure functions {\it vs} the
velocity scaling exponent, , is investigated and the resulting behavior
discussed.Comment: 4 pages, Latex, 4 figure
Stretching of polymers in a random three-dimensional flow
Behavior of a dilute polymer solution in a random three-dimensional flow with
an average shear is studied experimentally. Polymer contribution to the shear
stress is found to be more than two orders of magnitude higher than in a
laminar shear flow. The results indicate that the polymer molecules get
strongly stretched by the random motion of the fluid.Comment: 4 pages, 3 figure
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