# Inverse cascade and intermittency of passive scalar in one-dimensional smooth flow

@article{Chertkov1997InverseCA,
title={Inverse cascade and intermittency of passive scalar in one-dimensional smooth flow},
author={Michael Chertkov and Igor V. Kolokolov and M. Vegrassola},
journal={Physical Review E},
year={1997},
volume={56},
pages={5483-5499}
}
• Published 12 June 1997
• Mathematics
• Physical Review E
Random advection of a Lagrangian tracer scalar field $\ensuremath{\theta}(t,x)$ by a one-dimensional, spatially smooth and short-correlated in time velocity field is considered. Scalar fluctuations are maintained by a source concentrated at the integral scale $L.$ The statistical properties of both scalar differences and the dissipation field are analytically determined, exploiting the dynamical formulation of the model. The Gaussian statistics known to be present at small scales for…
• Physics
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2012
The negative filtered flux at large scales and the time-increasing total variance give evidences to the existence of an inverse cascade of the passive concentration, which is induced by the implosive collapse in the Lagrangian trajectories.
The main physical problem of the theory of developed turbulence is to understand the degree of universality of the statistics, that is independence of the conditions of excitation and dissipation.
• Physics
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2014
It is shown that various correlation functions of the scalar field, its powers and gradients, demonstrate anomalous scaling behavior in the inertial-convective range already for small values of y, and the corresponding anomalous exponents, identified with scaling (critical) dimensions of certain composite fields, can be systematically calculated as series in y.
• Physics
• 1998
A model of scalar turbulent advection in compressible flow is analytically investigated. It is shown that, depending on the dimensionality d of space and the degree of compressibility of the smooth
• Physics
Theoretical and Mathematical Physics
• 2019
Using a quantum field theory renormalization group, we consider models of advection of a vector field and a tracer field by a compressible turbulent flow. Both advected fields are considered passive,
• Physics
• 2017
The field theoretic renormalization group (RG) and the operator product expansion (OPE) are applied to the model of a density field advected by a random turbulent velocity field. The latter is
• Physics
• 2015
In this paper, we investigated the statistical differences between active and passive scalars in isotropic compressible turbulence. In the inertial range, the kinetic energy and scalar have the
• Physics
Physical review. E
• 2017
The existence of additional regimes, which could not be found using the direct perturbative approach of the previous work, are explored, and the crossover between different regimes is analyzed to determine them near the special value of space dimension 4 in the framework of double y and ɛ expansion.

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