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## Intermittent dissipation of a passive scalar in turbulence

Physical Review Letters. 1998. Vol. 80. No. 10. P. 2121-2124.

The probability density function (PDF) of passive scalar dissipation P sed is found analytically in
the limit of large Peclet and Prandtl numbers (Batchelor-Kraichnan regime) in two dimensions. The
tail of PDF is shown to be stretched exponent.

Kolokolov I., Chertkov M., Vergassola M., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 1997 Vol. 56 No. 5 P. 5483-5499

Random advection of a Lagrangian tracer scalar field u (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 ...

Added: March 6, 2017

Kolokolov I., Gamba A., Journal of Statistical Physics 1999 Vol. 94 No. 5/6 P. 759-777

We compute analytically the probability distribution function PP(ε) of the dissipation field ε=(∇θ)2 of a passive scalar θ advected by a d-dimensional random flow, in the limit of large Peclet and Prandtl numbers (Batchelor–Kraichnan regime). The tail of the distribution is a stretched exponential: for ε→∞, ln PP(ε)∼−(d2ε)1/3. ...

Added: March 5, 2017

Kolokolov I., Lebedev V., Chertkov M. et al., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 1995 Vol. 52 No. 5 P. 4924-4941

For a delta-correlated velocity field, simultaneous correlation functions
of a passive scalar satisfy closed equations. We analyze the equation for the
four-point function. To describe a solution completely, one has to solve the
matching problems at the scale of the source and at the diffusion scale.
We solve both the matching problems and thus
find the dependence of the four-point ...

Added: March 27, 2017

Kolokolov I., Chertkov M., Vergassola M., Physical Review Letters 1998 Vol. 80 P. 512

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 advecting velocity field, the cascade of the scalar is direct or inverse. If d>4 the cascade is always direct. For a small enough degree of compressibility, the cascade ...

Added: March 5, 2017

Kolokolov I., Chertkov M., Gamba A., Physics Letters A 1994 Vol. 192 No. 5-6 P. 435-443

We describe a new functional integral method for the computation of averages containing chronological exponentials of random matrices of arbitrary dimension. We apply these results to the rigorous study of the statistics of a passive scalar advected by a large-scale N-dimensional flow. In the delta-correlated case the statistics of the rate of line stretching appears to ...

Added: March 28, 2017

Lebedev V., Vergeles S. S., / Cornell University. Series Physics "arxiv.org". 2023.

Chaotic variations in flow speed up mixing of scalar fields via intensified stirring. This paper addresses the statistical properties of a passive scalar field mixing in a regular shear flow with random fluctuations against its background. We consider two-dimensional flow with shear component dominating over smooth fluctuations. Such flow is supposed to model passive scalar ...

Added: December 28, 2023

Kolokolov I., Lebedev V., Chertkov M. et al., International Journal of Modern Physics B 1996 Vol. 10 No. 18-19 P. 2273-2309

The steady statistics of a passive scalar advected by a random two-dimensional flow of an incompressible fluid is described at scales less than the correlation length of the flow and larger than the diffusion scale. The probability distribution of the scalar is expressed via the probability distribution of the line stretching rate. The description of ...

Added: March 28, 2017

Kolokolov I., Lebedev V., Chertkov M. et al., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 1995 Vol. 51 No. 6 P. 5609-5627

Steady statistics of a passive scalar advected by a random two-dimensional flow of an incompressible fluid is described in the range of scales between the correlation length of the flow and the diffusion scale. This corresponds to the so-called Batchelor regime where the velocity is replaced by its large-scale gradient. The probability distribution of the ...

Added: March 28, 2017

Kolokolov I., Lebedev V., Balkovsky E. et al., JETP Letters 1995 Vol. 61 No. 12 P. 1049-1054

Advection of a passive scalar $\theta$ in $d=2$ by a large-scale velocity
field rapidly changing in time is considered. The Gaussian feature of the
passive scalar statistics in the convective interval was discovered in
\cite{95CFKLa}. Here we examine deviations from the Gaussianity: we obtain
analytically the simultaneous fourth-order correlation function of $\theta$.
Explicit expressions for fourth-order objects,
like $\langle(\theta_1-\theta_2)^4\rangle$ are ...

Added: March 27, 2017

Kolokolov I., Lebedev V., Falkovich G. et al., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 1996 Vol. 54 No. 5 P. 4896

We describe the method for finding the non-Gaussian tails of the probability distribution function (PDF) for solutions of a stochastic differential equation, such as the convection equation for a passive scalar, the random driven Navier-Stokes equation, etc. The existence of such tails is generally regarded as a manifestation of the intermittency phenomenon. Our formalism is ...

Added: March 8, 2017

Kolokolov I., JETP Letters 2010 Vol. 92 No. 2 P. 107-109

The joint distribution function of two distances between three Lagrangian particles has been calculated in the
problem of chaotic twodimensional transport ...

Added: February 2, 2017

Kolokolov I., Turitsyn K., Journal of Experimental and Theoretical Physics 2002 Vol. 94 No. 6 P. 1193-1200

For the field u(x, t) governed by the Burgers equation with a thermal noise, short-time asymptotics
of multipoint correlators are obtained. Their exponential parts are independent of the correlator number. This
means that they are determined by a single rare fluctuation and exhibit the intermittency phenomenon ...

Added: February 25, 2017

Kolokolov I., Falkovich G., Chertkov M. et al., Physical Review Letters 1999 Vol. 83 No. 20 P. 4065-4068

Kinematic dynamo theory is presented here for turbulent conductive fluids. We describe how inhomogeneous magnetic fluctuations are generated below the viscous scale of turbulence where the spatial smoothness of the velocity permits a systematic analysis of the Lagrangian path dynamics. We find analytically the moments and multipoint correlation functions of the magnetic field at small ...

Added: March 5, 2017

Kolokolov I., Journal of Physics A: Mathematical and Theoretical 2017 Vol. 50 No. 155501 P. 1-12

The two-point correlation tensor of small-scale fluctuations of magnetic field B in a two-dimensional chaotic flow is studied. The analytic approach is developed in the framework of the Kraichnan–Kazantsev model. It is shown that the growth of the field fluctuations takes place in an essentially resistive regime and stops at large times in accordance with ...

Added: March 28, 2017

Kolokolov I., Nguyen Thanh T., Physics Letters A 2012 Vol. 376 P. 1836-1838

We study mixing of passive scalar by a chaotic velocity field with a relatively strong regular shear
component. We show that the tail of partition distribution function (PDF) of coarse-grained passive scalar
field differs qualitatively from the corresponding asymptotics in the case of isotropic flow statistics. ...

Added: December 28, 2016

Kolokolov I., Lebedev V., Falkovich G. et al., Physical Review Letters 1997 Vol. 78 No. 8 P. 1452-1455

We consider the tails of probability density function (PDF) for the velocity that satisfies Burgers equation driven by a Gaussian large-scale force. The saddle-point approximation is employed in the path integral so that the calculation of the PDF tails boils down to finding the special field-force configuration (instanton) that realizes the extremum of probability. For ...

Added: March 6, 2017

Kolokolov I., Lebedev V., Falkovich G. et al., International Journal of Modern Physics B 1997 Vol. 11 No. 26/27 P. 3223-3245

We consider
the tails of probability density functions (PDF) for different characteristics
of velocity that satisfies Burgers equation driven by a large-scale force.
The saddle-point approximation is employed in the path integral
so that the calculation of the PDF tails
boils down to finding the special field-force configuration (instanton) that
realizes the extremum of probability. We calculate high moments of the ...

Added: March 6, 2017

Kolokolov I., JETP Letters 2000 Vol. 71 No. 1 P. 12-14

Leading terms of the asymptotic behavior of the pair and higher order correlation functions for finite times and large distances have been calculated for the Burgers equation involving thermal noise. It is shown that an intermittence phenomenon occurs, whereby certain correlation functions are much greater than their reducible parts. ...

Added: March 5, 2017

Kolokolov I., Lebedev V., Chertkov M., Physics of Fluids 2007 Vol. 19 P. 101703-1-101703-4

Passive scalar turbulence forced steadily is characterized by the velocity correlation scale L,
injection scale l, and diffusive scale rd. The scales are well separated if the diffusivity is small,
rdl ,L, and one normally says that effects of diffusion are confined to smaller scales, rrd.
However, if the velocity is single scale, one finds that a weak ...

Added: February 10, 2017

Kolokolov I., Lebedev V., Kogan V. R., Journal of Physics A: Mathematical and Theoretical 2010 Vol. 43 P. 182001

We analyze the kinematic dynamo in a conducting fluid where the stationary shear flow is accompanied by relatively weak random velocity fluctuations. The diffusionless and diffusion regimes are described. The growth rates of the magnetic field moments are related to the statistical characteristics of the flow describing the divergence of Lagrangian trajectories. A degree of ...

Added: February 5, 2017

Окубо Ю. undefined., Journal of Physics: Conference Series 2017 Vol. 804 No. 012036 P. 1-8

We investigate the existence and the orthogonality of the generalized Jack symmetric functions which play an important role in the AGT relations. We show their orthogonality by deforming them to the generalized Macdonald symmetric functions. ...

Added: October 26, 2017

Andrew G. Semenov, Zaikin A., Physical Review B: Condensed Matter and Materials Physics 2013 Vol. 88 No. 5 P. 054505-1-054505-10

We investigate the effect of interacting quantum phase slips on persistent current and its fluctuations in ultrathin superconducting nanowires and nanorings pierced by the external magnetic flux. We derive the effective action for these systems and map the original problem onto an effective sine-Gordon theory on torus. We evaluate both the flux dependent persistent current ...

Added: February 9, 2015

Slunyaev A., Кокорина А. В., Water Waves, Springer 2019 P. 1-20

The issue of accounting of the wave breaking phenomenon in direct numerical simulations of oceanic waves is discussed. It is emphasized that this problem is crucial for the deterministic description of waves, and also for the dynamical calculation of extreme wave statistical characteristics, such as rogue wave height probability, asymmetry, etc. The conditions for accurate ...

Added: October 13, 2019

Marshakov A., Миронов А. Д., Морозов А. Ю., Journal of Geometry and Physics 2011 Vol. 61 P. 1203-1222

We present a summary of current knowledge about the AGT relations for conformal blocks with additional insertion of the simplest degenerate operator, and a special choice of the corresponding intermediate dimension, when the conformal blocks satisfy hypergeometric-type differential equations in position of the degenerate operator. A special attention is devoted to representation of conformal block ...

Added: February 28, 2013