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## Dissipation Statistics of a Passive Scalar in a Multidimensional Smooth Flow

Journal of Statistical Physics. 1999. Vol. 94. No. 5/6. P. 759-777.

Kolokolov I., Gamba A.

We compute analytically the probability distribution function P$P$(*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 P$P$(*ε*)∼−(*d*2*ε*)1/3.

Kolokolov I., Chertkov M., Falkovich G., 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. ...

Added: March 5, 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., 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., 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., 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., 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

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

Zybin K., Il'yn A. S., Physics-Uspekhi 2016 Vol. 59 No. 12 P. 1241-1244

This paper reviews the statistical properties and calculates the velocity structure functions of flows produced by a large-scale random scaling force in the Burgers model. ...

Added: September 22, 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

Ivchenko N., Журнал экспериментальной и теоретической физики 2023 Т. 163 № 5 С. 722-731

We study statistical properties of the passive scalar advection in a 2D flow that consist of a steady-state shear flow and a relatively weak smooth random component taking into account the effects of finite weak diffusion. The model is closely related to the dynamics of passive scalar transfer inside coherent vortices emerging as a result ...

Added: February 15, 2024

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., 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., 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

Bespalov P. A., O.N. Savina, Astronomy Letters 2015 Vol. 41 No. 10 P. 601-605

We discuss the connection of the formation and properties of solar atmosphere transition region
characterized by a steep electron temperature gradient with electrostatic turbulence, which provides a high
effective electron collision frequency and a low thermal conductivity of the medium. A simple dependence
of the noise electric field in the transition region on the effective collision frequency has ...

Added: September 30, 2015

Pelinovsky E., E.G. Shurgalina, Sergeeva A. et al., Physical Letters A 2013 Vol. 377 No. 1 P. 272-275

Two-soliton interactions play a definitive role in the formation of the structure of soliton turbulence in integrable systems. To quantify the contribution of these interactions to the dynamical and statistical characteristics of the nonlinear wave field of soliton turbulence we study properties of the spatial moments of the two-soliton solution of the Korteweg–de Vries (KdV) ...

Added: January 18, 2013

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., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2020 Vol. 102 No. 2 P. 1-5

We examine coherent vortices appearing as a result of the inverse cascade of two-dimensional turbulence in a
finite box in the case of pumping with arbitrary correlation time in the quasilinear regime. We demonstrate that
the existence of the vortices depends on the ratio between the values of the bottom friction coefficient α and the
viscous damping of ...

Added: October 6, 2020

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

Zybin K., Sirota V. A., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2013 Vol. 88 No. 4

The appearance of vortex filaments, the power-law dependence of velocity and vorticity correlations and their multiscaling behavior are derived from the Navier-Stokes equation. This is possible due to interpretation of the Navier-Stokes equation as an equation with multiplicative noise and remarkable properties of random matrix products. ...

Added: October 20, 2014

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

49606783, Mathematical notes 2017 Vol. 102 No. 2 P. 234-251

It is shown in the paper that the number pN(M) of partitions of a positive integer M
into N positive integer summands coincides with the Bose and Fermi distributions with logarithmic
accuracy if one identifies M with energy and N with the number of particles. We use the Gentile
statistics (a.k.a. parastatistics) to derive self-consistent algebraic equations that ...

Added: October 29, 2018

Khabarova O., Timothy Sagitov, Kislov R. et al., JOURNAL OF GEOPHYSICAL RESEARCH-SPACE PHYSICS 2021 Vol. 126 No. 8 P. 1-25

We propose a new method of the automated identification of current sheets (CSs) that represents a formalization of the visual inspection approach employed in case studies. CSs are often identified by eye via the analysis of characteristic changes in the interplanetary magnetic field (IMF) and plasma parameters. Known visual and semi-automated empirical methods of CS ...

Added: September 10, 2021

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., 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