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## Dynamic Correlations in a Thermalized System Described by the Burgers Equation

Journal of Experimental and Theoretical Physics. 2002. Vol. 94. No. 6. P. 1193-1200.

Kolokolov I., Turitsyn K.

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

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

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

П.А. Беспалов, О.Н. Савина, Письма в Астрономический журнал 2015 Т. 41 № 10 С. 651-656

The connection of between the formation and properties of areas characterized by the sharp gradient of electron temperature, with electrostatic turbulence, providing high a high effective electrons collision frequency and a low thermal conductivity of medium, is discussed. Simple dependences for the thermal conductivity, effective collision frequency and noise electric fields are obtained. For ...

Added: June 4, 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

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., 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., 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

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., 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

Zybin K., Sirota V. A., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2012 Vol. 85 No. 5

We develop a theory of turbulence based on the inviscid Navier-Stokes equation. We get a simple but exact stochastic solution (vortex filament model) which allows us to obtain a power law for velocity structure functions in the inertial range. Combining the model with the multifractal conjecture, we calculate the scaling exponents without using the extended ...

Added: October 20, 2014

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

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., 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

Ivchenko N., Vergeles S. S., Журнал экспериментальной и теоретической физики 2023 Т. 163 № 5 С. 724-733

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

Parfenyev V., Vointsev I., Skoba A. et al., Physics of Fluids 2021 Vol. 33 No. 6 P. 1-11

Strong rotation makes an underlying turbulent flow quasi-two-dimensional that leads to the upscale energy transfer. Recent numerical simulations show that under certain conditions, the energy is accumulated at the largest scales of the system, forming coherent vortex structures known as condensates. We analytically describe the interaction of a strong condensate with weak small-scale turbulent pulsations ...

Added: June 15, 2021

Kolokolov I., Lebedev V., Журнал экспериментальной и теоретической физики 2024 Т. 165 № 1 С. 128-140

We examine fluctuations of vorticity excited by an external random force in two-dimensional fluid in the presence of a strong external shear flow. The problem is motivated by the analysis of big coherent vortices appearing as a consequence of the inverse energy cascade in a finite box at large Reynolds numbers. We develop the perturbation ...

Added: January 29, 2024

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

Kolokolov I., Kostenko M., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2020 Vol. 101 No. 033108 P. 1-3

We consider two-dimensional turbulence in the presence of a condensate. The nondiagonal correlation
functions of the Lagrangian accelerations are calculated, and it is shown that they have the same universality
properties as the nondiagonal correlation functions of the velocity fluctuations. ...

Added: March 25, 2020

Zybin K., Ilyin A., Сирота В. А. et al., EPL 2020 Vol. 132 P. 24001

Evolution of a stochastically homogeneous magnetic field advected by an incompressible turbulent flow with large magnetic Prandtl numbers is considered at scales smaller than the Kolmogorov viscous scale. It is shown that, despite the unlimited growth of the magnetic field, its feedback on the fluid's dynamics remains negligibly small. ...

Added: December 23, 2020

Mikhailov E. A., Elistratov S. A., Grachev D., Computational Mathematics and Modeling 2021 Vol. 32 No. 1 P. 45-51

We investigate a stochastic model of the galactic dynamo in the planar approximation, assuming that turbulent diffusivity is a renewal process. For linear and nonlinear modifications of this model, numerical methods are applied to construct statistical moments and correlation tensors of the magnetic field. ...

Added: October 31, 2021

Parfenyev V., Vergeles S. S., Physics of Fluids 2021 Vol. 33 No. 11 Article 115128

In the presence of strong background rotation, the velocity field tends to become quasi-two-dimensional, which leads to the inverse energy cascade. If the damping is small enough, then the energy is accumulated at the largest scales of the system, forming coherent columnar vortex structures known as condensates. Recently, it was found that the radial velocity ...

Added: November 19, 2021

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., 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

Ilyin A., Kopyev A. V., Sirota V. A. et al., Physics of Fluids 2021 Vol. 33 No. 7 P. 075105-1-075105-10

Kinematic dynamo in incompressible isotropic turbulent flows with high magnetic Prandtl number is considered. The approach interpreting an arbitrary magnetic field distribution as a superposition of localized perturbations (blobs) is developed. We derive a general relation between stochastic properties of an isolated blob and a stochastically homogenous distribution of magnetic field advected by the same ...

Added: July 20, 2021