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## Vortex filament model and multifractal conjecture

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2012. Vol. 85. No. 5.

Zybin K., Sirota V. A.

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 self-similarity approach. The results obtained are shown to be in very good agreement with numerical simulations and experimental data. The role of more general stochastic solutions of the Navier-Stokes equation is discussed.

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

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

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

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., 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

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

Abrashkin A. A., Gromov E., Tyutin V. V., Труды НГТУ им. Р.Е. Алексеева 2010 № 2 (81) С. 39–43

The system of equations for average velocity and Reynolds stresses are examined supposing the smallness of diffusive, relaxation and viscous processes. Such turbulent state is named ideal. It is shown that the spectrum of turbulence has the form of spectrum of absolutely black body. ...

Added: May 21, 2012

Vladimirova N., Shavit M., Belan S. et al., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2021 Vol. 104 No. 1 Article 014129

When two resonantly interacting modes are in contact with a thermostat, their statistics is exactly Gaussian and the modes are statistically independent despite strong interaction. Considering a noise-driven system, we show that when one mode is pumped and another dissipates, the statistics of such cascades is never close to Gaussian, no matter what is the ...

Added: September 22, 2021

Pavlov D., Galigerov V., Kolotinskii D. et al., International Journal of High Performance Computing Applications 2024 Vol. 38 No. 1 P. 34–49

Fluid dynamics is a ubiquitous problem that arises in different branches of science and industry. It is usually tackled by numerically solving differential equations on a finite grid. Molecular dynamics was not a feasible tool to approach fluid dynamics until very recently due to its disproportional computational complexity. In this paper we propose a new ...

Added: July 18, 2023

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

Parfenyev V., Vointsev I., Skoba A. et al., Physics of Fluids 2021 Vol. 33 No. 6 Article 065117

Added: June 15, 2021

Parfenyev V., Mogilevskiy E., Falkovich G., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2023 Vol. 107 No. 5 Article 054114

We suggest a new computer-assisted approach to the development of turbulence theory. It allows one to impose lower and upper bounds on correlation functions using sum-of-squares polynomials. We demonstrate it on the minimal cascade model of two resonantly interacting modes when one is pumped and the other dissipates. We show how to present correlation functions ...

Added: May 16, 2023

Попель С.И., Морозова Т. И., Физика плазмы 2017 Т. 43 № 5 С. 474–484

The wave processes that take place under the interaction of the Earth’s magnetosphere with dusty plasma near the lunar surface are considered. It is shown that the waves can be excited for the photoelectron parameters corresponding to the quantum yield of the lunar regolith reported by Willis et al. [Photon and Particle Interactions with Surfaces ...

Added: January 12, 2018

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., 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

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

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., 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

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

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

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

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

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

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