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I. V. Kolokolov

Publications and source records attributed to I. V. Kolokolov.

At least 19 recordsLinked to original sources
arXiv2026

Correlations of the phase gradients of the light wave propagating in a turbulent medium in the regime of strong scintillations

We investigate analytically and numerically correlation functions of the phase of light waves that propagate through turbulent media. We examine the case of strong scintillations that occur at large values of the Rytov dispersion, $σ^2_R$. Then, it is possible to relate the pair correlation function of phase gradients to the known pair correlation function of the envelope dependent on the distance $r$ assuming Gaussianity of the envelope of the beam. Our direct numerical simulations show that the profile of the pair correlation function for phase gradients gradually approaches the theoretical expression as the value of $σ_R^2$ increases, if $r<r_0$ where $r_0$ is the Fried length. For larger $r$ the behavior of the computed correlation function is quite different because of destroying the Gaussianity.

physics.optics↗
arXiv2026

Correlations of the phase gradients of the light wave propagating in a turbulent medium in the regime of weak scintillations

We investigate numerically correlation functions of the phase of light waves that propagate through turbulent media. Special attention is paid to the off-diagonal component of the correlation function of the phase gradients which is insensitive to the outer scale of turbulence. The results of our simulations are in a good agreement with the analytical expressions obtained in Ref. \cite{KLS25}. Thus, we numerically confirm expectations based on uniformity of the perturbation theory for the logarithm of the envelope.

physics.optics↗
arXiv2026

Perturbation theory for phase correlations of a light wave propagating in a turbulent medium

We theoretically investigate the correlation functions of the phase of a light wave propagating through a turbulent medium. We use an equation for the logarithm of a wave packet envelope, which includes a second-order nonlinear term. Based on this equation, we develop a diagrammatic technique to calculate corrections to the correlation function obtained in the linear approximation. We calculate the first corrections determined by one-loop diagrams and find its asymptotic behaviors. Some non-perturbative conclusions are made using the symmetry properties of the equation. These results allow us to conclude that the applicability condition for the perturbation theory is the smallness of the Rytov dispersion, $σ_R^2$, and this condition holds uniformly over the distances between observation points.

physics.optics↗
arXiv2025

Geometric Intermittency in Turbulence

Equal-time scaling exponents in fully developed turbulence typically exhibit non anomalous scaling in the inverse cascade of two-dimensional (2D) turbulence and anomalous scaling in three dimensions. We demonstrate that multiscaling is not confined to longitudinal, scalar velocity increments, but also emerges in increments associated with the magnitude and orientation of the velocity vector. This decomposition uncovers a multiscaling in the 2D inverse cascade, which remains obscured when using conventional structure functions. Our results highlight a decoupling between velocity amplitude and flow geometry, offering new insight into the statistical structure of turbulent cascades as well as showing how different classes of multiscaling emerge.

physics.flu-dyn↗
arXiv2024

Pair correlation function of vorticity in a coherent vortex

We study the correlations of vorticity fluctuations inside a coherent vortex resulting from the inverse energy cascade in two-dimensional turbulence. The presence of a coherent flow, which is a differential rotation, suppresses small-scale fluctuations of the flow, which are created by an external force, and lead to the fact that these fluctuations can be considered as non-interacting and, therefore, examined in a linear approximation. We calculate the pair correlation function of vorticity and demonstrate that it has a power-law behavior both in space and in time. The obtained results allow us to start a systematic study of the effects associated with the nonlinear interaction of fluctuations, which play an essential role on the periphery of a coherent vortex. Our results are also applicable to the statistics of a passive scalar in a strong shear flow.

physics.flu-dyn↗
arXiv2024

Correlations in a weakly interacting two-dimensional random flow

We analytically examine fluctuations of vorticity excited by an external random force in two-dimensional fluid. We develop the perturbation theory enabling one to calculate nonlinear corrections to correlation functions of the flow fluctuations found in the linear approximation. We calculate the correction to the pair correlation function and the triple correlation function. It enables us to establish the criterion of validity of the perturbation theory for different ratios of viscosity and bottom friction. We find that the corrections to the second moment are anomalously weak in the cases of small bottom friction and small viscosity and relate the weakness to the energy and enstrophy balances. We demonstrate that at small bottom friction the triple correlation function is characterized by universal scaling behavior in some region of lengths. The developed perturbation method was verified and confirmed by direct numerical simulations.

physics.flu-dyn↗
arXiv2017

Profile of a coherent vortex in two-dimensional turbulence at static pumping

We examine the velocity profile of coherent vortices appearing as a consequence of the inverse cascade of two-dimensional turbulence in a finite box in the case of static pumping. We demonstrate that in the passive regime the flat velocity profile is realized, as in the case of pumping short correlated in time. However, in the static case the energy flux to large scales is dependent on the system parameters. We demonstrate that it is proportional to $f^{4/3}$ where $f$ is the characteristic force exciting turbulence.

physics.flu-dyn↗
arXiv2016

Velocity statistics inside coherent vortices generated by the inverse cascade of $2d$ turbulence

We analyze velocity fluctuations inside coherent vortices generated as a result of the inverse cascade in the two-dimensional ($2d$) turbulence in a finite box. As we demonstrated in \cite{16KL}, the universal velocity profile, established in \cite{14LBFKL}, corresponds to the passive regime of flow fluctuations. The property enables one to calculate correlation functions of the velocity fluctuations in the universal region. We present results of the calculations that demonstrate a non-trivial scaling of the structure function. In addition the calculations reveal strong anisotropy of the structure function.

physics.flu-dyn↗
arXiv2009

Explicit solution of the optimal fluctuation problem for an elastic string in random potential

The free-energy distribution function of an elastic string in a quenched random potential, P(F), is investigated with the help of the optimal-fluctuation approach. The form of the far-right tail of P(F) is found by constructing the exact solution of the non-linear saddle-point equations describing the asymptotic form of the optimal fluctuation. The solution of the problem is obtained for two different types of boundary conditions and for an arbitrary dimension of the imbeding space 1+d with d from the interval 0<d<2. The results are also applicable for the description of the far-left tail of the height distribution function in the stochastic growth problem described by the d-dimensional Kardar-Parisi-Zhang equation.

cond-mat.dis-nn↗
arXiv2008

Universal and non-universal tails of distribution functions in the directed polymer and KPZ problems

The optimal fluctuation approach is applied to study the most distant (non-universal) tails of the free-energy distribution function P(F) for an elastic string (of a large but finite length L) interacting with a quenched random potential. A further modification of this approach is proposed which takes into account the renormalization effects and allows one to study the most close (universal) parts of the tails. The problem is analyzed for different dimensions of a space in which the polymer is imbedded. In terms the stochastic growth problem, the same distribution function describes the distribution of heights in the regime of a non-stationary growth in a situation when an interface starts to grow from a flat configuration.

cond-mat.dis-nn↗
arXiv2007

Optimal fluctuation approach to a directed polymer in a random medium

A modification of the optimal fluctuation approach is applied to study the tails of the free energy distribution function P(F) for an elastic string in quenched disorder both in the regions of the universal behavior of P(F) and in the regions of large fluctuations, where the behavior of P(F) is non-universal. The difference between the two regimes is shown to consist in whether it is necessary or not to take into account the renormalization of parameters by the fluctuations of disorder in the vicinity of the optimal fluctuation.

cond-mat.dis-nn↗
arXiv2000

About Probability Tails in Forced Burgers Turbulence

We consider asymptotics of the velocity derivatives probability distribution functions (PDFs) in Burgers' turbulence. We argue that in the forced case the same power laws as in the decaying case are realized for an infinite system.

nlin.CD↗
arXiv2000

Intermittency effects in Burgers equation driven by thermal noise

For the Burgers equation driven by thermal noise leading asymptotics of pair and high-order correlators of the velocity field are found for finite times and large distances. It is shown that the intermittency takes place: some correlators are much larger than their reducible parts.

nlin.CD↗
arXiv1999

Slow Magnetic Monopole: Interaction with Matter and New Possibility of Their Detection

The possibility of existence of a magnetic monopole has been surveyed by P. Dirac even in 1931, and then from the point of view of the modern theory by A.M. Polyakov and G.~ 'tHooft in 1974. Numerous and unsuccessful attempts of experimental search for monopole in cosmic rays and on accelerators in high energy particle collisions have been done. Also the searches have been carried out in mica for monopole tracks as well as for relict monopoles, entrapped by ferromagnetic inclusions in iron-ores, moon rock and meteorites. These entrapped monopoles, when released, would have the lowest velocities $β<10^{-6}$ and do not yield ionization at all, and are hard to detect. Therefore it is necessary to examine thoroughly the mechanisms of slow heavy monopole interaction with matter and their scale of energy loss. We discuss here the interaction of a massive slow magnetic monopole with magnetically ordered matter, with conductors, superconductors and with condensed matter in general. Our results indicate that the energy loss of a slow supermassive monopole reach $10^{8} eV/cm$ and more if we take into consideration the Cherenkov radiation of magnons or phonons and conductivity of the media. A new method of search for cosmic and relict monopoles by magnetically ordered film is considered too. This approach resembles the traditional method of nuclear emulsion chamber. Apparently the proposed method is particularly attractive for detection of relict monopoles, released from melting iron ore.

hep-ph↗
arXiv1999

Detection of Slow Magnetic Monopole

Numerous and all unsuccessful attempts of experimental search for monopole in cosmic rays and on accelerators in high energy particle collisions have been done since the possibility of existence of a magnetic monopole has been surveyed in 1931. Also the searches have been carried out in mica for monopole tracks as well as for relict monopoles, entrapped by ferromagnetic inclusions in iron-ores, moon rock and meteorites. A new method of search for supermassive cosmic and relict monopoles by magnetically ordered film is considered. This approach resembles the traditional method of nuclear emulsion chamber. Apparently the proposed method is particularly attractive for detection of relict monopoles, released from melting iron ore.

hep-ph↗
arXiv1998

Dissipation statistics of a passive scalar in a multidimensional smooth flow

We compute analytically the probability distribution function ${\cal P}(ε)$ of the dissipation field $ε=(\nabla θ)^{2}$ 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 $ε\to \infty$, $\ln {\cal P}(ε)\sim -(d^2ε)^{1/3}$.

chao-dyn↗
arXiv1996

The Lyapunov Spectrum of a Continuous Product of Random Matrices

We expose a functional integration method for the averaging of continuous products $\hat{P}_t$ of $N\times N$ random matrices. As an application, we compute exactly the statistics of the Lyapunov spectrum of $\hat{P}_t$. This problem is relevant to the study of the statistical properties of various disordered physical systems, and specifically to the computation of the multipoint correlators of a passive scalar advected by a random velocity field. Apart from these applications, our method provides a general setting for computing statistical properties of linear evolutionary systems subjected to a white noise force field.

cond-mat.dis-nn↗