arXiv subjects

Natalia Vladimirova

Publications and source records attributed to Natalia Vladimirova.

17 recordsLinked to original sources

arXiv2025

Universal regimes of strong turbulence in the multi-component Gross-Pitaevskii model

The Gross-Pitaevskii (GP) model, also known as the nonlinear Schrödinger equation, is arguably the most universal model in classical and quantum physics, describing spectrally narrow or long-wavelength distributions of interacting waves or particles. Modern applications -- from oceanic and atmospheric flows to photonics and cold atoms -- predominantly involve states that are far from equilibrium, culminating in the regime of fully developed turbulence. To date, a consistent theoretical description of such states has only existed for weakly interacting quasiparticles. Here we present a theory of strong turbulence in the two-dimensional $N$-component Gross-Pitaevskii model for both repulsive and attractive interactions, corresponding to the defocusing and focusing cases, respectively. In the focusing case, we show that attraction is enhanced by multi-wave effects, leading to a critical-balance state independent of the pumping level. In the defocusing case, repulsion is suppressed by collective effects, giving rise to another type of universality in strong turbulence -- independence from the bare coupling constant. The theory is confirmed by analytical results in the many-component limit and by direct numerical simulations of the single-component GP model.

cond-mat.quant-gas↗

arXiv2023

Multi-mode correlations and the entropy of turbulence

We suggest a new focus for turbulence studies -- multi-mode correlations -- which reveal the hitherto hidden nature of turbulent state. We apply this approach to shell models describing basic properties of turbulence. The family of such models allows one to study turbulence close to thermal equilibrium, which happens when the interaction time weakly depends on the mode number. As the number of modes increases, the one-mode statistics approaches Gaussian (like in weak turbulence), the occupation numbers grow, while the three-mode cumulant describing the energy flux stays constant. Yet we find that higher multi-mode cumulants grow with the order. We derive analytically and confirm numerically the scaling law of such growth. The sum of all squared dimensionless cumulants is equal to the relative entropy between the full multi-mode distribution and the Gaussian approximation of independent modes; we argue that the relative entropy could grow as the logarithm of the number of modes, similar to the %mutual information and entanglement entropy in critical phenomena. Therefore, the multi-mode correlations give a new way to characterize turbulence states and possibly divide them into universality classes.

nlin.CD↗

arXiv2021

Fibonacci turbulence

Never is the difference between thermal equilibrium and turbulence so dramatic, as when a quadratic invariant makes the equilibrium statistics exactly Gaussian with independently fluctuating modes. That happens in two very different yet deeply connected classes of systems: incompressible hydrodynamics and resonantly interacting waves. This work presents the first case of a detailed information-theoretic analysis of turbulence in such strongly interacting systems. The analysis elucidates the fundamental roles of space and time in setting the cascade direction and the changes of the statistics along it. We introduce a beautifully simple yet rich family of discrete models with neighboring triplet interactions and show that it has families of quadratic conservation laws defined by the Fibonacci numbers. Depending on the single model parameter, three types of turbulence were found: single direct cascade, double cascade, and the first ever case of a single inverse cascade. We describe quantitatively how deviation from thermal equilibrium all the way to turbulent cascades makes statistics increasingly non-Gaussian and find the self-similar form of the one-mode probability distribution. We reveal where the information (entropy deficit) is encoded and disentangle the communication channels between modes, as quantified by the mutual information in pairs and the interaction information inside triplets.

nlin.CD↗

arXiv2018

Turbulence appearance and non-appearance in thin fluid layers

Flows in fluid layers are ubiquitous in industry, geophysics and astrophysics. Large-scale flows in thin layers can be considered two-dimensional (2d) with bottom friction added. Here we find that the properties of such flows depend dramatically on the way they are driven. We argue that wall-driven (Couette) flow cannot sustain turbulence at however small viscosity and friction. Direct numerical simulations (DNS) up to the Reynolds number $Re=10^6$ confirm that all perturbations die in a plane Couette flow. On the contrary, for sufficiently small viscosity and friction, we show that finite perturbations destroy the pressure-driven laminar (Poiseuille) flow. What appears instead is a traveling wave in the form of a jet slithering between wall vortices. For $10^4<Re<5\cdot10^4$, the mean flow has remarkably simple structure: the jet is sinusoidal with a parabolic velocity profile, vorticity is constant inside vortices, while the fluctuations are small. At higher $Re$ strong fluctuations appear, yet the mean traveling wave survives. Considering the momentum flux barrier in such a flow, we derive a new scaling law for the $Re$-dependence of the friction factor and confirm it by DNS.

physics.flu-dyn↗

arXiv2017

Evolution of inverse cascades and formation of precondensate in Gross-Pitaevskii turbulence in two dimensions

Here we study how coherence appears in a system driven by noise at small scales. In the wave turbulence modeled by the Gross-Pitaevskii / nonlinear Schrödinger equation, we observe states with correlation scales less than the system size but much larger than the excitation scale. We call such state precondensate to distinguish it from condensate defined as a system-wide coherent state. Both condensate and precondensate are characterized by large scale phase coherence and narrow distribution of amplitudes. When one excites small scales, precondensate is achieved relatively quickly by an inverse cascade heating quasi-equilibrium distribution of large-scale modes. The transition from the precondensate to the system-wide condensate requires much longer time. The spectra of precondensate differ from quasi-equilibrium and are characterized by two bending points, one on the scale of the average distance between vortex pairs, and the other on the scale of the distance between vortices in a pair. We suggest temporal evolution laws for both lengths and use them to predict the probability of the transition to condensate.

physics.flu-dyn↗

arXiv2017

Toward defeating diffraction and randomness for laser beam propagation in turbulent atmosphere

A large distance propagation in turbulent atmosphere results in disintegration of laser beam into speckles. We find that the most intense speckle approximately preserves both the Gaussian shape and the diameter of the initial collimated beam while loosing energy during propagation. One per 1000 of atmospheric realizations produces at 7km distance an intense speckle above 20\% of the initial power. Such optimal realizations create effective extended lenses focusing the intense speckle beyond the diffraction limit of vacuum propagation. Atmospheric realizations change every several milliseconds. We propose to use intense speckles to greatly increase the time-averaged power delivery to the target plane by triggering the pulsed laser operations only at times of optimal realizations. Resulting power delivery and laser irradiance at the intense speckles well exceeds both intensity of diffraction-limited beam and intensity averaged over typical realizations.

physics.optics↗

arXiv2015

Nonlinear combining of multiple laser beams in Kerr medium

We consider combining of multiple laser beams into a single near diffraction-limited beam by beam self-focusing (collapse) in a Kerr medium. The beams with the total power above critical are combined in the near field and then propagated in the Kerr medium. Nonlinearity results in self-focusing event, combining multiple beams into nearly a diffraction-limited beam that carries the critical power. Beam quality of the combined beam is analyzed as a function of the number of combining beams and the level of random fluctuations of the combining beams phases.

nlin.PS↗

arXiv2015

Cascades in nonlocal turbulence

We consider developed turbulence in the 2D Gross-Pitaevsky model, which describes wide classes of phenomena from atomic and optical physics to condensed matter, fluids and plasma. The well-known difficulty of the problem is that the hypothetical local spectra of both inverse and direct cascades in the weak-turbulence approximation carry fluxes which are either zero or have the wrong sign; such spectra cannot be realized. We analytically derive the exact flux constancy laws (analogs of Kolmogorov's 4/5-law for incompressible fluid turbulence), expressed via the fourth-order moment and valid for any nonlinearity. We confirm the flux laws in direct numerical simulations. We show that a constant flux is realized by non-local wave interaction in both the direct and inverse cascades. Wave spectra (second-order moments) are close to slightly (logarithmically) distorted thermal equilibrium in both cascades.

nlin.CD↗

arXiv2014

Nonlinear combining of laser beams

We propose to combine multiple laser beams into a single diffraction-limited beam by the beam self-focusing (collapse) in the Kerr medium. The beams with the total power above critical are first combined in the near field and then propagated in the optical fiber/waveguide with the Kerr nonlinearity. Random fluctuations during propagation eventually trigger strong self-focusing event and produce diffraction-limited beam carrying the critical power.

nlin.PS↗

arXiv2013

Vlasov multi-dimensional model dispersion relation

A hybrid model of the Vlasov equation in multiple spatial dimension $D>1$ [H. A. Rose and W. Daughton, Physics of Plasmas v. 18, 122109 (2011)], the Vlasov multi dimensional model (VMD), consists of standard Vlasov dynamics along a preferred direction, the $z$ direction, and $N$ flows. At each $z$ these flows are in the plane perpendicular to the $z$ axis. They satisfy Eulerian-type hydrodynamics with coupling by self-consistent electric and magnetic fields. Every solution of the VMD is an exact solution of the original Vlasov equation. We show convergence of the VMD Langmuir wave dispersion relation in thermal plasma to that of Vlasov-Landau as $N$ increases. Rotational symmetry about the $z$ axis in $3D$ of small perpendicular wavenumber Langmuir fluctuations is demonstrated for $N\geq 6$, with flows arranged uniformly over the azimuthal angle.

physics.plasm-ph↗

arXiv2013

Oscillations in turbulence-condensate system

We consider developed turbulence in the Gross-Pitaevsky model where condensate appears due to an inverse cascade. Despite being fully turbulent, the system demonstrates non-decaying periodic oscillations around a steady state, when turbulence and condensate periodically exchange a small fraction of waves. We show that these collective oscillations are not of a predator-prey type, as was suggested earlier; they are due to phase coherence and anomalous correlations imposed by the condensate.

nlin.CD↗

arXiv2013

Beyond leading order logarithmic scaling in the catastrophic self-focusing (collapse) of a laser beam in Kerr media

We study the catastrophic stationary self-focusing (collapse) of laser beam in nonlinear Kerr media. The width of a self-similar solutions near collapse distance $z=z_c$ obeys $(z_c-z)^{1/2}$ scaling law with the well-known leading order modification of loglog type $\propto (\ln|\ln(z_c-z)|)^{-1/2}$. We show that the validity of the loglog modification requires double-exponentially large amplitudes of the solution $\sim {10^{10}}^{100}$, which is unrealistic to achieve in either physical experiments or numerical simulations. We derive a new equation for the adiabatically slow parameter which determines the system self-focusing across a large range of solution amplitudes. Based on this equation we develop a perturbation theory for scaling modifications beyond the leading loglog. We show that for the initial pulse with the optical power moderately above ($\lesssim 1.2$) the critical power of self-focusing, the new scaling agrees with numerical simulations beginning with amplitudes around only three times above of the initial pulse.

nlin.PS↗

arXiv2013

Logarithmic scaling of the collapse in the critical Keller-Segel equation

A reduced Keller-Segel equation (RKSE) is a parabolic-elliptic system of partial differential equations which describes bacterial aggregation and the collapse of a self-gravitating gas of brownian particles. We consider RKSE in two dimensions, where solution has a critical collapse (blow-up) if the total number of bacteria exceeds a critical value. We study the self-similar solutions of RKSE near the blow-up point. Near the collapse time, $t=t_c$, the critical collapse is characterized by the $L\propto (t_c-t)^{1/2}$ scaling law with logarithmic modification, where $L$ is the spatial width of collapsing solution. We develop an asymptotic perturbation theory for these modifications and show that the resulting scaling agrees well with numerical simulations. The quantitative comparison of the theory and simulations requires to take into account several terms of the perturbation series.

nlin.PS↗

arXiv2011

Phase transitions in optical turbulence

We consider turbulence in the Gross-Pitaevsky model and study the creation of a coherent condensate via an inverse cascade originated at small scales. The growth of the condensate leads to a spontaneous breakdown of symmetries of small-scale over-condensate fluctuations: first, statistical isotropy is broken, then series of phase transitions mark the change of symmetry from the two-fold to three-fold to four-fold. At the highest condensate level reached, we observe a short-range positional and long-range orientational order (similar to a hexatic phase in the condensed matter physics). In other words, the longer one pumps the system the more ordered it becomes. We show that these phase transitions happen when the driving term corresponds to an instability (i.e. it is multiplicative in the k-space) but not when the system is pumped by a random force. Thus we demonstrate for the first time non-universality of the inverse-cascade turbulence. We also describe anisotropic spectral flux flows in k-space, anomalous correlations of fluctuations and collective oscillations of turbulence-condensate system.

nlin.CD↗

arXiv2010

Non-Gaussian Statistics of Multiple Filamentation

We consider the statistics of light amplitude fluctuations for the propagation of a laser beam subjected to multiple filamentation in an amplified Kerr media, with both linear and nonlinear dissipation. Dissipation arrests the catastrophic collapse of filaments, causing their disintegration into almost linear waves. These waves form a nearly-Gaussian random field which seeds new filaments. For small amplitudes the probability density function (PDF) of light amplitude is close to Gaussian, while for large amplitudes the PDF has a long power-like tail which corresponds to strong non-Gaussian fluctuations, i.e. intermittency of strong optical turbulence. This tail is determined by the universal form of near singular filaments and the PDF for the maximum amplitudes of the filaments.

nlin.CD↗

arXiv2008

Self-Similarity and Universality in Rayleigh-Taylor, Boussinesq Turbulence

We report and discuss case study simulations of the Rayleigh-Taylor instability in the Boussinesq, incompressible regime developed to turbulence. Our main focus is on a statistical analysis of density and velocity fluctuations inside of the already developed and growing in size mixing zone. Novel observations reported in the manuscript concern self-similarity of the velocity and density fluctuations spectra inside of the mixing zone snapshot, independence of the spectra of the horizontal slice level, and universality showing itself in a virtual independence of the internal structure of the mixing zone, measured in the re-scaled spatial units, of the initial interface perturbations.

physics.flu-dyn↗

arXiv2002

Flame Enhancement and Quenching in Fluid Flows

We perform direct numerical simulations (DNS) of an advected scalar field which diffuses and reacts according to a nonlinear reaction law. The objective is to study how the bulk burning rate of the reaction is affected by an imposed flow. In particular, we are interested in comparing the numerical results with recently predicted analytical upper and lower bounds. We focus on reaction enhancement and quenching phenomena for two classes of imposed model flows with different geometries: periodic shear flow and cellular flow. We are primarily interested in the fast advection regime. We find that the bulk burning rate v in a shear flow satisfies v ~ a*U+b where U is the typical flow velocity and a is a constant depending on the relationship between the oscillation length scale of the flow and laminar front thickness. For cellular flow, we obtain v ~ U^{1/4}. We also study flame extinction (quenching) for an ignition-type reaction law and compactly supported initial data for the scalar field. We find that in a shear flow the flame of the size W can be typically quenched by a flow with amplitude U ~ alpha*W. The constant alpha depends on the geometry of the flow and tends to infinity if the flow profile has a plateau larger than a critical size. In a cellular flow, we find that the advection strength required for quenching is U ~ W^4 if the cell size is smaller than a critical value.

physics.flu-dyn↗