arXiv subjects

S. Nazarenko

Publications and source records attributed to S. Nazarenko.

13 recordsLinked to original sources

arXiv2025

Observation of Relaxation Stages in a Nonequilibrium Closed Quantum System: Decaying Turbulence in a Trapped Superfluid

The dynamics of non-equilibrium closed quantum systems and their route to thermalization are of fundamental interest to several fields, from cosmology to particle physics. However, a comprehensive description of non-equilibrium phenomena still presents a significant challenge. In this work, we report the observation of distinct stages during the relaxation of the decaying turbulence in trapped Bose-Einstein condensates. Our findings show a direct particle cascade from low to high momenta, a consequence of the energy injection in the system, exhibiting a characteristic universal scaling. This stage is followed by an inverse particle cascade responsible for repopulating the previously depleted condensate. Both cascades can be explained through self-similar solutions provided by wave turbulence theory. These findings provide important insights into the relaxation stages of out-of-equilibrium quantum many-body systems.

cond-mat.quant-gas↗

arXiv2022

Vortex creation, annihilation and nonlinear dynamics in atomic vapors

We exploit new techniques for generating vortices and controlling their interactions in an optical beam in a nonlinear atomic vapor. A precise control of the vortex positions allows us to observe strong interactions leading to vortex dynamics involving annihilations. With this improved controlled nonlinear system, we get closer to the pure hydrodynamic regime than in previous experiments while a wavefront sensor offers us a direct access to the fluid's density and velocity. Finally, we developed a relative phase shift method which mimics a time evolution process without changing non-linear parameters. These observations are an important step toward the experimental implementation of 2D turbulent state

physics.atom-ph↗

arXiv2021

On the investigation of properties of superfluid $^4$He turbulence using a hot-wire signal

We report hot-wire measurements performed in two very different, co- and counter-rotating flows, in normal and superfluid helium at 1.6 K, 2 K, and 2.3 K. As recently reported, the power spectrum of the hot-wire signal in superfluid flows exhibits a significant bump at high frequency (Diribarne et al. [1]). We confirm that the bump frequency does not depend significantly on the temperature and further extend the previous analysis of the velocity dependence of the bump, over more than one decade of velocity. The main result is that the bump frequency depends on the turbulence intensity of the flow, and that using the turbulent Reynolds number rather than the velocity as a control parameter collapses results from both co- and counter-rotating flows. The vortex shedding model previously proposed, in its current form, does not account for this observation. This suggests that the physical origin of the bump is related to the small scale turbulence properties of the flow. We finally propose some qualitative physical mechanism by which the smallest structures of the flow, at intervortex distance, could affect the heat flux of the hot-wire.

physics.flu-dyn↗

arXiv2012

Dual local and non-local cascades in 3D turbulent Beltrami flows

We discuss the possibility of dual local and non-local cascades in a 3D turbulent Beltrami flow, with inverse energy cascade and direct helicity cascade, by analogy with 2D turbulence. We discuss the corresponding energy spectrum in both local and non-local case. Comparison with a high Reynolds number turbulent von Karman flow is provided and discussed.

physics.flu-dyn↗

arXiv2008

Statistics of surface gravity wave turbulence in the space and time domains

We present experimental results on simultaneous space-time measurements for the gravity wave turbulence in a large laboratory flume. We compare these results with predictions of the weak turbulence theory (WTT) based on random waves, as well as with predictions based on the coherent singular wave crests. We see that both wavenumber and the frequency spectra are not universal and dependent on the wave strength, with some evidence in favor of WTT at larger wave intensities when the finite flume effects are minimal. We present further theoretical analysis of the role of the random and coherent waves in the wave probability density function (PDF) and the structure functions (SFs). Analyzing our experimental data we found that the random waves and the coherent structures/breaks coexist: the former show themselves in a quasi-gaussian PDF core and in the low-order SFs, and the latter - in the PDF tails and the high-order SF's. It appears that the x-space signal is more intermittent than the t-space signal, and the x-space SFs capture more singular coherent structures than do the t-space SFs. We outline an approach treating the interactions of these random and coherent components as a turbulence cycle characterized by the turbulence fluxes in both the wavenumber and the amplitude spaces.

nlin.CD↗

arXiv2008

Double Kelvin Wave Cascade in Superfluid Helium

We study the double cascade of energy and wave action in a local model of superfluid vortex filaments. The model is obtained from a truncated expansion of the 2D Local Induction Approximation and it is shown to support six-wave interactions. We argue that, because of the uncertainty in the vortex core profile, this model has the same status of validity as the traditionally used Biot-Savart model with cutoff, but it has advantage of being much simpler. Our minimal model leads to a wave kinetic equation for which we predict existence of two distinct power-law scaling in the spectrum, corresponding to a direct cascade of energy and an inverse one of wave action. Direct numerical simulations confirm the theoretical predictions in the weak turbulence regime.

nlin.CD↗

arXiv2007

Large-Scale Magnetic Field Re-generation by Resonant MHD Wave Interactions

We investigate numerically the long-time behavior of balanced Alfven wave turbulence forced at intermediate scales. Whereas the usual constant-flux solution is found at the smallest scales, two new scalings are obtained at the forcing scales and at the largest scales of the system. In the latter case we show, in particular, that the spectrum evolves first to a state determined by Loitsyansky invariant and later a state close to the thermodynamic equipartition solution predicted by wave turbulence. The astrophysical implications for galactic magnetic field generation are discussed.

astro-ph↗

arXiv2003

Small-scale turbulent dynamo - a numerical investigation

We present the results of a numerical investigation of the turbulent kinematic dynamo problem in a high Prandtl number regime. The scales of the magnetic turbulence we consider are far smaller than the Kolmogorov dissipative scale, so that the magnetic wavepackets evolve in a nearly smooth velocity field. Firstly, we consider the Kraichnan-Kazantsev model (KKM) in which the strain matrix is taken to be independent of coordinate and Gaussian white in time. To simulate the KKM we use a stochastic Euler-Maruyama method. We test the theoretical predictions for the growth of rates of the magnetic energy and higher order moments (Kazantsev, 1968; Kulsrud & Anderson, 1992; Chertkov et al., 1999), the shape of the energy spectrum (Kazantsev, 1968; Kulsrud & Anderson, 1992; Schekochihin et al., 2000a; Nazarenko et al., 2003) and the behaviour of the polarisation and spectral flatness Nazarenko et al., 2003). In general, the results appear to be in good agreement with the theory, with the exception that the predicted decay of the polarisation in time is not reproduced well in the stochastic numerics. Secondly, in order to study the sensitivity of the KKM predictions to the choice of strain statistics, we perform additional simulations for the case of a Gaussian strain with a finite correlation time and also for a strain taken from a DNS data set. These experiments are based on non-stochastic schemes, using a timestep that is much smaller than the correlation time of the strain. We find that the KKM is generally insensitive to the choice of strain statistics and most KKM results, including the decay of the polarisation, are reproduced well. The only exception appears to be the flatness whose spectrum is not reproduced in accordance with the KKM predictions in these simulations.

astro-ph↗

arXiv2003

Analytical solution for nonlinear Schrodinger vortex reconnection

Analysis of the nonlinear Schrodinger vortex reconnection is given in terms of coordinate-time power series. The lowest order terms in these series correspond to a solution of the linear Schrodinger equation and provide several interesting properties of the reconnection process, in particular the non-singular character of reconnections, the anti-parallel configuration of vortex filaments and a square-root law of approach just before/after reconnections. The complete infinite power series represents a fully nonlinear analytical solution in a finite volume which includes the reconnection point, and is valid for finite time provided the initial condition is an analytic function. These series solutions are free from the periodicity artifacts and discretization error of the direct computational approaches and they are easy to analyze using a computer algebra program.

physics.flu-dyn↗

arXiv2003

Fourier space intermittency of the small-scale turbulent dynamo

The small-scale turbulent dynamo in the high Prandtl number regime is described in terms of the one-point Fourier space correlators. The second order correlator of this kind is the energy spectrum and it has been previously studied in detail. We examine the higher order k-space correlators which contain important information about the phases of the magnetic wavepackets and about the dominant structures of the magnetic turbulence which cause intermittency. In particular, the fourth-order correlators contain information about the mean-square phase difference between any two components of the magnetic field in a plane transverse to the wavevector. This can be viewed as a measure of the magnetic field's polarization. Examining this new quantity, the magnetic field is shown to become plane polarized in the Kazantsev-Kraichnan model at large time, corresponding to a strong deviation from Gaussianity. We derive a closed equation for the generating function of the Fourier correlators and find the large-time asymptotic solutions of these correlators at all orders. The time scaling of these solutions implies the magnetic field has log-normal statistics, whereas the wavenumber scaling indicates that the field is dominated by intermittent fluctuations at high k.

astro-ph↗

arXiv2003

A model for rapid stochastic distortions of small-scale turbulence

We present a model describing evolution of the small-scale Navier-Stokes turbulence due to its stochastic distortions by much larger turbulent scales. This study is motivated by numerical findings (laval, 2001) that such interactions of separated scales play important role in turbulence intermittency. We introduce description of turbulence in terms of the moments of the k-space quantities using a method previously developed for the kinematic dynamo problem (Nazarenko, 2003). Working with the $k$-space moments allows to introduce new useful measures of intermittency such as the mean polarization and the spectral flatness. Our study of the 2D turbulence shows that the energy cascade is scale invariant and Gaussian whereas the enstrophy cascade is intermittent. In 3D, we show that the statistics of turbulence wavepackets deviates from gaussianity toward dominance of the plane polarizations. Such turbulence is formed by ellipsoids in the $k$-space centered at its origin and having one large, one neutral and one small axes with the velocity field pointing parallel to the smallest axis.

physics.flu-dyn↗

arXiv2001

Fast Numerical simulations of 2D turbulence using a dynamic model for Subgrid Motions

We present numerical simulation of 2D turbulent flow using a new model for the subgrid scales which are computed using a dynamic equation linking the subgrid scales with the resolved velocity. This equation is not postulated, but derived from the constitutive equations under the assumption that the non-linear interactions of subgrid scales between themselves are equivalent to a turbulent viscosity.The performances of our model are compared with Direct Numerical Simulations of decaying and forced turbulence. For a same resolution, numerical simulations using our model allow for a significant reduction of the computational time (of the order of 100 in the case we consider), and allow the achievement of significantly larger Reynolds number than the direct method.

physics.flu-dyn↗

arXiv2001

Non-locality and Intermittency in 3D Turbulence

Numerical simulations are used to determine the influence of the non-local and local interactions on the intermittency corrections in the scaling properties of 3D turbulence. We show that neglect of local interactions leads to an enhanced small-scale energy spectrum and to a significantly larger number of very intense vortices (tornadoes) and stronger intermittency. On the other hand, neglect of the non-local interactions results in even stronger small-scale spectrum but significantly weaker intermittency. Based on these observations, a new model of turbulence is proposed, in which non-local (RDT-like) interactions couple large and small scale via a multiplicative process with additive noise and the local interactions are modeled by a turbulent viscosity. This model is used to derive a simple toy version of the Langevin equations for small-scale velocity increments. A Gaussian approximation for the large scale fields yields the Fokker-Planck equation for the probability distribution function of the velocity increments. Steady state solutions of this equation allows to qualitatively explain the anomalous corrections and the skewness generation along scale.

physics.flu-dyn↗