arXiv subjects

Sergey Nazarenko

Publications and source records attributed to Sergey Nazarenko.

At least 55 records · Page 3Linked to original sources

arXiv2017

Nonstationary distributions of wave intensities in Wave Turbulence

We obtain a general solution for the probability density function of wave intensities in non-stationary Wave Turbulence. The solution is expressed in terms of the wave action spectrum evolving according the the wave-kinetic equation. We establish that, in absence of wave breaking, the wave statistics asymptotes to a Gaussian distribution in forced-dissipated wave systems that approach a steady state. Also, in non-stationary systems, if the statistics is Gaussian initially, it will remain Gaussian at any time. Generally, the statistics that is not Gaussian initially will remain non-Gaussian over the characteristic nonlinear time of the wave spectrum. In freely decaying wave turbulence, substantial deviations from Gaussianity may persist infinitely long.

cond-mat.stat-mech↗

arXiv2015

Anomalous spectral laws in differential models of turbulence

Differential models for hydrodynamic, passive-scalar and wave turbulence given by nonlinear first- and second-order evolution equations for the energy spectrum in the $k$-space were analysed. Both types of models predict formation an anomalous transient power-law spectra. The second-order models were analysed in terms of self-similar solutions of the second kind, and a phenomenological formula for the anomalous spectrum exponent was constructed using numerics for a broad range of parameters covering all known physical examples. The first-order models were examined analytically, including finding an analytical prediction for the anomalous exponent of the transient spectrum and description of formation of the Kolmogorov-type spectrum as a reflection wave from the dissipative scale back into the inertial range. The latter behaviour was linked to pre-shock/shock singularities similar to the ones arising in the Burgers equation. Existence of the transient anomalous scaling and the reflection-wave scenario are argued to be a robust feature common to the finite-capacity turbulence systems. The anomalous exponent is independent of the initial conditions but varies for for different models of the same physical system.

physics.flu-dyn↗

arXiv2015

Wave turbulence description of interacting particles: Klein-Gordon model with a Mexican-hat potential

In field theory, particles are waves or excitations that propagate on the fundamental state. In experiments or cosmological models one typically wants to compute the out-of-equilibrium evolution of a given initial distribution of such waves. Wave Turbulence deals with out-of-equilibrium ensembles of weakly nonlinear waves, and is therefore well-suited to address this problem. As an example, we consider the complex Klein-Gordon equation with a Mexican-hat potential. This simple equation displays two kinds of excitations around the fundamental state: massive particles and massless Goldstone bosons. The former are waves with a nonzero frequency for vanishing wavenumber, whereas the latter obey an acoustic dispersion relation. Using wave turbulence theory, we derive wave kinetic equations that govern the coupled evolution of the spectra of massive and massless waves. We first consider the thermodynamic solutions to these equations and study the wave condensation transition, which is the classical equivalent of Bose-Einstein condensation. We then focus on nonlocal interactions in wavenumber space: we study the decay of an ensemble massive particles into massless ones. Under rather general conditions, these massless particles accumulate at low wavenumber. We study the dynamics of waves coexisting with such a strong condensate, and we compute rigorously a nonlocal Kolmogorov-Zakharov solution, where particles are transferred non-locally to the condensate, while energy cascades towards large wave numbers through local interactions. This nonlocal cascading state constitute the intermediate asymptotics between the initial distribution of waves and the thermodynamic state reached in the long-time limit.

nlin.CD↗

arXiv2014

Rossby and Drift Wave Turbulence and Zonal Flows: the Charney-Hasegawa-Mima model and its extensions

A detailed study of the Charney-Hasegawa-Mima model and its extensions is presented. These simple nonlinear partial differential equations suggested for both Rossby waves in the atmosphere and also drift waves in a magnetically-confined plasma exhibit some remarkable and nontrivial properties, which in their qualitative form survive in more realistic and complicated models, and as such form a conceptual basis for understanding the turbulence and zonal flow dynamics in real plasma and geophysical systems. Two idealised scenarios of generation of zonal flows by small-scale turbulence are explored: a modulational instability and turbulent cascades. A detailed study of the generation of zonal flows by the modulational instability reveals that the dynamics of this zonal flow generation mechanism differ widely depending on the initial degree of nonlinearity. A numerical proof is provided for the extra invariant in Rossby and drift wave turbulence -zonostrophy and the invariant cascades are shown to be characterised by the zonostrophy pushing the energy to the zonal scales. A small scale instability forcing applied to the model demonstrates the well-known drift wave - zonal flow feedback loop in which the turbulence which initially leads to the zonal flow creation, is completely suppressed and the zonal flows saturate. The turbulence spectrum is shown to diffuse in a manner which has been mathematically predicted. The insights gained from this simple model could provide a basis for equivalent studies in more sophisticated plasma and geophysical fluid dynamics models in an effort to fully understand the zonal flow generation, the turbulent transport suppression and the zonal flow saturation processes in both the plasma and geophysical contexts as well as other wave and turbulence systems where order evolves from chaos.

physics.flu-dyn↗

arXiv2014

Bose-Einstein condensation and Berezinskii-Kosterlitz-Thouless transition in 2D Nonlinear Schrödinger model

We analyse the Bose-Einstein condensation process and the Berezinskii-Kosterlitz-Thouless phase transition within the Gross-Pitaevskii model and their interplay with wave turbulence theory. By using numerical experiments we study how the condensate fraction and the first order correlation function behave with respect to the mass, the energy and the size of the system. By relating the free-particle energy to the temperature we are able to estimate the Berezinskii-Kousterlitz-Thouless transition temperature. Below this transition we observe that for a fixed temperature the superfluid fraction appears to be size-independent leading to a power-law dependence of the condensate fraction with respect to the system size.

physics.flu-dyn↗

arXiv2013

Modulational Instability in Basic Plasma and Geophysical Models

This is a review of the theory of the modulational instability in idealised fluid models of strongly magnetised plasmas and reduced models of geophysical fluid dynamics, particularly the role it plays in the formation of zonal flows. The discussion focusses on the Charney-Hasegawa-Mima and Hasegawa-Wakatani models. Particular attention is paid to the wave turbulence - zonal flow feedback loop whereby large scale zonal flows which are initially generated by modulational instability of small-scale drift/Rossby waves tend to subsequently suppress these small scale waves by their shearing action. This negative feedback can result in a dynamic equilibrium in which large scale zonal flows grow by drawing energy from small scale turbulence but suppress the small scale turbulence in the process until a balance is reached. In this regime, the level of small scale turbulence is greatly reduced compared to the level one would observe in the absence of the zonal flows.

nlin.CD↗

arXiv2012

One-Dimensional Optical Wave Turbulence: Experiment and Theory

We present a review of the latest developments in 1D OWT. Based on an original experimental setup that allows for the implementation of 1D OWT, we are able to show that an inverse cascade occurs through the spontaneous evolution of the nonlinear field up to the point when modulational instability leads to soliton formation. After solitons are formed, further interaction of the solitons among themselves and with incoherent waves leads to a final condensate state dominated by a single strong soliton. Motivated by the observations, we develop a theoretical description, showing that the inverse cascade develops through six-wave interaction, and that this is the basic mechanism of nonlinear wave coupling for 1D OWT. We describe theory, numerics and experimental observations while trying to incorporate all the different aspects into a consistent context.

physics.optics↗

arXiv2011

Kelvin-wave turbulence in superfluids

We study the statistical and dynamical behavior of turbulent Kelvin waves propagating on quantized vortices in superfluids, and address the controversy concerning the energy spectrum that is associated with these excitations. Finding the correct energy spectrum is important because Kelvin waves play a major role in the dissipation of energy in superfluid turbulence at near-zero temperatures. In this paper, we show analytically that the solution proposed in Ref. \cite{10LN} enjoys existence, uniqueness and regularity of the pre-factor. Furthermore, we present numerical results of the dynamical equation that describes to leading order the non-local regime of the Kelvin wave dynamics. We compare our findings with the analytical results from the proposed local and non-local theories for Kelvin wave dynamics and show an agreement with the non-local predictions. Accordingly, the spectrum proposed in Ref. \cite{10LN} should be used in future theories of quantum turbulence. Finally, for weaker wave forcing we observe an intermittent behavior of the wave spectrum with a fluctuating dissipative scale, which we interpreted as a finite-size effect characteristic to mesoscopic wave turbulence.

cond-mat.stat-mech↗

arXiv2011

Warm turbulence in the Boltzmann equation

We study the single-particle distributions of three-dimensional hard sphere gas described by the Boltzmann equation. We focus on the steady homogeneous isotropic solutions in thermodynamically open conditions, i.e. in the presence of forcing and dissipation. We observe nonequilibrium steady state solution characterized by a warm turbulence, that is an energy and particle cascade superimposed on the Maxwell-Boltzmann distribution. We use a dimensional analysis approach to relate the thermodynamic quantities of the steady state with the characteristics of the forcing and dissipation terms. In particular, we present an analytical prediction for the temperature of the system which we show to be dependent only on the forcing and dissipative scales. Numerical simulations of the Boltzmann equation support our analytical predictions.

nlin.CD↗

arXiv2011

Nonequilibrium steady solutions of the Boltzmann equation

We report a study of the homogeneous isotropic Boltzmann equation for an open system. We seek for nonequilibrium steady solutions in presence of forcing and dissipation. Using the language of weak turbulence theory, we analyze the possibility to observe Kolmogorov-Zakharov steady distributions. We derive a differential approximation model and we find that the expected nonequilibrium steady solutions have always the form of warm cascades. We propose an analytical prediction for relation between the forcing and dissipation and the thermodynamic quantities of the system. Specifically, we find that the temperature of the system is independent of the forcing amplitude and determined only by the forcing and dissipation scales. Finally, we perform direct numerical simulations of the Boltzmann equation finding consistent results with our theoretical predictions.

nlin.CD↗

arXiv2010

The life-cycle of drift-wave turbulence driven by small scale instability

We demonstrate theoretically and numerically the zonal-flow/drift-wave feedback mechanism for the LH transition in an idealised model of plasma turbulence driven by a small scale instability. Zonal flows are generated by a secondary modulational instability of the modes which are directly driven by the primary instability. The zonal flows then suppress the small scales thereby arresting the energy injection into the system, a process which can be described using nonlocal wave turbulence theory. Finally, the arrest of the energy input results in saturation of the zonal flows at a level which can be estimated from the theory and the system reaches stationarity without damping of the large scales.

nlin.CD↗

arXiv2010

Nonlocal wave turbulence in the Charney-Hasegawa-Mima equation: a short review

Rossby wave turbulence, as modelled by the Charney-Hasegawa-Mima (CHM) equation, is nonlocal in scale. As a result, the formal stationary Kolmogorov-Zakharov solutions of the Rossby wave kinetic equation, which describe local cascades, are not valid. Rather the solution of the kinetic equation is dominated by interactions between the large and small scales. This suggests an alternative analytic approach based on an expansion of the collision integral in a small parameter obtained from scale separation. This expansion approximates the integral collision operator in the kinetic equation by anisotropic diffusion operators in wavenumber space as first shown in a series of papers by Balk, Nazarenko and Zakharov in the early 1990's. In this note we summarize the foundations of this theory and provide the technical details which were absent from the original papers.

nlin.CD↗

arXiv2010

Sustained turbulence in the three-dimensional Gross-Pitaevskii model

We study the 3D forced-dissipated Gross-Pitaevskii equation. We force at relatively low wave numbers, expecting to observe a direct energy cascade and a consequent power-law spectrum of the form $k^{-α}$. Our numerical results show that the exponent $α$ strongly depends on how the inverse particle cascade is attenuated at $k$'s lower than the forcing wave number. If the inverse cascade is arrested by a friction at low $k$'s, we observe an exponent which is in good agreement with the weak wave turbulence prediction $k^{-1}$. For a hypo-viscosity, a $k^{-2}$ spectrum is observed which we explain using a critical balance argument. In simulations without any low-$k$ dissipation, a condensate at $k=0$ is growing and the system goes through a strongly-turbulent transition from a four-wave to a three-wave weak turbulence acoustic regime with $k^{-3/2}$ Zakharov-Sagdeev spectrum. In this regime, we also observe a spectrum for the incompressible kinetic energy which formally resembles the Kolmogorov $k^{-5/3}$, but whose correct explanation should be in terms of the Kelvin wave turbulence. The probability density functions for the velocities and the densities are also discussed.

nlin.CD↗

arXiv2010

The interaction of Kelvin waves and the non-locality of the energy transfer in superfluids

We argue that the physics of interacting Kelvin Waves (KWs) is highly non-trivial and cannot be understood on the basis of pure dimensional reasoning. A consistent theory of KW turbulence in superfluids should be based upon explicit knowledge of their interactions. To achieve this, we present a detailed calculation and comprehensive analysis of the interaction coefficients for KW turbulence, thereby, resolving previous mistakes stemming from unaccounted contributions. As a first application of this analysis, we derive a new Local Nonlinear (partial differential) Equation. This equation is much simpler for analysis and numerical simulations of KWs than the Biot-Savart equation, and in contrast to the completely integrable Local Induction Approximation (in which the energy exchange between KWs is absent), describes the nonlinear dynamics of KWs. Secondly, we show that the previously suggested Kozik-Svistunov energy spectrum for KWs, which has often been used in the analysis of experimental and numerical data in superfluid turbulence, is irrelevant, because it is based upon an erroneous assumption of the locality of the energy transfer through scales. Moreover, we demonstrate the weak non-locality of the inverse cascade spectrum with a constant particle-number flux and find resulting logarithmic corrections to this spectrum.

nlin.CD↗

arXiv2010

Spectrum of Kelvin-wave turbulence in superfluids

We derive a type of kinetic equation for Kelvin waves on quantized vortex filaments with random large-scale curvature, that describes step-by-step (local) energy cascade over scales caused by 4-wave interactions. Resulting new energy spectrum $E\Sb{LN}(k)\propto k^{-5/3}$ must replace in future theory (e.g. in finding the quantum turbulence decay rate) the previously used spectrum $E\Sb {KS}(k)\propto k^{-7/5}$, which was recently shown to be inconsistent due to nonlocality of the 6-wave energy cascade.

nlin.CD↗

arXiv2009

Modeling Kelvin Wave Cascades in Superfluid Helium

We study two different types of simplified models for Kelvin wave turbulence on quantized vortex lines in superfluids near zero temperature. Our first model is obtained from a truncated expansion of the Local Induction Approximation (Truncated-LIA) and it is shown to possess the same scalings and the essential behaviour as the full Biot-Savart model, being much simpler than the latter and, therefore, more amenable to theoretical and numerical investigations. The Truncated-LIA model supports six-wave interactions and dual cascades, which are clearly demonstrated via the direct numerical simulation of this model in the present paper. In particular, our simulations confirm presence of the weak turbulence regime and the theoretically predicted spectra for the direct energy cascade and the inverse wave action cascade. The second type of model we study, the Differential Approximation Model (DAM), takes a further drastic simplification by assuming locality of interactions in $k$-space via a differential closure that preserves the main scalings of the Kelvin wave dynamics. DAMs are even more amenable to study and they form a useful tool by providing simple analytical solutions in the cases when extra physical effects are present, e.g. forcing by reconnections, friction dissipation and phonon radiation. We study these models numerically and test their theoretical predictions, in particular the formation of the stationary spectra, and the closeness of the numerics for the higher-order DAM to the analytical predictions for the lower-order DAM .

nlin.CD↗

arXiv2009

Optical wave turbulence and condensation of light

In an optical experiment, we report a wave turbulence regime that, starting with weakly nonlinear waves with randomized phases, shows an inverse cascade of photons towards the lowest wavenumbers. We show that the cascade is induced by a six-wave resonant interaction process and is characterized by increasing nonlinearity. At low wavenumbers the nonlinearity becomes strong and leads to modulational instability developing into solitons, whose number is decreasing further along the beam.

physics.optics↗

arXiv2009

Comment on "Superfluid turbulence from quantum Kelvin wave to classical Kolmogorov cascades" [arXiv:0905.0159] by J. Yepez, G. Vahala, L.Vahala and M. Soe

Both the Kelvin wave and the Kolmogorov turbulence interpretations presented in the PRL, [v. 103, 084501 (2009) by J. Yepez, G. Vahala, L.Vahala and M. Soe, arXiv:0905.0159] are misleading, and much more theoretical analysis needs to be done for the interpretation of the important numerical results obtained by the authors. A way to do this is suggested.

nlin.CD↗