Gregory Falkovich

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• PhD
• Professor at Weizmann Institute of Science

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 correlat...

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 correla...

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 models describing basic properties of both vortex turbulence and strong wave turbulence. The family of such models allows one to study turbulence close to thermal equilibrium, which happens...

Vortices are the hallmarks of hydrodynamic flow. Strongly interacting electrons in ultrapure conductors can display signatures of hydrodynamic behaviour, including negative non-local resistance1–4, higher-than-ballistic conduction5–7, Poiseuille flow in narrow channels8–10 and violation of the Wiedemann–Franz law¹¹. Here we provide a visualization...

Swirling vortices have been directly observed in a flow of electric current for the first time. Unlike conventional viscous fluids, collective fluid-like behaviour in this case is not caused by particle–particle collisions, but results from a previously unidentified mechanism involving single electrons scattering from material surfaces at small ang...

Vortices are the hallmarks of hydrodynamic flow. Recent studies indicate that strongly-interacting electrons in ultrapure conductors can display signatures of hydrodynamic behavior including negative nonlocal resistance, Poiseuille flow in narrow channels, and a violation of the Wiedemann-Franz law. Here we provide the first visualization of whirlp...

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 wha...

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 pre...

We consider the developed turbulence of capillary waves on shallow water. Analytic theory shows that an isotropic cascade spectrum is unstable with respect to small angular perturbations, in particular, to spontaneous breakdown of the reflection symmetry and generation of nonzero momentum. By computer modeling we show that indeed a random pumping,...

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 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 the...

We consider the developed turbulence of capillary waves on shallow water. Analytic theory shows that an isotropic cascade spectrum is unstable with the respect to small angular perturbations, in particular, to spontaneous breakdown of the reflection symmetry and generation of nonzero momentum. By computer modeling we show that indeed a random pumpi...

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 pre...

How weak is the weak turbulence? Here, we analyze turbulence of weakly interacting waves using the tools of information theory. It offers a unique perspective for comparing thermal equilibrium and turbulence. The mutual information between modes is stationary and small in thermal equilibrium, yet it is shown here to grow with time for weak turbulen...

In hydrodynamics, vortex generation upon the transition from smooth laminar flows to turbulence is generally accompanied by increased dissipation. However, vortices in the plane can provide transport barriers and decrease losses, as it happens in numerous geophysical, astrophysical flows and in tokamaks. Photon interactions with matter can affect l...

We show that rotating particles at the liquid–gas interface can be efficiently manipulated using the surface-wave analogue of optical lattices. Two orthogonal standing waves generate surface flows of counter-rotating half-wavelength unit cells, the liquid interface metamaterial, whose geometry is controlled by the wave phase shift. Here we demonstr...

Here we analyze wave turbulence using the tools of information theory, in particular, the mutual information (MI) between modes. For weakly interacting waves, the first non-vanishing contribution is shown to be proportional to the square of the lowest cumulant. We compute it in thermal equilibrium and in turbulence. The mutual information is statio...

We discover dramatic impact of vortex formation in the transverse component of the Poynting vector of the fundamental core mode in solid core micro-structured optical fibers on the energy dissipation. The vortices can reduce losses of the mode by several orders of magnitude under proper selection of the fiber parameters at a given wavelength. © 201...

Electronic fluids bring into hydrodynamics a new setting: equipotential flow sources embedded inside the fluid. Here we show that the nonlocal relation between the current and electric field due to momentum-conserving interparticle collisions leads to a total or partial field expulsion from such flows. That results in freely flowing currents in the...

In hydrodynamics, vortex generation upon the transition from smooth laminar flows to turbulence is generally accompanied by increased dissipation. However, plane vortices can provide transport barriers and decrease losses, as it happens in numerous geophysical, astrophysical flows and in tokamaks. Photon interactions with matter can affectlight tra...

Electronic fluids bring into hydrodynamics a new setting: equipotential flow sources embedded inside the fluid. Here we show that nonlocal relation between current and electric field due to momentum-conserving inter-particle collisions leads to a total or partial field expulsion from such flows. That results in freely flowing currents in the bulk a...

Viscous electron fluids have emerged recently as a new paradigm of strongly-correlated electron transport in solids. Here we report on a direct observation of the transition to this long-sought-for state of matter in a high-mobility electron system in graphene. Unexpectedly, the electron flow is found to be interaction-dominated but non-hydrodynami...

An electric field that builds in the direction against current, known as negative nonlocal resistance, arises naturally in viscous flows and is thus often taken as a telltale of this regime. Here, we predict negative resistance for the ballistic regime, wherein the ee collision mean free path is greater than the length scale at which the system is...

Flows in fluid layers are ubiquitous in industry, geophysics, and astrophysics. Large-scale flows in thin layers can be considered two dimensional with bottom friction added. Here we find that the properties of such flows depend dramatically on the way they are driven. We argue that a wall-driven (Couette) flow cannot sustain turbulence, no matter...

An electric field that builds in the direction against current, known as negative nonlocal resistance, arises naturally in viscous flows and is thus often taken as a telltale of this regime. Here we predict negative resistance for the ballistic regime, wherein the ee collision mean free path is greater than the length scale at which the system is b...

Electron hydrodynamics has emerged recently as a new paradigm of correlated electron transport in solids, describing phenomena dominated by particle collisions.At the lengthscales exceeding the collision mean free path $l_{\rm ee}$, such systems can be treated as macroscopic fluids. In contrast, when the system size is comparable to $l_{\rm ee}$, t...

This corrects the article DOI: 10.1038/ncomms7214.

Scrupulous measurements and detailed data analysis of the torque in a swirling turbulent flow driven by counter-rotating bladed disks reveals an apparent breaking of the law of similarity. Potentially, such breakdown could arise from several possible factors, including dependence on dimensionless numbers other that $Re$ or velocity coupling to othe...

Scrupulous measurements and detailed data analysis of the torque in a swirling turbulent flow driven by counter-rotating bladed disks reveals an apparent breaking of the law of similarity. Potentially, such breakdown could arise from several possible factors, including dependence on dimensionless numbers other that $Re$ or velocity coupling to othe...

We study pressure-driven and wall-driven channel flows in two dimensions and find that their properties are dramatically different. We show analytically that wall-driven (Couette) flows can- not sustain turbulence at however small viscosity and friction; this dramatic difference from three dimensions is due to the role of vorticity. We confirm by d...

This article introduces the Focus Issue on Two-Dimensional Turbulence appearing in Physics of Fluids (Volume 29, Issue 11, November 2017).

Strong interaction among charge carriers can make them move like viscous fluid. Here we explore alternating current (AC) effects in viscous electronics. In the Ohmic case, incompressible current distribution in a sample adjusts fast to a time-dependent voltage on the electrodes, while in the viscous case, momentum diffusion makes for retardation an...

Strong interaction among charge carriers can make them move like viscous fluid. Here we explore alternating current (AC) effects in viscous electronics. In the Ohmic case, incompressible current distribution in a sample adjusts fast to a time-dependent voltage on the electrodes, while in the viscous case, momentum diffusion makes for retardation an...

Large-scale turbulence in fluid layers and other quasi two-dimensional compressible systems consists of planar vortices and waves. Separately, wave turbulence usually produces direct energy cascade, while solenoidal planar turbulence transports energy to large scales by an inverse cascade. Here we consider turbulence at finite Mach numbers when int...

Large-scale turbulence in fluid layers and other quasi-two-dimensional compressible systems consists of planar vortices and waves. Separately, wave turbulence usually produces a direct energy cascade, while solenoidal planar turbulence transports energy to large scales by an inverse cascade. Here, we consider turbulence at finite Mach numbers when...

Electron-electron (e-e) collisions can impact transport in a variety of surprising and sometimes counterintuitive ways. Despite strong interest, experiments on the subject proved challenging because of the simultaneous presence of different scattering mechanisms that suppress or obscure consequences of e-e scattering. Only recently, sufficiently cl...

Electron-electron (e-e) collisions can impact transport in a variety of surprising and sometimes counterintuitive ways. Despite strong interest, experiments on the subject proved challenging because of the simultaneous presence of different scattering mechanisms that suppress or obscure consequences of e-e scattering. Only recently, sufficiently cl...

Interactions in electron systems can lead to viscous flows in which correlations allow electrons to avoid disorder scattering, reducing momentum loss and dissipation. We illustrate this behavior in a viscous pinball model, describing electrons moving in the presence of dilute point-like defects. Conductivity is found to obey an additive relation $\...

An inverse cascade - energy transfer to progressively larger scales - is a salient feature of two-dimensional turbulence. If the cascade reaches the system scale, it creates a coherent flow expected to have the largest available scale and conform with the symmetries of the domain. In a doubly periodic rectangle, the mean flow with zero total moment...

An inverse cascade - energy transfer to progressively larger scales - is a salient feature of two-dimensional turbulence. If the cascade reaches the system scale, it creates a coherent flow expected to have the largest available scale and conform with the symmetries of the domain. In a doubly periodic rectangle, the mean flow with zero total moment...

This short note is written to call attention to an analytic approach to the interaction of developed turbulence with mean flows of simple geometry (jets and vortices). It is instructive to compare cases in two and three dimensions and see why the former are solvable and the latter are not (yet). We present the analytical solutions for two-dimension...

Significance Free electron flows through constrictions in metals are often regarded as an ultimate high-conduction charge transfer. We predict that electron fluids can flow with a resistance that is much smaller than the fundamental quantum mechanical ballistic limit for nanoscale electronics. The “superballistic” low-dissipation transport is parti...

Strongly interacting electrons can move in a neatly coordinated way, reminiscent of the movement of viscous fluids. Here we show that in viscous flows interactions facilitate transport, allowing conductance to exceed the fundamental Landauer's ballistic limit $G_{\rm ball}$. The effect is particularly striking for the flow through a viscous point c...

Viscous electronics is an emerging field dealing with systems in which strongly interacting electrons behave as a fluid. Electron viscous flows are governed by a nonlocal current-field relation which renders the spatial patterns of current and electric field strikingly distinct. Notably, driven by the viscous friction force from adjacent layers, cu...

Viscous electronics is an emerging field dealing with systems in which strongly interacting electrons behave as a fluid. Electron viscous flows are governed by a nonlocal current-field relation which renders the spatial patterns of current and electric field strikingly distinct. Notably, driven by the viscous friction force from adjacent layers, cu...

We address theoretically the longstanding problem of particle dispersion in the lower atmosphere. The evolution of particle concentration under an absorbing boundary condition at the ground is described. We derive a close-form solution for the downwind surface density of deposited particles and find how the number of airborne particles decreases wi...

The inelastic collapse of stochastic trajectories of a randomly accelerated particle moving in half-space $z > 0$ has been discovered by McKean and then independently re-discovered by Cornell et. al. The essence of this phenomenon is that particle arrives to a wall at $z = 0$ with zero velocity after an infinite number of inelastic collisions if th...

It was recently suggested that the sign of particle drift in inhomogeneous temperature or turbulence depends on the particle inertia: weakly inertial particles localize near minima of temperature or turbulence intensity (effects known as thermophoresis and turbophoresis), while strongly inertial particles fly away from minima in an unbounded space....

Quantum-critical states of diverse strongly correlated systems are predicted to feature universal collision-dominated transport resembling that of viscous fluids. However, investigation of these phenomena has been hampered by the lack of known macroscopic signatures of the hydrodynamic regime at criticality. Here we identify vorticity as such a sig...

We experimentally and theoretically describe formation of random fiber laser's optical spectrum. We propose a new concept of active cycled wave kinetics from which we derive first ever nonlinear kinetic theory describing laser spectrum.

We discuss general features of the operator product expansion and use it to infer multi-point manifestations of the energy cascade in turbulence. We calculate explicitly the possible form of the three-point velocity correlation function when one distance is smaller than two others. We elucidate manifestation of direct and inverse energy cascades in...

Traditional wave kinetics describes the slow evolution of systems with many degrees of freedom to equilibrium via numerous weak non-linear interactions and fails for very important class of dissipative (active) optical systems with cyclic gain and losses, such as lasers with non-linear intracavity dynamics. Here we introduce a conceptually new clas...

We consider developed turbulence in 2D Gross-Pitaevsky model, which describes wide classes of phenomena, from cold atoms and optics to condensed matter, fluids and plasma. Well-known difficulty of the problem is that the hypothetical local spectra of both inverse and direct cascades in weak-turbulence approximation carry fluxes which either is zero...

In statistically homogeneous turbulent flows, pressure forces provide the main mechanism to redistribute kinetic energy among fluid elements, without net contribution to the overall energy budget. This holds true in both two-dimensional (2D) and three-dimensional (3D) flows, which show fundamentally different physics. As we demonstrate here, pressu...

We investigate time-irreversibility from the point of view of a single particle in Burgers turbulence. Inspired by the recent work for incompressible flows [Xu et al., PNAS 111.21 (2014) 7558], we analyze the evolution of the kinetic energy for fluid markers and use the fluctuations of the instantaneous power as a measure of time irreversibility. F...

The ability to send a wave to fetch an object from a distance would find a broad range of applications. Quasi-standing Faraday waves on water create horizontal vortices, yet it is not known whether propagating waves can generate large-scale flows—small-amplitude irrotational waves only push particles in the direction of propagation. Here we show th...

Can one send a wave to bring an object from a distance? The general idea is inspired by the recent success in moving micro particles using light and the development of a tractor beam concept. For fluid surfaces, however, the only known paradigm is the Stokes drift model, where linear planar waves push particles in the direction of the wave propagat...

An inverse turbulent cascade in a restricted two-dimensional periodic domain creates a condensate\char22{}a pair of coherent system-size vortices. We perform extensive numerical simulations of this system and carry out theoretical analysis based on momentum and energy exchanges between the turbulence and the vortices. We show that the vortices have...

Significance Irreversibility is a fundamental aspect of the evolution of natural systems, and quantifying its manifestations is a challenge in any attempt to describe nonequilibrium systems. In the case of fluid turbulence, an emblematic example of a system very far from equilibrium, we show that the motion of a single fluid particle provides a cle...

A side remark in the old paper by Zeldovich and co-authors leads to the recent discovery of a universal conservation law of turbulent dispersion.

Small aerosols drift down temperature or turbulence gradient since faster particles fly longer distances before equilibration. That fundamental phenomenon, called thermophoresis or turbophoresis, is widely encountered in nature and used in industry. It is universally believed that particles moving down the kinetic energy gradient must concentrate i...

We describe ideal incompressible hydrodynamics on the hyperbolic plane which is an infinite surface of constant negative curvature. We derive equations of motion, general symmetries and conservation laws, and then consider turbulence with the energy density linearly increasing with time due to action of small-scale forcing. In a flat space, such en...

The turbulent energy flux through scales, $\bar{\epsilon}$, remains constant and non vanishing in the limit of zero viscosity, which results in the fundamental anomaly of time irreversibility. It was considered straightforward to deduce from this the Lagrangian velocity anomaly, $\left< d u^2/dt\right>=-4 \bar{\epsilon}$ at $t=0$, where $\vec{u}$ i...

Studying transition to a highly disordered state of turbulence from a linearly stable coherent laminar state is conceptually and technically challenging and immensely important, e.g. all pipe and channel flows are of that type. In optics, understanding how systems lose coherence with increase of spatial size or excitation level is an open fundament...

The breaking of detailed balance, the symmetry between forward and backward probability transition between two states, is crucial to understand irreversible systems. In hydrodynamic turbulence, a far-from equilibrium system, we observe a strong manifestation of the breaking of detailed balance by following the evolution of the kinetic energy of ind...

We consider developed turbulence in the Gross-Pitaevsky model, where a condensate appears due to an inverse cascade. Despite being fully turbulent, the system demonstrates nondecaying periodic oscillations around a steady state, when turbulence and condensate periodically exchange a small fraction of waves. We show that these collective oscillation...

We review recent progress in optical wave turbulence with a specific focus on the fast growing field of fiber lasers. Weak irregular nonlinear interactions between a large number of resonator modes are responsible for practically important characteristics of fiber lasers such as the spectral broadening of radiation. Wave turbulence is a fundamental...

We develop an analytic formalism and derive new exact relations that express the short-time dispersion of fluid particles via the single-time velocity correlation functions in homogeneous isotropic and incompressible turbulence. The formalism establishes a bridge between single-time Eulerian and long-time Lagrangian pictures of turbulent flows. In...

We develop an analytic formalism and derive new exact relations that express the short-time dispersion of fluid particles via the single-time velocity correlation functions in homogeneous isotropic and incompressible turbulence. The formalism establishes a bridge between single-time Eulerian and long-time Lagrangian pictures of turbulent flows. In...

Using data from a large-scale three-dimensional simulation of supersonic isothermal turbulence, we have tested the validity of an exact flux relation derived analytically from the Navier--Stokes equation by Falkovich, Fouxon and Oz [2010 New relations for correlation functions in Navier--Stokes turbulence. J. Fluid Mech. 644, 465]. That relation, f...

The length distribution of streamline segments in homogeneous isotropic decaying turbulence Phys. Fluids 24, 045104 (2012) Conditional vorticity budget of coherent and incoherent flow contributions in fully developed homogeneous isotropic turbulence Phys. Fluids 24, 035108 (2012) Near-field investigation of turbulence produced by multi-scale grids...

We study numerically optical turbulence using the particular example of a recently created, ultra-long fibre laser. For normal fibre dispersion, we observed an intermediate state with an extremely narrow spectrum (condensate), which experiences instability and a sharp transition to a fluctuating regime with a wider spectrum. We demonstrate that the...

In turbulence, ideas of energy cascade and energy flux, substantiated by the exact Kolmogorov relation, lead to the determination of scaling laws for the velocity spatial correlation function. Here we ask whether similar ideas can be applied to temporal correlations. We critically review the relevant theoretical and experimental results concerning...

Geometric statistics open the window into the most fundamental aspect of turbulence flows, their symmetries, both broken and emerging. On one hand, the study of the stochastic geometry of multi-point configurations reveals the statistical conservation laws which are responsible for the breakdown of scale invariance in direct turbulence cascades. On...

The steady statistics of a passive scalar advected by a random two-dimensional flow of an incompressible fluid is described at scales less than the correlation length of the flow and larger than the diffusion scale. The probability distribution of the scalar is expressed via the probability distribution of the line stretching rate. The description...

We consider turbulence within the Gross-Pitaevsky model and look into the creation of a coherent condensate via an inverse cascade originating at small scales. The growth of the condensate leads to a spontaneous breakdown of statistical symmetries of overcondensate fluctuations: First, isotropy is broken, then a series of phase transitions marks th...

Flows in natural fluid layers are often forced simultaneously at scales smaller and much larger than the depth. For example, Earth atmospheric flows are powered by gradients of solar heating: vertical gradients cause three-dimensional (3D) convection while horizontal gradients drive planetary scale flows. Nonlinear interactions spread energy over s...

A passive scalar field was studied under the action of pumping, diffusion and advection by a 2D smooth flow with Lagrangian chaos. We present theoretical arguments showing that the scalar statistics are not conformally invariant and formulate a new effective semi-analytic algorithm to model scalar turbulence. We then carry out massive numerics of s...

Flows in natural fluid layers are often forced simultaneously at scales smaller and much larger than the depth. For example, the Earth’s atmospheric flows are powered by gradients of solar heating: vertical gradients cause three-dimensional (3D) convection whereas horizontal gradients drive planetary scale flows. Nonlinear interactions spread energ...

For the direct cascade of steady two-dimensional (2D) Navier-Stokes turbulence, we derive analytically the probability of strong vorticity fluctuations. When ϖ is the vorticity coarse-grained over a scale R, the probability density function (PDF), P(ϖ), has a universal asymptotic behavior lnP~-ϖ/ϖ(rms) at ϖ≫ϖ(rms)=[Hln(L/R)](1/3), where H is the en...

The multidisciplinary field of fluid mechanics is one of the most actively developing fieldsof physics, mathematics and engineering. In this book, the fundamental ideas of fluid mechanics are presented from a physics perspective. Using examples taken from everyday life, from hydraulic jumps ina kitchen sink to Kelvin–Helmholtz instabilities in clou...

We study statistical properties of turbulent inverse cascades in a class of nonlinear models describing a scalar field transported by a two-dimensional incompressible flow. The class is characterized by a linear relation between the transported field and the velocity, and include several cases of physical interest, such as Navier-Stokes, surface qu...

For the steady-state direct cascade of two-dimensional Navier-Stokes turbulence, we derive analytically the probability of strong vorticity fluctuations. The probability density function (pdf) of the vorticity coarse-grained over a scale in the inertial interval is shown to have a universal self-similar form, in distinction from other known direct...

This is the key chapter of the first volume. Here we deal with stationary distributions of weak turbulence. In Sects. 3.1–4 we describe the universal Kolmogorov-like spectra in the inertial interval. We obtain the Kolmogorov spectra as exact solutions of kinetic equations for scale-invariant media, both isotropic and nonisotropic, and for nearly sc...

In this chapter we shall go over from the dynamic description of wave systems to the statistical one. This will be done in terms of pair correlators of a wave field. They represent the occupation numbers (density) of waves in k-space. In Sect. 2.1 we shall obtain the kinetic equation for the occupation numbers of waves as the main mathematical obje...

We present experimental results on the properties of bounded turbulence in thin fluid layers. In contrast with the theory of two-dimensional �2D� turbulence, the effects of the bottom friction and of the spectral condensation of the turbulence energy are important in our experiment. Here we investigate how these two factors affect statistical momen...

A finite-amplitude propagating wave induces a drift in fluids. Understanding how drifts produced by many waves disperse pollutants has broad implications for geophysics and engineering. Previously, the effective diffusivity was calculated for a random set of small-amplitude surface and internal waves. Now, this is extended by Bühler & Holmes-Cerfon...

We consider the steady-state statistics of turbulence sustained by a large-scale force. The Kolmogorov flux relation (4/5-law) is shown to be a particular case of the general relation on the current-density correlation function. Using that, we derive an analog of the flux relation for compressible turbulence and a new exact relation for incompressi...

We study optical wave turbulence using as a particular example recently created ultralong-fiber laser. We show that the sign of the cavity dispersion has a critical impact on the spectral and temporal properties of generated radiation that are directly relevant to the fiber laser performance. For a normal dispersion, we observe an intermediate stat...

A Reply to the Comment by Erik Lindborg.

The emphasis of this review is on fundamental properties, degree of universality and symmetries of the turbulent state. The central questions are which symmetries remain broken even when the symmetry-breaking factor reaches zero, and which symmetries, in contrast, emerge in the state of developed turbulence. We shall see that time reversibility is...

We present experimental results on turbulence generated in thin fluid layers in the presence of a large-scale coherent flow, or a spectral condensate. It is shown that the condensate modifies the third-order velocity moment in a much wider interval of scales than the second one. The modification may include the change of sign of the third moment in...

We present a mean-field model of cloud evolution that describes droplet growth due to condensation and collisions and droplet loss due to fallout. The model accounts for the effects of cloud turbulence both in a large-scale turbulent mixing and in a microphysical enhancement of condensation and collisions. The model allows for an effective numerica...

Cloud physics has for a long time been an important segment of atmospheric science. It is common knowledge that clouds are crucial for our understanding of weather and climate. Clouds are also interesting by themselves (not to mention that they are beautiful). Complexity is hidden behind the common picture of these beautiful and interesting objects...

We present experimental results on turbulence generated in thin fluid layers in the presence of a large-scale coherent flow, or a spectral condensate. It is shown that the condensate modifies the third-order velocity moment in a much wider interval of scales than the second one. The modification may include the change of sign of the third moment in...

We discuss fluctuation relations in simple cases of non-equilibrium Langevin dynamics. In particular, we show that close to non-equilibrium steady states with non-vanishing probability currents some of these relations reduce to a modified version of the fluctuation-dissipation theorem. The latter may be interpreted as the equilibrium-like relation...

Measurements of atmospheric winds in the mesoscale range (10-500 km) reveal remarkably universal spectra with the $k^{-5/3}$ power law. Despite initial expectations of the inverse energy cascade, as in two-dimensional (2D) turbulence, measurements of the third velocity moment in atmosphere, suggested a direct energy cascade. Here we propose a possi...