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G. Falkovich

Publications and source records attributed to G. Falkovich.

At least 19 recordsLinked to original sources
arXiv2021

Second harmonic generation as a minimal model of turbulence

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 interaction/noise relation. One finds substantial phase correlation in the limit of strong interaction (weak noise). Surprisingly, for both cascades, the mutual information between modes increases and entropy further decreases when interaction strength decreases. We use the model to elucidate the fundamental problem of far-from equilibrium physics: where the information (entropy deficit) is encoded and how singular measures form. For an instability-driven system (a laser), even a small added noise leads to large fluctuations of the relative phase near the stability threshold, while far from it we show that the conversion into the second harmonic is weakly affected by noise.

nlin.CD↗
arXiv2017

Superballistic flow of viscous electron fluid through graphene constrictions

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 clean electron systems with transport dominated by e-e collisions have become available, showing behavior characteristic of highly viscous fluids. Here we study electron transport through graphene constrictions and show that their conductance below 150 K increases with increasing temperature, in stark contrast to the metallic character of doped graphene. Notably, the measured conductance exceeds the maximum conductance possible for free electrons. This anomalous behavior is attributed to collective movement of interacting electrons, which 'shields' individual carriers from momentum loss at sample boundaries. The measurements allow us to identify the conductance contribution arising due to electron viscosity and determine its temperature dependence. Besides fundamental interest, our work shows that viscous effects can facilitate high-mobility transport at elevated temperatures, a potentially useful behavior for designing graphene-based devices.

cond-mat.mes-hall↗
arXiv2016

Inelastic collapse and near-wall localization of randomly accelerated particles

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 the restitution coefficient $β$ of particle velocity is smaller than the critical value $β_c=\exp(-π/\sqrt{3})$. We demonstrate that inelastic collapse takes place also in a wide class of models with spatially inhomogeneous random force and, what is more, that the critical value $β_c$ is universal. That class includes an important case of inertial particles in wall-bounded random flows. To establish how the inelastic collapse influence the particle distribution, we construct an exact equilibrium probability density function $ρ(z,v)$ for particle position and velocity. The equilibrium distribution exists only at $β<β_c$ and indicates that inelastic collapse does not necessarily mean the near-wall localization.

nlin.CD↗
arXiv2014

Localization-delocalization transitions in turbophoresis of inertial particles

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 in minima (say, on walls in turbulence). Here we show that this is incorrect: escaping minima is possible for inertial particles whose time of equilibration is longer than the time to reach the minimum. The best way out is always through: particles escape by flying through minima or reflecting from walls. We solve the problem analytically and find the phase transition as a sign change of the mean velocity. That means separation: light particles concentrate in a minimum while heavy particles spread away from it (gravity can reverse the effect). That discovery changes understanding of that fundamental phenomenon and may find numerous applications.

nlin.CD↗
arXiv2014

The laminar-turbulent transition in a fibre laser

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 fundamental problem of practical importance. Here we identify, arguably, the simplest system where this classical problem can be studied: we learnt to operate a fibre laser in laminar and turbulent regimes. We show that laminar phase is an analogue of a one-dimensional coherent condensate and turbulence onset is through a spatial loss of coherence. We discover a new mechanism of laminar-turbulent transition in laser operation: condensate destruction by the clustering of dark and grey solitons. This is important both for the design of devices exploiting coherent dynamics and for conceptually new technologies based on systems operating far from thermodynamic equilibrium.

physics.optics↗
arXiv2010

Conformal Invariance in Inverse Turbulent Cascades

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 quasi-geostrophic and Charney-Hasegawa-Mima equations. We find that some statistical properties of the inverse turbulent cascades in such systems are conformal invariant. In particular, the zero-isolines of the scalar field are statistically equivalent to conformal invariant curves within the resolution of our numerics. We show that the choice of the conformal class is determined by the properties of a transporting velocity rather than those of a transported field and discover a phase transition when the velocity turns from a large-scale field to a small-scale one.

cond-mat.stat-mech↗
arXiv2008

Turbulence-condensate interaction in two dimensions

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 the inverse cascade. This observation may help resolve a controversy on the energy flux in mesoscale atmospheric turbulence (10-500 km): to recover a correct energy flux from the third velocity moment one needs first to subtract the coherent flow. We find that the condensate also increases the velocity flatness.

physics.flu-dyn↗
arXiv2008

What drives mesoscale atmospheric turbulence?

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 possible solution to this controversy by accounting for the presence of a large-scale coherent flow, or a spectral condensate. We present new experimental laboratory data and show that the presence of a large-scale shear flow modifies the third-order velocity moment in spectrally condensed 2D turbulence, making it, in some conditions, similar to that observed in the atmosphere.

physics.flu-dyn↗
arXiv2007

Inertial particles driven by a telegraph noise

We present a model for the Lagrangian dynamics of inertial particles in a compressible flow, where fluid velocity gradients are modelled by a telegraph noise. The model allows for an analytic investigation of the role of time correlation of the flow in the aggregation-disorder transition of inertial particle. The dependence on Stokes and Kubo numbers of the Lyapunov exponent of particle trajectories reveals the presence of a region in parameter space (St, Ku) where the leading Lyapunov exponent changes sign, thus signaling the transition. The asymptotics of short and long-correlated flows are discussed, as well as the fluid-tracer limit.

nlin.CD↗
arXiv2006

Clustering of matter in waves and currents

The growth rate of small-scale density inhomogeneities (the entropy production rate) is given by the sum of the Lyapunov exponents in a random flow. We derive an analytic formula for the rate in a flow of weakly interacting waves and show that in most cases it is zero up to the fourth order in the wave amplitude. We then derive an analytic formula for the rate in a flow of potential waves and solenoidal currents. Estimates of the rate and the fractal dimension of the density distribution show that the interplay between waves and currents is a realistic mechanism for providing patchiness of pollutant distribution on the ocean surface.

nlin.CD↗
arXiv2006

Inverse turbulent cascades and conformally invariant curves

We offer a new example of conformal invariance far from equilibrium -- the inverse cascade of Surface Quasi-Geostrophic (SQG) turbulence. We show that temperature isolines are statistically equivalent to curves that can be mapped into a one-dimensional Brownian walk (called Schramm-Loewner Evolution or SLE$_κ$). The diffusivity is close to $κ=4$, that is iso-temperature curves belong to the same universality class as domain walls in the O(2) spin model. Several statistics of temperature clusters and isolines are measured and shown to be consistent with the theoretical expectations for such a spin system at criticality. We also show that the direct cascade in two-dimensional Navier-Stokes turbulence is not conformal invariant. The emerging picture is that conformal invariance may be expected for inverse turbulent cascades of strongly interacting systems.

nlin.CD↗
arXiv2006

Conformal invariance in two-dimensional turbulence

Simplicity of fundamental physical laws manifests itself in fundamental symmetries. While systems with an infinity of strongly interacting degrees of freedom (in particle physics and critical phenomena) are hard to describe, they often demonstrate symmetries, in particular scale invariance. In two dimensions (2d) locality often promotes scale invariance to a wider class of conformal transformations which allow for nonuniform re-scaling. Conformal invariance allows a thorough classification of universality classes of critical phenomena in 2d. Is there conformal invariance in 2d turbulence, a paradigmatic example of strongly-interacting non-equilibrium system? Here, using numerical experiment, we show that some features of 2d inverse turbulent cascade display conformal invariance. We observe that the statistics of vorticity clusters is remarkably close to that of critical percolation, one of the simplest universality classes of critical phenomena. These results represent a new step in the unification of 2d physics within the framework of conformal symmetry.

nlin.CD↗
arXiv2005

Clustering of floaters by waves

We study experimentally how waves affect distribution of particles that float on a water surface. We show that clustering of small particles in a standing wave is a nonlinear effect with the clustering time decreasing as the square of the wave amplitude. In a set of random waves, we show that small floaters concentrate on a multi-fractal set.

nlin.CD↗
arXiv2004

Rain initiation time in turbulent warm clouds

We present a mean-field model that describes droplet growth due to condensation and collisions and droplet loss due to fallout. The model allows for an effective numerical simulation. We study how the rain initiation time depends on different parameters. We also present a simple model that allows one to estimate the rain initiation time for turbulent clouds with an inhomogeneous concentration of cloud condensation nuclei. In particular, we show that over-seeding even a part of a cloud by small hygroscopic nuclei one can substantially delay the onset of precipitation.

physics.ao-ph↗
arXiv2001

Particles and fields in fluid turbulence

The understanding of fluid turbulence has considerably progressed in recent years. The application of the methods of statistical mechanics to the description of the motion of fluid particles, i.e. to the Lagrangian dynamics, has led to a new quantitative theory of intermittency in turbulent transport. The first analytical description of anomalous scaling laws in turbulence has been obtained. The underlying physical mechanism reveals the role of statistical integrals of motion in non-equilibrium systems. For turbulent transport, the statistical conservation laws are hidden in the evolution of groups of fluid particles and arise from the competition between the expansion of a group and the change of its geometry. By breaking the scale-invariance symmetry, the statistically conserved quantities lead to the observed anomalous scaling of transported fields. Lagrangian methods also shed new light on some practical issues, such as mixing and turbulent magnetic dynamo.

cond-mat.stat-mech↗
arXiv2000

Clustering of inertial particles in turbulent flows

We consider inertial particles suspended in an incompressible turbulent flow. Due to inertia of particles, their velocity field acquires small compressible component. Its presence leads to a new qualitative effect --- possibility of clustering. We show that this effect is significant for heavy particles, leading to strong fluctuations of the concentration.

chao-dyn↗
arXiv2000

Statistics of soliton-bearing systems with additive noise

We present a consistent method to calculate the probability distribution of soliton parameters in systems with additive noise. Even though a weak noise is considered, we are interested in probabilities of large fluctuations (generally non-Gaussian) which are beyond perturbation theory. Our method is a further development of the instanton formalism (method of optimal fluctuation) based on a saddle-point approximation in the path integral. We first solve a fundamental problem of soliton statistics governing by noisy Nonlinear Schrödinger Equation (NSE). We then apply our method to optical soliton transmission systems using signal control elements (filters, amplitude and phase modulators).

nlin.CD↗