arXiv subjects

Gregory Falkovich

Publications and source records attributed to Gregory Falkovich.

At least 37 records · Page 2Linked to original sources

arXiv2018

Precise measurements of torque in von Karman swirling flow driven by a bladed disk

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 other fields such as temperature. However, careful redesign and calibration of the experiment showed that this unexpected result was due to background errorscaused by minute misalignments which lead to a noisy and irreproducible torque signal at low rotation speeds and prevented correct background subtraction normally ascribed to frictional losses. An important lesson to be learnt is that multiple minute misalignments can nonlinearly couple to the torque signal and provide a dc offset that cannot be removed by averaging. That offset can cause the observed divergence of the friction coefficient C_f from its constant value observed in the turbulent regime. To minimize the friction and misalignments, we significantly modified the experimental setup and carried out the experiment with one bladed disk where the disk, torque meter and motor shaft axes can be aligned with significantly smaller error, close to the torque meter resolution. As a result we made precise measurements with high resolution and sensitivity of the small torques produced for low rotation speeds for several water-glycerin solutions of different viscosities and confirmed the similarity law in a wide range of Re in particular in low viscosity fluids.

physics.flu-dyn↗

arXiv2017

Alternating currents and shear waves in viscous electronics

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 and for the possibility of propagating slow shear waves. We focus on specific geometries that showcase interesting aspects of such waves: current parallel to a one-dimensional defect and current applied across a long strip. We find that the phase velocity of the wave propagating along the strip respectively increases/decreases with the frequency for no-slip/no-stress boundary conditions. This is so because when the frequency or strip width goes to zero (alternatively, viscosity go to infinity), the wavelength of the current pattern tends to infinity in the no-stress case and to a finite value in a general case. We also show that for DC current across a strip with no-stress boundary, there only one pair of vortices, while there is an infinite vortex chain for all other types of boundary conditions.

cond-mat.mes-hall↗

arXiv2017

How vortices and shocks provide for a flux loop in two-dimensional compressible turbulence

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 the interaction between acoustic waves and vortices is substantial. We employ solenoidal pumping at intermediate scales and show how both direct and inverse energy cascades are formed starting from the pumping scale. We show that there is an inverse cascade of kinetic energy up to a scale $\ell$, where a typical velocity reaches the speed of sound; this creates shock waves, which provide for a compensating direct cascade. When the system size is less than $\ell$, the steady state contains a system-size pair of long-living condensate vortices connected by a system of shocks. Thus turbulence in fluid layers processes energy via a loop: Most energy first goes to large scales via vortices and is then transported by waves to small-scale dissipation.

physics.flu-dyn↗

arXiv2017

Higher-Than-Ballistic Conduction of Viscous Electron Flows

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 contact, a constriction exhibiting the quantum-mechanical ballistic transport at $T=0$ but governed by electron hydrodynamics at elevated temperatures. We develop a theory of the ballistic-to-viscous crossover using an approach based on quasi-hydrodynamic variables. Conductance is found to obey an additive relation $G=G_{\rm ball}+G_{\rm vis}$, where the viscous contribution $G_{\rm vis}$ dominates over $G_{\rm ball}$ in the hydrodynamic limit. We argue that superballistic, low-dissipation transport is a generic feature of viscous electronics.

cond-mat.mes-hall↗

arXiv2017

Stokes Paradox, Back Reflections and Interaction-Enhanced Conduction

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 $σ=σ_0+Δσ$, with a non-interacting Drude contribution $σ_0$ and a contribution $Δσ>0$ describing conductivity enhancement due to interactions. The quantity $Δσ$ is enhanced by a logarithmically large factor originating from the Stokes paradox at the hydrodynamic lengthscales and, in addition, from an effect of repeated returns to the same scatterer due to backreflection in the carrier-carrier collisions occurring at the ballistic lengthscales. The interplay between these effects is essential at the ballistic-to-viscous crossover.

cond-mat.mes-hall↗

arXiv2016

Jets or vortices - what flows are generated by an inverse turbulent cascade?

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 momentum was therefore believed to be unidirectional, with two jets along the short side; while for an aspect ratio close to unity, a vortex dipole was expected. Using direct numerical simulations, we show that in fact neither the box symmetry is respected nor the largest scale is realized: the flow is never purely unidirectional since the inverse cascade produces coherent vortices, whose number and relative motion are determined by the aspect ratio. This spontaneous symmetry breaking is closely related to the hierarchy of averaging times. Long-time averaging restores translational invariance due to vortex wandering along one direction, and gives jets whose profile, however, can be deduced neither from the largest-available-scale argument, nor from the often employed maximum-entropy principle or quasi-linear approximation.

nlin.CD↗

arXiv2016

Linking Spatial Distributions of Potential and Current in Viscous Electronics

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, current can flow against the electric field, generating negative resistance, vorticity and vortices. Moreover, different current flows can result in identical potential distributions. This sets a new situation where inferring the electron flow pattern from the measured potentials presents a nontrivial problem. Using the inherent relation between these patterns through the complex analysis, here we propose a method for extracting the current flows from potential distributions measured in the presence of a magnetic field.

cond-mat.mes-hall↗

arXiv2016

Electron Viscosity, Current Vortices and Negative Nonlocal Resistance in Graphene

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 signature and link it with an easily verifiable striking macroscopic transport behavior. Produced by the viscous flow, vorticity can drive electric current against an applied field, resulting in a negative nonlocal voltage. We argue that the latter may play the same role for the viscous regime as zero electrical resistance does for superconductivity. Besides offering a diagnostic of viscous transport which distinguishes it from ohmic currents, the sign-changing electrical response affords a robust tool for directly measuring the viscosity-to-resistivity ratio. The strongly interacting electron-hole plasma in high-mobility graphene provides a bridge between quantum-criticality and the wealth of fluid mechanics phenomena.

cond-mat.mes-hall↗

arXiv2015

Time-irreversibility of the statistics of a single particle in a compressible turbulence

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. For short times, starting from a uniform distribution of markers, we find the scaling $\left<[E(t)-E(0)]^n\right>\propto t$ and $\left \propto \textrm{Re}^{n-1}$ for the power as a function of the Reynolds number. Both observations can be explained using the "flight-crash" model, suggested by Xu et al. Furthermore, we use a simple model for shocks which reproduces the moments of the energy difference including the pre-factor for $\left $. To complete the single particle picture for Burgers we compute the moments of the Lagrangian velocity difference and show that they are bi-fractal. This arises in a similar manner to the bi-fractality of Eulerian velocity differences. In the above setting time irreversibility is directly manifest as particles eventually end up in shocks. We additionally investigate time irreversibility in the long-time limit when all particles are located inside shocks and the Lagrangian velocity statistics are stationary. We find the same scalings for the power and energy differences as at short times and argue that this is also a consequence of rare "flight-crash" events related to shock collisions.

physics.flu-dyn↗

arXiv2015

Phase transitions in the distribution of inelastically colliding inertial particles

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. The problem of a particle near minima of turbulence intensity is related to that of two particles in a random flow, so that the localization-delocalization transition in the former corresponds to the path-coalescence transition in the latter. The transition is signaled by the sign change of the Lyapunov exponent that characterizes the mean rate of particle approach to the minimum (which could be wall or another particle). Here we solve analytically this problem for inelastic collisions and derive the phase diagram for the transition in the inertia-inelasticity plane. An important feature of the phase diagram is the region of inelastic collapse: if the restitution coefficient of particle velocity is smaller than some critical value, then the particle is localized for any inertia. We present direct numerical simulations which support the theory and in addition reveal the dependence of the transition of the flow correlation time, characterized by the Stokes number.

nlin.CD↗

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

New type of anomaly in turbulence

The turbulent energy flux through scales, $\barε$, 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, $\left< d u^2/dt\right>=-4 \barε$ at $t=0$, where $\vec{u}$ is the velocity difference of a pair of particles, initially separated by a fixed distance. In this letter we demonstrate that this derivation assumed first taking the limit $t \to 0$ and then $ν\to 0$, while the true anomaly requires taking viscosity to zero first. For compressible turbulence we find that the limits $t \to 0$ and $ν\to 0$ do not commute and the Lagrangian anomaly is completely altered: $\left< d u^2/dt\right>$ has different values forward and backward in time. We show that this new anomaly is related to the particles entering/exiting shocks forward/backward in time. For incompressible flows, on the other hand, we show that the limits can be interchanged and the Lagrangian anomaly is still induced by the flux law, apparently due to a homogeneous distribution of fluid particles at all times.

nlin.CD↗

arXiv2014

Power Fluctuations and Irreversibility in Turbulence

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 individual fluid elements. We found in all the flows that we have investigated that fluid elements decelerate faster than they accelerate, giving rise to negative third moment of energy increments, independently of space dimensionality. The exchange of energy between fluid elements however is fundamentally different in two and three dimensions. While pressure forces do not provide net energy change to slow or fast particles in two dimensions, they tend to transfer energy from {\it slow} to {\it fast} particles in three dimensions, possibly implying a runaway of energy.

physics.flu-dyn↗

arXiv2014

Tractor beam on the water surface

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 propagation. Here we show how to fetch a macroscopic floater from a large distance by sending a surface wave towards it. We develop a new method of remote manipulation of floaters by forming inward and outward surface jets, stationary vortices, and other complex surface flows using nonlinear waves generated by a vertically oscillating plunger. The flows can be engineered by changing the geometry and the power of a wave maker, and the flow dissipation. The new method is robust and works both for long gravity and for short capillary waves. We use a novel method of visualising 3D particle trajectories on the surface. This letter introduces a new conceptual framework for understanding wave-driven flows. The results form the basis for remote manipulation of objects on the fluid surfaces and will help better understanding motion of floaters on the ocean surface and the generation of wave-driven jets.

physics.flu-dyn↗

arXiv2014

Universal profile of the vortex condensate in two-dimensional turbulence

An inverse turbulent cascade in a restricted two-dimensional periodic domain leads to the creation of condensate -- a pair of coherent system-size vortices. We perform extensive numerical simulations of this system and carry on detailed theoretical analysis based upon momentum and energy exchanges between the turbulence fluctuations and the mean coherent condensate (vortices). The theory predicts the vortex profile and amplitude which perfectly agree with the numerical data.

physics.flu-dyn↗

arXiv2014

Turbulence on hyperbolic plane: the fate of inverse cascade

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 energy growth is due to an inverse cascade, which builds a constant part of the velocity autocorrelation function proportional to time and expanding in scales, while the moments of the velocity difference saturate during a time depending on the distance. For the curved space, we analyze the long-time long-distance scaling limit, that lives in a degenerate conical geometry, and find that the energy-containing mode linearly growing with time is not constant in space. The shape of the velocity correlation function indicates that the energy builds up in vortical rings of arbitrary diameter but of width comparable to the curvature radius of the hyperbolic plane. The energy current across scales does not increase linearly with the scale, as in a flat space, but reaches a maximum around the curvature radius. That means that the energy flux through scales decreases at larger scales so that the energy is transferred in a non-cascade way, that is the inverse cascade spills over to all larger scales where the energy pumped into the system is cumulated in the rings. The time-saturated part of the spectral density of velocity fluctuations contains a finite energy per unit area, unlike in the flat space where the time-saturated spectrum behaves as k^{-5/3}.

nlin.CD↗

arXiv2013

What a single snapshot reveals about the future and the past of turbulent flow

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 particular, we derive an exact formula for a short-term analog of the long-time Richardson law, and we identify a conservation law of turbulent dispersion which is true even in non-stationary turbulence.

nlin.CD↗

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↗