arXiv subjects

Anna Frishman

Publications and source records attributed to Anna Frishman.

At least 19 recordsLinked to original sources

arXiv2026

Laminar gaps mirror turbulent puffs in pipe flow

Pipe flow at intermediate Reynolds numbers, between the laminar and fully turbulent regimes, takes the form of several spatially and temporally intermittent phases in which turbulent and laminar states coexist. In the lower range, $Re\in (1750,2300)$, turbulence appears in the form of localized traveling structures called "puffs", which form long-lived chaotic dynamical states, whose stochastic decays and splits control the steady state intermittency. At the other end, $Re\in (2300,3000)$, puffs are replaced by an extended turbulent state, with laminar pockets intermittently forming and disappearing within it. Using direct numerical simulations of pipe flow at $Re = 2400, 2450, 2500, 2550$, we provide evidence that these laminar gaps form a distinct dynamical state analogous to puffs: a traveling laminar pocket in a turbulent surrounding, stabilized by a shear-dependent self-tuning mechanism. We analyse the mean spatial profile of these gaps and show that their lifetimes are exponentially distributed, suggesting that gap closing corresponds to an escape from a chaotic saddle. Finally, we suggest these laminar gaps become unstable and disappear at a finite Reynolds number, $Re\sim 2900$, which can be interpreted as the onset point of spatially and temporally homogeneous turbulence.

physics.flu-dyn↗

arXiv2026

Conservation laws, fluxes, and symmetries: lessons from a perturbative approach for self-organized turbulence

Some turbulent flows self-organize into large-scale structures, rather than breaking up into ever-smaller scales. Underpinning this phenomenon is the existence of two sign-definite quantities which are conserved by the dynamics. Two-dimensional turbulence is a prime example, where large-scale mean flows, termed condensates, spontaneously emerge. We review a perturbative theoretical framework for the statistical description of such inhomogeneous turbulence, offering new perspectives on the role of the two conserved quantities. We illustrate the universal properties of the theory, comparing results from two-dimensional Navier-Stokes to those from the large-scale-quasi-geostrophic equation. These two models are limiting cases of the shallow water quasi-geostrophic equation, the former exhibiting long-range fluid element interactions, while the latter has local interactions. We then demonstrate these theoretical ideas in two new settings: first, in rotating three-dimensional turbulence, where two-dimensional condensates are known to form. Considering jet-type condensates, we derive the mean-flow profile and discuss a surprising symmetry breaking. Second, we vary the Rossby deformation radius in the shallow water quasi-geostrophic equation. We obtain novel domain-spanning condensates in all tested regimes and show that they follow two-dimensional Navier-Stokes for deformation radii above the forcing scale, and the large-scale quasi-geostrophic equation for those below, demonstrating the power of these asymptotic models.

physics.flu-dyn↗

arXiv2025

Helicity controls the direction of fluxes in rotating turbulence

Turbulence sustains out-of-equilibrium energy fluxes shaped by conservation laws. Three-dimensional flows conserve energy and sign-indefinite helicity, both being transferred to small scales. Yet in 3D rotating turbulence, energy is observed to flow simultaneously toward large-scale two-dimensional structures and toward small-scale three-dimensional waves. We uncover the origin of this dual behavior. When sufficiently fast inertial waves interact with a large-scale 2D flow, they conserve their helicity separately by sign, enforcing an inverse transfer of energy from 3D waves to 2D motions and promoting spectral condensation. Slower modes, by contrast, exchange helicity across opposite-sign sectors and thus behave as in non-rotating turbulence, driving a forward transfer. Using a mean-wave kinetic theory, we derive analytical expressions for these competing bi-directional transfers and quantitatively predict the rotation- and Reynolds-number dependence of the large-scale 2D flow in fully nonlinear simulations, unifying the picture from zero to infinite rotation.

physics.flu-dyn↗

arXiv2025

Waves maintain large-scale 2D flows in rotating turbulence and cause their demise

Turbulence follows a few well-known organizational principles, rooted in conservation laws. One such principle states that a system conserving two sign-definite invariants self-organizes into large-scale structures. Ordinary three-dimensional turbulence does not fall within this paradigm, but is profoundly altered when subject to rotation. In rotating turbulence, 3D inertial waves coexist alongside emergent two-dimensional structures, which tend to take the form of domain-scale flows called condensates. This interplay raises a fundamental question: why and when are 2D flows sustained if only 3D waves are excited? We develop a quasi-linear wave-kinetic theory to answer this question. We show that near-resonant interactions between 3D waves and a large-scale 2D flow impose an additional conservation law: waves must conserve their helicity separately for each helicity sign. This emergent sign-definite invariant constrains the waves to transfer their energy to large-scale 2D motions, which maintains the latter in statistical steady state. We derive analytical expressions for the 3D-2D energy transfer as a function of rotation, Reynolds number and domain geometry in a rotation dominated regime, and compare them with extensive numerical simulations of the rotating 3D Navier-Stokes equations. As rotation increases, the energy transfer from the waves to the 2D flow progressively vanishes as the two decouple, leading to a transition between distinct classes of turbulence: from 2D-dominated to 3D-dominated wave turbulence. Our theory shows that this gradual transition is caused by a depletion of modes satisfying the resonance conditions, and exhibits good agreement with numerical simulations when the number of near-resonant modes is not too small. We discuss such limitations of our theory, as well as the validity range of its underlying assumptions.

physics.flu-dyn↗

arXiv2025

Self-Replication of Turbulent Puffs: On the edge between chaotic saddles

Pipe flow is a canonical example where turbulence first appears intermittently in space and time, taking the form of localized structures termed puffs. Turbulence spreads via puff self-replication, which must out-compete puff decays to sustain it. Here we study the self-replication process, a transition from one to two puffs, using direct numerical simulations. We identify an edge state on the phase space boundary between the two states, demonstrate that it mediates the transition, and show that self-replication follows a previously proposed mechanism, with the edge state as its tipping point.

physics.flu-dyn↗

arXiv2024

Out-of-equilibrium fluxes shape the self-organization of locally-interacting turbulence

We study the self-organization of turbulence in a geophysically motivated two-dimensional fluid with local interactions. Using simulations and theory, we show that the out-of-equilibrium flux to small scales imposes a constraint on the large-scale emergent flow. Consequently, a rich phase diagram of large-scale configurations emerges, replacing the unique state found in flows with energy injection below the interaction scale. We explain what sets the boundaries between the different phases, and the occurrence of spontaneous symmetry breaking. Our work demonstrates that the selection mechanism of large-scale structures in quasi-geostrophic flows can be dramatically altered by forcing above the interaction scale.

physics.flu-dyn↗

arXiv2024

Single-parameter effective dynamics of warm cloud precipitation

Cloud observables such as precipitation efficiency and cloud lifetime are key quantities in weather and climate, but understanding their quantitative connection to initial conditions such as initial cloud water mass or droplet size remains challenging. Here we study the evolution of cloud droplets with a bin microphysics scheme, modeling both gravitational coagulation as well as fallout, and develop analytical formulae to describe the evolution of bulk cloud and rain water. We separate the dynamics into a mass-conserving and fallout-dominated regime, which reveals that the overall dynamics are governed by a single non-dimensional parameter $\mu$, the ratio of accretion and sedimentation time scales. Cloud observables from the simulations accordingly collapse as a function of $\mu$. We also find an unexpected relationship between cloud water and accumulated rain, and that fallout can be modeled with a bulk fall speed which is constant in time despite an evolving raindrop distribution.

physics.ao-ph↗

arXiv2023

Statistics of inhomogeneous turbulence in large scale quasi-geostrophic dynamics

A remarkable feature of two-dimensional turbulence is the transfer of energy from small to large scales. This process can result in the self-organization of the flow into large, coherent structures due to energy condensation at the largest scales. We investigate the formation of this condensate in a quasi-geostropic flow in the limit of small Rossby deformation radius, namely the large scale quasi-geostrophic model. In this model potential energy is transferred up-scale while kinetic energy is transferred down-scale in a direct cascade. We focus on a jet mean flow and carry out a thorough investigation of the second order statistics for this flow, combining a quasi-linear analytical approach with direct numerical simulations. We show that the quasi-linear approach applies in regions where jets are strong and is able to capture all second order correlators in that region, including those related to the kinetic energy. This is a consequence of the blocking of the direct cascade by the mean flow in jet regions, suppressing fluctuation-fluctuation interactions. The suppression of the direct cascade is demonstrated using a local coarse-graining approach allowing to measure space dependent inter-scale kinetic energy fluxes, which we show are concentrated in between jets in our simulations. We comment on the possibility of a similar direct cascade arrest in other two-dimensional flows, arguing that it is a special feature of flows in which the fluid element interactions are local in space

physics.flu-dyn↗

arXiv2023

Universality of satellites in the breakup of a stretched fluid bridge

As a fluid object breaks, it often leaves behind satellite fragments. Here we show that satellite formation can follow universal dynamics, leading to robust satellite sizes. Specifically, we consider the breakup of a slowly stretched fluid bridge, which we realize experimentally using a soap-film bubble suspended between two plates. Combining experiments and one-dimensional simulations, we show that a main satellite bubble always forms as the bridge breaks. We discover that the size of the bubble is highly reproducible and can be dramatically increased by stretching the bridge faster or increasing its volume. The satellite size is a simple function of two non-dimensional parameters: the normalized volume of the bridge and the Weber number, measuring inertia due to stretching as compared to surface tension. These observations can be explained by tracing the bridge evolution over a series of dynamical stages in which the bridge: (i) closely follows a sequence of equilibrium bridge configurations; (ii) stretches as it begins to breakup after reaching an unstable equilibrium; and (iii) follows a universal breakup solution. The last stage takes place over a finite region, the corresponding length scale determined by stretching during the previous stage. This length scale controls the satellite size, and the universality of the dynamics makes the system highly reproducible. This work suggests universal satellite formation dynamics may provide a route for understanding satellite bubble sizes in turbulent flows.

physics.flu-dyn↗

arXiv2023

Two-dimensional turbulence with local interactions: statistics of the condensate

Two-dimensional turbulence self-organizes through a process of energy accumulation at large scales, forming a coherent flow termed a condensate. We study the condensate in a model with local dynamics, the large-scale quasi-geostrophic equation, observed here for the first time. We obtain analytical results for the mean flow and the two-point, second-order correlation functions, and validate them numerically. The condensate state requires parity+time-reversal symmetry breaking. We demonstrate distinct universal mechanisms for the even and odd correlators under this symmetry. We find that the model locality is imprinted in the small scale dynamics, which the condensate spatially confines.

physics.flu-dyn↗

arXiv2022

Mechanism for turbulence proliferation in subcritical flows

The subcritical transition to turbulence, as occurs in pipe flow, is believed to generically be a phase transition in the directed percolation universality class. At its heart is a balance between the decay rate and proliferation rate of localized turbulent structures, called puffs in pipe flow. Here we propose the first-ever dynamical mechanism for puff proliferation -- the process by which a puff splits into two. In the first stage of our mechanism, a puff expands into a slug. In the second stage, a laminar gap is formed within the turbulent core. The notion of a split-edge state, mediating the transition from a single puff to a two puff state, is introduced and its form is predicted. The role of fluctuations in the two stages of the transition, and how splits could be suppressed with increasing Reynolds number, are discussed. Using numerical simulations, the mechanism is validated within the stochastic Barkley model. Concrete predictions to test the proposed mechanism in pipe and other wall bounded flows, and implications for the universality of the directed percolation picture, are discussed.

physics.flu-dyn↗

arXiv2022

Dynamical landscape of transitional pipe flow

The transition to turbulence in pipes is characterized by a coexistence of laminar and turbulent states. At the lower end of the transition, localized turbulent pulses, called puffs, can be excited. Puffs can decay when rare fluctuations drive them close to an edge state lying at the phase-space boundary with laminar flow. At higher Reynolds numbers, homogeneous turbulence can be sustained, and dominates over laminar flow. Here we complete this landscape of localized states, placing it within a unified bifurcation picture. We demonstrate our claims within the Barkley model, and motivate them generally. Specifically, we suggest the existence of an antipuff and a gap-edge -- states which mirror the puff and related edge state. Previously observed laminar gaps forming within homogeneous turbulence are then naturally identified as antipuffs nucleating and decaying through the gap edge.

physics.flu-dyn↗

arXiv2021

Perspectives on viscoelastic flow instabilities and elastic turbulence

Viscoelastic fluids are a common subclass of rheologically complex materials that are encountered in diverse fields from biology to polymer processing. Often the flows of viscoelastic fluids are unstable in situations where ordinary Newtonian fluids are stable, owing to the nonlinear coupling of the elastic and viscous stresses. Perhaps more surprisingly, the instabilities produce flows with the hallmarks of turbulence -- even though the effective Reynolds numbers may be $O(1)$ or smaller. We provide perspectives on viscoelastic flow instabilities by integrating the input from speakers at a recent international workshop: historical remarks, characterization of fluids and flows, discussion of experimental and simulation tools, and modern questions and puzzles that motivate further studies of this fascinating subject. The materials here will be useful for researchers and educators alike, especially as the subject continues to evolve in both fundamental understanding and applications in engineering and the sciences.

physics.flu-dyn↗

arXiv2019

Learning force fields from stochastic trajectories

When monitoring the dynamics of stochastic systems, such as interacting particles agitated by thermal noise, disentangling deterministic forces from Brownian motion is challenging. Indeed, we show that there is an information-theoretic bound, the capacity of the system when viewed as a communication channel, that limits the rate at which information about the force field can be extracted from a Brownian trajectory. This capacity provides an upper bound to the system's entropy production rate, and quantifies the rate at which the trajectory becomes distinguishable from pure Brownian motion. We propose a practical and principled method, Stochastic Force Inference, that uses this information to approximate force fields and spatially variable diffusion coefficients. It is data efficient, including in high dimensions, robust to experimental noise, and provides a self-consistent estimate of the inference error. In addition to forces, this technique readily permits the evaluation of out-of-equilibrium currents and the corresponding entropy production with a limited amount of data.

cond-mat.soft↗

arXiv2018

The culmination of an inverse cascade: mean flow and fluctuations

Two dimensional turbulence has a remarkable tendency to self-organize into large, coherent structures, forming a mean flow. The purpose of this paper is to elucidate how these structures are sustained, and what determines them and the fluctuations around them. A recent theory for the mean flow will be reviewed. The theory assumes turbulence is excited by a forcing supported on small scales, and uses a linear shear model to relate the turbulent momentum flux to the mean shear rate. Extending the theory, it will be shown here that the relation between the momentum flux and mean shear is valid, and the momentum flux is non-zero, for both an isotropic and an anisotropic forcing, independent of the dissipation mechanism at small scales. This conclusion requires taking into account that the linear shear model is an approximation to the real system. The proportionality between the momentum flux and the inverse of the shear can then be inferred most simply on dimensional grounds. Moreover, for a homogeneous pumping, the proportionality constant can be determined by symmetry considerations, recovering the result of the original theory. The regime of applicability of the theory, its compatibility with observations from simulations, a formula for the momentum flux for an inhomogeneous pumping, and results for the statistics of fluctuations, will also be discussed.

physics.flu-dyn↗

arXiv2017

Turbulence statistics in a 2D vortex condensate

Disentangling the evolution of a coherent mean-flow and turbulent fluctuations, interacting through the non-linearity of the Navier-Stokes equations, is a central issue in fluid mechanics. It affects a wide range of flows, such as planetary atmospheres, plasmas or wall-bounded flows, and hampers turbulence models. We consider the special case of a two-dimensional flow in a periodic box, for which the mean-flow, a pair of box-size vortices called \emph{condensate}, emerges from turbulence through an inverse cascade process. As was recently shown, a perturbative closure describes correctly the condensate when turbulence is excited at small scales. In this context, we obtain explicit results for the statistics of turbulence, encoded in the Reynolds stress tensor. We demonstrate that the two components of the Reynolds stress, the momentum flux and the turbulent energy, are determined by different mechanisms. It was suggested previously that the momentum flux is fixed by a balance between forcing and mean-flow advection: using unprecedently long numerical simulations, we provide the first direct evidence supporting this prediction. By contrast, combining analytical computations with numerical simulations, we show that the turbulent energy is determined only by mean-flow advection, and obtain for the first time a formula describing its profile in the vortex.

physics.flu-dyn↗

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↗

arXiv2015

A statistical conservation law in two and three dimensional turbulent flows

Particles in turbulence live complicated lives. It is nonetheless sometimes possible to find order in this complexity. It was proposed in [Falkovich et al., Phys. Rev. Lett. 110, 214502 (2013)] that pairs of Lagrangian tracers at small scales, in an incompressible isotropic turbulent flow, have a statistical conservation law. More specifically, in a d-dimensional flow the distance $R(t)$ between two neutrally buoyant particles, raised to the power $-d$ and averaged over velocity realizations, remains at all times equal to the initial, fixed, separation raised to the same power. In this work we present evidence from direct numerical simulations of two and three dimensional turbulence for this conservation. In both cases the conservation is lost when particles exit the linear flow regime. In 2D we show that, as an extension of the conservation law, a Evans-Cohen-Morriss/Gallavotti-Cohen type fluctuation relation exists. We also analyse data from a 3D laboratory experiment [Liberzon et al., Physica D 241, 208 (2012)], finding that although it probes small scales they are not in the smooth regime. Thus instead of $\left $, we look for a similar, power-law-in-separation conservation law. We show that the existence of an initially slowly varying function of this form can be predicted but that it does not turn into a conservation law. We suggest that the conservation of $\left $, demonstrated here, can be used as a check of isotropy, incompressibility and flow dimensionality in numerical and laboratory experiments that focus on small scales.

nlin.CD↗