Persistence Problem in Two-Dimensional Fluid Turbulence

Perlekar, Prasad; Ray, Samriddhi Sankar; Mitra, Dhrubaditya; Pandit, Rahul

doi:10.1103/physrevlett.106.054501

Cited by 52 publications

(59 citation statements)

References 16 publications

(15 reference statements)

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“…We have become aware of another paper [32] that also uses the Okubo-Weiss parameter to distinguish the behaviors of Lagrangian particles in vortical and extensional regions in two-dimensional fluid turbulence. We thank Dr. P. Perlekar for providing us with this reference.…”

Section: Discussionmentioning

confidence: 99%

Lagrangian statistics and flow topology in forced two-dimensional turbulence

et al. 2011

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A study of the relationship between Lagrangian statistics and flow topology in fluid turbulence is presented. The topology is characterized using the Weiss criterion, which provides a conceptually simple tool to partition the flow into topologically different regions: elliptic (vortex dominated), hyperbolic (deformation dominated), and intermediate (turbulent background). The flow corresponds to forced two-dimensional Navier-Stokes turbulence in doubly periodic and circular bounded domains, the latter with no-slip boundary conditions. In the double periodic domain, the probability density function (pdf) of the Weiss field exhibits a negative skewness consistent with the fact that in periodic domains the flow is dominated by coherent vortex structures. On the other hand, in the circular domain, the elliptic and hyperbolic regions seem to be statistically similar. We follow a Lagrangian approach and obtain the statistics by tracking large ensembles of passively advected tracers. The pdfs of residence time in the topologically different regions are computed introducing the Lagrangian Weiss field, i.e., the Weiss field computed along the particles' trajectories. In elliptic and hyperbolic regions, the pdfs of the residence time have self-similar algebraic decaying tails. In contrast, in the intermediate regions the pdf has exponential decaying tails. The conditional pdfs (with respect to the flow topology) of the Lagrangian velocity exhibit Gaussian-like behavior in the periodic and in the bounded domains. In contrast to the freely decaying turbulence case, the conditional pdfs of the Lagrangian acceleration in forced turbulence show a comparable level of intermittency in both the periodic and the bounded domains. The conditional pdfs of the Lagrangian curvature are characterized, in all cases, by self-similar power-law behavior with a decay exponent of order -2.

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Section: Discussionmentioning

confidence: 99%

Lagrangian statistics and flow topology in forced two-dimensional turbulence

et al. 2011

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“…Persistence properties of a two dimensional fluid (on a thin film) has been investigated recently by numerically solving the 2-d Navier-Stokes equation driven by Kolmogorov forcing [370]. Persistence was studied in both the Eulerian and Lagrangian framework.…”

Section: Turbulent Fluid In 2 Dimensionsmentioning

confidence: 99%

“…Persistence was studied in both the Eulerian and Lagrangian framework. In the Eulerian framework, the authors monitored the time series Λ(t), at a fixed point (x, y) in space, where the Okubo-Weiss parameter Λ(t) takes the value +1 (if the flow at (x, y) is vortical) and −1 (if the flow at (x, y) is extensional) [370]. In this case, the + and − persistences Q E ± (t) (probability that Λ(t) does not change sign in [0, t]) both were found to decay exponentially with time.…”

Section: Turbulent Fluid In 2 Dimensionsmentioning

confidence: 99%

“…In this case, the + and − persistences Q E ± (t) (probability that Λ(t) does not change sign in [0, t]) both were found to decay exponentially with time. In contrast, in the Lagrangian framework, one moves with a Lagrangian particle and monitors the probability Q L ± (t) that the particle stays in a vortical (+) or extensional (−) regime up to time t. In this case, it was found numerically that while Q L − (t) decays exponentially, Q L + (t) ∼ t −θ with θ ≈ 2.9 ± 0.2 [370]. Note that the two persistence probabilities Q E (t) and Q L (t) are analogues of the 'site' persistence and the 'walker' persistence in the reaction-diffusion systems discussed in section 5.1 and section 17.2.…”

Section: Turbulent Fluid In 2 Dimensionsmentioning

confidence: 99%

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Persistence and first-passage properties in nonequilibrium systems

Bray

Majumdar

Schehr

2013

Advances in Physics

519

669

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In this review we discuss the persistence and the related first-passage properties in extended many-body nonequilibrium systems. Starting with simple systems with one or few degrees of freedom, such as random walk and random acceleration problems, we progressively discuss the persistence properties in systems with many degrees of freedom. These systems include spins models undergoing phase ordering dynamics, diffusion equation, fluctuating interfaces etc. Persistence properties are nontrivial in these systems as the effective underlying stochastic process is non-Markovian. Several exact and approximate methods have been developed to compute the persistence of such non-Markov processes over the last two decades, as reviewed in this article. We also discuss various generalisations of the local site persistence probability. Persistence in systems with quenched disorder is discussed briefly. Although the main emphasis of this review is on the theoretical developments on persistence, we briefly touch upon various experimental systems as well.

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“…(2) in vorticitystream function formulation Eq. (4) and numerically integrate it using using a pseudospectral method [33]:…”

Section: Direct Numerical Simulationsmentioning

confidence: 99%

Front structure and dynamics in dense colonies of motile bacteria: Role of active turbulence

2016

Self Cite

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We study the spreading of a bacterial colony undergoing turbulent like collective motion. We present two minimalistic models to investigate the interplay between population growth and coherent structures arising from turbulence. Using Direct Numerical Simulation (DNS) of the proposed models we find that turbulence has two prominent effects on the spatial growth of the colony: (a) the front speed is enhanced, and (b) the front gets crumpled. Both these effects, which we highlight by using statistical tools, are markedly different in our two models. We also show that the crumpled front structure and the passive scalar fronts in random flows are related in certain regimes.

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Persistence Problem in Two-Dimensional Fluid Turbulence

Cited by 52 publications

References 16 publications

Lagrangian statistics and flow topology in forced two-dimensional turbulence

Lagrangian statistics and flow topology in forced two-dimensional turbulence

Persistence and first-passage properties in nonequilibrium systems

Front structure and dynamics in dense colonies of motile bacteria: Role of active turbulence

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