Elementary models with probability distribution function intermittency for passive scalars with a mean gradient

A. Bourlioux, A. J. Majda

Research output: Contribution to journalArticle

Abstract

The single-point probability distribution function (PDF) for a passive scalar with an imposed mean gradient is studied here. Elementary models are introduced involving advection diffusion of a passive scalar by a velocity field consisting of a deterministic or random shear flow with a transverse time-periodic transverse sweep. Despite the simplicity of these models, the PDFs exhibit scalar intermittency, i.e., a transition from a Gaussian PDF to a broader than Gaussian PDF with large variance as the Péclet number increases with a universal self-similar shape that is determined analytically by explicit formulas. The intermittent PDFs resemble those that have been found recently in numerical simulations of much more complex models. The examples presented here unambiguously demonstrate that neither velocity fields inducing chaotic particle trajectories with positive Lyapunov exponents nor strongly turbulent velocity fields are needed to produce scalar intermittency with an imposed mean gradient. The passive scalar PDFs in these models are given through exact solutions that are processed in a transparent fashion via elementary stationary phase asymptotics and numerical quadrature of one-dimensional formulas.

Original languageEnglish (US)
Pages (from-to)881-897
Number of pages17
JournalPhysics of Fluids
Volume14
Issue number2
DOIs
StatePublished - Feb 2002

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probability distribution functions
intermittency
Probability distributions
Distribution functions
scalars
gradients
velocity distribution
Advection
Shear flow
particle trajectories
advection
shear flow
quadratures
Trajectories
exponents
Computer simulation
simulation

ASJC Scopus subject areas

  • Fluid Flow and Transfer Processes
  • Computational Mechanics
  • Mechanics of Materials
  • Physics and Astronomy(all)
  • Condensed Matter Physics

Cite this

Elementary models with probability distribution function intermittency for passive scalars with a mean gradient. / Bourlioux, A.; Majda, A. J.

In: Physics of Fluids, Vol. 14, No. 2, 02.2002, p. 881-897.

Research output: Contribution to journalArticle

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