### 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 language | English (US) |
---|---|

Pages (from-to) | 881-897 |

Number of pages | 17 |

Journal | Physics of Fluids |

Volume | 14 |

Issue number | 2 |

DOIs | |

State | Published - Feb 2002 |

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### ASJC Scopus subject areas

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

### Cite this

*Physics of Fluids*,

*14*(2), 881-897. https://doi.org/10.1063/1.1430736

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

Research output: Contribution to journal › Article

*Physics of Fluids*, vol. 14, no. 2, pp. 881-897. https://doi.org/10.1063/1.1430736

}

TY - JOUR

T1 - Elementary models with probability distribution function intermittency for passive scalars with a mean gradient

AU - Bourlioux, A.

AU - Majda, A. J.

PY - 2002/2

Y1 - 2002/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0036470346&partnerID=8YFLogxK

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U2 - 10.1063/1.1430736

DO - 10.1063/1.1430736

M3 - Article

VL - 14

SP - 881

EP - 897

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 2

ER -