### Abstract

The first prediction of the probability distribution function (PDF) of self-organized shear flows is presented in a nonlinear diffusion model where shear flows are generated by a stochastic forcing while diffused by a nonlinear eddy diffusivity. A novel nonperturbative method based on a coherent structure is utilized for the prediction of the strongly intermittent exponential PDF tails of the gradient of shear flows. Numerical simulations using Gaussian forcing not only confirm these predictions but also reveal the significant contribution from the PDF tails with a large population of supercritical gradients. The validity of the nonlinear diffusion model is then examined using a threshold model where eddy diffusivity is given by discontinuous values, elucidating an important role of relative time scales of relaxation and disturbance in the determination of the PDFs.

Original language | English |
---|---|

Article number | 052304 |

Journal | Physics of Plasmas |

Volume | 16 |

Issue number | 5 |

DOIs | |

Publication status | Published - 10 Jun 2009 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*Physics of Plasmas*,

*16*(5), [052304]. https://doi.org/10.1063/1.3132631

**Probability distribution function for self-organization of shear flows.** / Kim, Eun Jin; Liu, Han Li; Anderson, Johan.

Research output: Contribution to journal › Article

*Physics of Plasmas*, vol. 16, no. 5, 052304. https://doi.org/10.1063/1.3132631

}

TY - JOUR

T1 - Probability distribution function for self-organization of shear flows

AU - Kim, Eun Jin

AU - Liu, Han Li

AU - Anderson, Johan

PY - 2009/6/10

Y1 - 2009/6/10

N2 - The first prediction of the probability distribution function (PDF) of self-organized shear flows is presented in a nonlinear diffusion model where shear flows are generated by a stochastic forcing while diffused by a nonlinear eddy diffusivity. A novel nonperturbative method based on a coherent structure is utilized for the prediction of the strongly intermittent exponential PDF tails of the gradient of shear flows. Numerical simulations using Gaussian forcing not only confirm these predictions but also reveal the significant contribution from the PDF tails with a large population of supercritical gradients. The validity of the nonlinear diffusion model is then examined using a threshold model where eddy diffusivity is given by discontinuous values, elucidating an important role of relative time scales of relaxation and disturbance in the determination of the PDFs.

AB - The first prediction of the probability distribution function (PDF) of self-organized shear flows is presented in a nonlinear diffusion model where shear flows are generated by a stochastic forcing while diffused by a nonlinear eddy diffusivity. A novel nonperturbative method based on a coherent structure is utilized for the prediction of the strongly intermittent exponential PDF tails of the gradient of shear flows. Numerical simulations using Gaussian forcing not only confirm these predictions but also reveal the significant contribution from the PDF tails with a large population of supercritical gradients. The validity of the nonlinear diffusion model is then examined using a threshold model where eddy diffusivity is given by discontinuous values, elucidating an important role of relative time scales of relaxation and disturbance in the determination of the PDFs.

UR - http://www.scopus.com/inward/record.url?scp=66449124188&partnerID=8YFLogxK

U2 - 10.1063/1.3132631

DO - 10.1063/1.3132631

M3 - Article

VL - 16

JO - Physics of Plasmas

JF - Physics of Plasmas

SN - 1070-664X

IS - 5

M1 - 052304

ER -