### Abstract

Recently, one of the authors, studying a model for turbulent diffusion involving a large-scale velocity field rapidly fluctuating in time, rigorously demonstrated intermittency in a diffusing scalar field by exhibiting broader than Gaussian tails in the scalar PDF. Here, we explore this model further with exact formulas within the context of general initial data possessing both a mean and a fluctuating component. Several new phenomena due to the presence of a nonzero scalar mean are documented here. We will establish that the limiting long time scalar PDF has long tails, as well as persisting skewness. Further, we show that the limiting PDF depends on the large-scale energy of initial temperature fluctuations and exhibits long time memory of the initial data. Additionally, we will exhibit an explicit phase transition occurring in the scalar PDF as this large scale energy is varied, whereby the limiting PDF switches between states arising from deterministic initial data and states dominated by fluctuation.

Original language | English (US) |
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Pages (from-to) | 536-547 |

Number of pages | 12 |

Journal | Physics of Fluids |

Volume | 8 |

Issue number | 2 |

State | Published - Feb 1996 |

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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*,

*8*(2), 536-547.

**An explicit example with non-Gaussian probability distribution for nontrivial scalar mean and fluctuation.** / McLaughlin, Richard M.; Majda, Andrew J.

Research output: Contribution to journal › Article

*Physics of Fluids*, vol. 8, no. 2, pp. 536-547.

}

TY - JOUR

T1 - An explicit example with non-Gaussian probability distribution for nontrivial scalar mean and fluctuation

AU - McLaughlin, Richard M.

AU - Majda, Andrew J.

PY - 1996/2

Y1 - 1996/2

N2 - Recently, one of the authors, studying a model for turbulent diffusion involving a large-scale velocity field rapidly fluctuating in time, rigorously demonstrated intermittency in a diffusing scalar field by exhibiting broader than Gaussian tails in the scalar PDF. Here, we explore this model further with exact formulas within the context of general initial data possessing both a mean and a fluctuating component. Several new phenomena due to the presence of a nonzero scalar mean are documented here. We will establish that the limiting long time scalar PDF has long tails, as well as persisting skewness. Further, we show that the limiting PDF depends on the large-scale energy of initial temperature fluctuations and exhibits long time memory of the initial data. Additionally, we will exhibit an explicit phase transition occurring in the scalar PDF as this large scale energy is varied, whereby the limiting PDF switches between states arising from deterministic initial data and states dominated by fluctuation.

AB - Recently, one of the authors, studying a model for turbulent diffusion involving a large-scale velocity field rapidly fluctuating in time, rigorously demonstrated intermittency in a diffusing scalar field by exhibiting broader than Gaussian tails in the scalar PDF. Here, we explore this model further with exact formulas within the context of general initial data possessing both a mean and a fluctuating component. Several new phenomena due to the presence of a nonzero scalar mean are documented here. We will establish that the limiting long time scalar PDF has long tails, as well as persisting skewness. Further, we show that the limiting PDF depends on the large-scale energy of initial temperature fluctuations and exhibits long time memory of the initial data. Additionally, we will exhibit an explicit phase transition occurring in the scalar PDF as this large scale energy is varied, whereby the limiting PDF switches between states arising from deterministic initial data and states dominated by fluctuation.

UR - http://www.scopus.com/inward/record.url?scp=0029673858&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029673858&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0029673858

VL - 8

SP - 536

EP - 547

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 2

ER -