### Abstract

Recent experimental and computational observations demonstrate the occurrence of large-scale intermittency for diffusing passive scalars, as manifested by broader than Gaussian probability distribution functions. Here, a family of explicit exactly solvable examples is developed which demonstrates these effects of large-scale intermittency at any positive time through simple formulas for the higher flatness factors without any phenomenological approximations. The exact solutions involve advection-diffusion with velocity fields involving a uniform shear flow perturbed by a random fluctuating uniform shear flow. Through an exact quantum mechanical analogy, the higher-order statistics for the scalar in these models are solved exactly by formulas for the quantum-harmonic oscillator. These explicit formulas also demonstrate that the large time asymptotic limiting probability distribution function for the normalized scalar can be either broader than Gaussian or Gaussian depending on the relative strength of the mean flow and the fluctuating velocity field.

Original language | English (US) |
---|---|

Pages (from-to) | 1963-1970 |

Number of pages | 8 |

Journal | Physics of Fluids A |

Volume | 5 |

Issue number | 8 |

State | Published - 1992 |

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### ASJC Scopus subject areas

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

### Cite this

**The random uniform shear layer : An explicit example of turbulent diffusion with broad tail probability distributions.** / Majda, Andrew J.

Research output: Contribution to journal › Article

*Physics of Fluids A*, vol. 5, no. 8, pp. 1963-1970.

}

TY - JOUR

T1 - The random uniform shear layer

T2 - An explicit example of turbulent diffusion with broad tail probability distributions

AU - Majda, Andrew J.

PY - 1992

Y1 - 1992

N2 - Recent experimental and computational observations demonstrate the occurrence of large-scale intermittency for diffusing passive scalars, as manifested by broader than Gaussian probability distribution functions. Here, a family of explicit exactly solvable examples is developed which demonstrates these effects of large-scale intermittency at any positive time through simple formulas for the higher flatness factors without any phenomenological approximations. The exact solutions involve advection-diffusion with velocity fields involving a uniform shear flow perturbed by a random fluctuating uniform shear flow. Through an exact quantum mechanical analogy, the higher-order statistics for the scalar in these models are solved exactly by formulas for the quantum-harmonic oscillator. These explicit formulas also demonstrate that the large time asymptotic limiting probability distribution function for the normalized scalar can be either broader than Gaussian or Gaussian depending on the relative strength of the mean flow and the fluctuating velocity field.

AB - Recent experimental and computational observations demonstrate the occurrence of large-scale intermittency for diffusing passive scalars, as manifested by broader than Gaussian probability distribution functions. Here, a family of explicit exactly solvable examples is developed which demonstrates these effects of large-scale intermittency at any positive time through simple formulas for the higher flatness factors without any phenomenological approximations. The exact solutions involve advection-diffusion with velocity fields involving a uniform shear flow perturbed by a random fluctuating uniform shear flow. Through an exact quantum mechanical analogy, the higher-order statistics for the scalar in these models are solved exactly by formulas for the quantum-harmonic oscillator. These explicit formulas also demonstrate that the large time asymptotic limiting probability distribution function for the normalized scalar can be either broader than Gaussian or Gaussian depending on the relative strength of the mean flow and the fluctuating velocity field.

UR - http://www.scopus.com/inward/record.url?scp=0027392523&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027392523&partnerID=8YFLogxK

M3 - Article

VL - 5

SP - 1963

EP - 1970

JO - Physics of fluids. A, Fluid dynamics

JF - Physics of fluids. A, Fluid dynamics

SN - 0899-8213

IS - 8

ER -