The random uniform shear layer: An explicit example of turbulent diffusion with broad tail probability distributions

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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 languageEnglish (US)
Pages (from-to)1963-1970
Number of pages8
JournalPhysics of Fluids A
Volume5
Issue number8
StatePublished - 1992

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turbulent diffusion
shear layers
Shear flow
Probability distributions
Distribution functions
probability distribution functions
intermittency
scalars
shear flow
Higher order statistics
Advection
velocity distribution
flatness
advection
harmonic oscillators
statistics
occurrences
approximation

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

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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.",
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