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

Richard M. McLaughlin, Andrew J. Majda

Research output: Contribution to journalArticlepeer-review

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 languageEnglish (US)
Pages (from-to)536-547
Number of pages12
JournalPhysics of Fluids
Volume8
Issue number2
DOIs
StatePublished - Feb 1996

ASJC Scopus subject areas

  • Computational Mechanics
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes

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