Elementary models for turbulent diffusion with complex physical features: Eddy diffusivity, spectrum and intermittency

Andrew J. Majda, Boris Gershgorin

Research output: Contribution to journalArticle


This paper motivates, develops and reviews elementary models for turbulent tracers with a background mean gradient which, despite their simplicity, have complex statistical featuresmimicking crucial aspects of laboratory experiments and atmospheric observations. These statistical features include exact formulas for tracer eddy diffusivity which is non-local in space and time, exact formulas and simple numerics for the tracer variance spectrum in a statistical steady state, and the transition to intermittent scalar probability density functions with fat exponential tails as certain variances of the advecting mean velocity are increased while satisfying important physical constraints. The recent use of such simple models with complex statistics as unambiguous test models for central contemporary issues in both climate change science and the realtime filtering of turbulent tracers from sparse noisy observations is highlighted throughout the paper.

Original languageEnglish (US)
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number1982
StatePublished - Jan 13 2013



  • Eddy diffusivity
  • Exactly solvable model
  • Intermittency
  • Turbulent diffusion
  • White noise limit

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

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