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

This paper motivates, develops and reviews elementary models for turbulent tracers with a background mean gradient which, despite their simplicity, have complex statistical features mimicking crucial aspects of laboratory experiments and atmospheric observations. These statistical features include e...

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Bibliographic Details
Published in:Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences physical, and engineering sciences, 2013-01, Vol.371 (1982), p.1-36
Main Authors: Majda, Andrew J., Gershgorin, Boris
Format: Article
Language:English
Subjects:
Climate change
Determinism
Diffusion coefficient
Noise spectra
Scalars
Shear flow
Statistical variance
Turbulence models
Velocity distribution
White noise
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Summary:This paper motivates, develops and reviews elementary models for turbulent tracers with a background mean gradient which, despite their simplicity, have complex statistical features mimicking 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.
ISSN:1364-503X