Probability distribution function of self-organization of shear flows

Eun Jin Kim, Han Li Liu, Johan Anderson

Research output: Chapter in Book/Report/Conference proceedingConference proceedingpeer-review


We present a statistical theory of self-organisation of shear flows, modeled by a nonlinear diffusion equation driven by a stochastic forcing. A non-perturbative method based on a coherent structure is utilized for the prediction of the PDFs, showing strong intermittency with exponential tails. We confirm these results by numerical simulations. Furthermore, the results reveal a significant probability of supercritical states due to stochastic perturbation, which could have crucial implications in a variety of systems. To elucidate a crucial role of relative time scales of relaxation and disturbance in the determination of the PDFs, we present numerical simulation results obtained in a threshold model where the diffusion is given by discontinuous values. Our results highlight the importance of the statistical description of gradients, rather than their average value as has conventionally been done.

Original languageEnglish
Title of host publicationTwelfth International Solar Wind Conference Proceedings
EditorsM Maksimovic, N Meyer-Vernet, M Moncuquet, F Pantellini
PublisherAIP Publishing
Number of pages4
ISBN (Print)9780735407596
Publication statusPublished - 14 May 2010
Externally publishedYes
Event12th International Solar Wind Conference - Saint-Malo, France
Duration: 21 Jun 200926 Jun 2009

Publication series

NameAIP Conference Proceedings
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616


Conference12th International Solar Wind Conference


  • PDFs
  • Self-organisation
  • Shear flows
  • Transport properties

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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