Geometric statistics in turbulence

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224 Scopus citations


The author presents results regarding certain average properties of incompressible fluids derived from the equations of motion. The author estimates the average dissipation rate, the average dimension rate, the average dimension of level sets. The role played by the field of direction of vorticity in the three-dimensional Euler and Navier-Stokes equations is discussed and a class of two-dimensional equations that are useful models of incompressible dynamics is described. The author presents results concerning scaling exponents in turbulence.

Original languageEnglish (US)
Pages (from-to)73-98
Number of pages26
JournalSIAM Review
Issue number1
StatePublished - 1994
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computational Mathematics
  • Applied Mathematics


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