Turbulent Prandtl number effect on passive scalar advection

Weinan E, Eric Vanden-Eijnden

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22 Scopus citations


A generalization of Kraichnan's model of passive scalar advection is considered. Physically motivated regularizations of the model are considered which take into account both the effects of viscosity and molecular diffusion. The balance between these two effects on the inertial range behavior for the scalar is shown to be parameterized by a new turbulent Prandtl number. Three different regimes are identified in the parameter space depending on degrees of compressibility. In the strongly and weakly compressible regimes, the inertial range behavior of the scalar does not depend on the turbulent Prandtl number. In the regime of intermediate compressibility, the inertial range behavior does depend on the turbulent Prandtl number.

Original languageEnglish (US)
Pages (from-to)636-645
Number of pages10
JournalPhysica D: Nonlinear Phenomena
StatePublished - May 15 2001

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


  • Kraichnan model
  • Passive scalar advections
  • Regularizations
  • Turbulence
  • Turbulent Prandtl number


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