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Stochastic Modeling of Isotropic Turbulence

  • Robert H. Kraichnan
Conference paper

Abstract

This paper reviews some stochastic models for Navier-Stokes turbulence and related problems. Discussion is confined to exactly soluble dynamical models that have intrinsic consistency properties and are constructed systematically from the equations of motion. Such models provide a unified framework for the examination of a number of approximation methods developed during the past few decades. The stochastic models that have been most studied predict the evolution of low-order moments. Their achievements include the description of error growth (sensitivity to perturbation), the deduction of generalized (non-local) eddy damping from the equations of motion, the representation of energy cascade and vorticity intensification, and discrimination between the behaviors of Eulerian and Lagrangian time correlations. Fairly good quantitative predictions of wavenumber spectra have been obtained at all Reynolds numbers. A current challenge is the intermittency of small scales at moderate as well as high Reynolds numbers. New models, based on nonlinear mappings of stochastic fields, offer closures for probability distributions and are a promising tool for attacking the intermittency problem.

Keywords

Reynolds Number Stochastic Modeling Isotropic Turbulence Collective Field Inertial Range 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1991

Authors and Affiliations

  • Robert H. Kraichnan

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