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Realizability of second-moment closure via stochastic analysis

Published online by Cambridge University Press:  26 April 2006

P. A. Durbin  and
C. G. Speziale
P. A. Durbin
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA 94305-3030, USA
C. G. Speziale
Affiliation:
Aerospace & Mechanical Engineering Department, Boston University, Boston, MA 02215, USA
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Abstract

It is shown that realizability of second-moment turbulence closure models can be established by finding a Langevin equation for which they are exact. All closure models currently in use can be derived formally from the type of Langevin equation described herein. Under certain circumstances a coefficient in that formalism becomes imaginary. The regime in which models are realizable is, at least, that for which the coefficient is real. The present method does not imply unrealizable solutions when the coefficient is imaginary, but it does guarantee realizability when the coefficient is real; hence, this method provides sufficient, but not necessary, conditions for realizability. Illustrative computations of homogeneous shear flow are presented. It is explained how models can be modified to guarantee realizability in extreme non-equilibrium situations without altering their behaviour in the near-equilibrium regime for which they were formulated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 280 , 10 December 1994 , pp. 395 - 407
Copyright
© 1994 Cambridge University Press

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