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On the temporal evolution of finite ensembles

Part of: Basic methods in fluid mechanics

Published online by Cambridge University Press:  26 February 2010

A. P. Rothmayer  and
D. W. Black
A. P. Rothmayer
Affiliation:
Department of Aerospace Engineering and Engineering Mechanics, Iowa State University, Ames, Iowa 50011, U.S.A.
D. W. Black
Affiliation:
Department of Aerospace Engineering and Engineering Mechanics, Iowa State University, Ames, Iowa 50011, U.S.A.
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Abstract

The temporal evolution of nonlinear, incompressible ensembles is examined first for the one-dimensional Burgers' equation and then for the incompressible, unsteady Navier-Stokes equations. It is shown that local closure of the averaged problem can be obtained for finite ensembles of Burgers' equation in the limit as the number of moments tends to infinity. This limit behaviour is verified via direct numerical computations for the onedimensional inviscid and viscous Burgers' equation. Closure is found to occur at reasonably low order. It is shown that this technique can be extended to obtain a local closure of the convective terms of the Navier-Stokes Reynoldsaveraged equations.

MSC classification

Secondary: 76M35: Stochastic analysis
Type
Research Article
Information
Mathematika , Volume 39 , Issue 2 , December 1992 , pp. 291 - 318
Copyright
Copyright © University College London 1992

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