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Matrix exponential-based closures for the turbulent subgrid-scale stress tensor

Li, Y., Chevillard, L., Eyink, G. and Meneveau, C. (2009) Matrix exponential-based closures for the turbulent subgrid-scale stress tensor. Physical Review E, 79 (1). Art. No. 016305. ISSN 1550-2376

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Two approaches for closing the turbulence subgrid-scale stress tensor in terms of matrix exponentials are introduced and compared. The first approach is based on a formal solution of the stress transport equation in which the production terms can be integrated exactly in terms of matrix exponentials. This formal solution of the subgrid-scale stress transport equation is shown to be useful to explore special cases, such as the response to constant velocity gradient, but neglecting pressure-strain correlations and diffusion effects. The second approach is based on an Eulerian-Lagrangian change of variables, combined with the assumption of isotropy for the conditionally averaged Lagrangian velocity gradient tensor and with the recent fluid deformation approximation. It is shown that both approaches lead to the same basic closure in which the stress tensor is expressed as the matrix exponential of the resolved velocity gradient tensor multiplied by its transpose. Short-time expansions of the matrix exponentials are shown to provide an eddy-viscosity term and particular quadratic terms, and thus allow a reinterpretation of traditional eddy-viscosity and nonlinear stress closures. The basic feasibility of the matrix-exponential closure is illustrated by implementing it successfully in large eddy simulation of forced isotropic turbulence. The matrix-exponential closure employs the drastic approximation of entirely omitting the pressure-strain correlation and other nonlinear scrambling terms. But unlike eddy-viscosity closures, the matrix exponential approach provides a simple and local closure that can be derived directly from the stress transport equation with the production term, and using physically motivated assumptions about Lagrangian decorrelation and upstream isotropy.

Item Type: Article
Copyright, Publisher and Additional Information: © 2009 The American Physical Society. This is an author produced version of a paper published in 'Physical Review E'. Uploaded in accordance with the publisher's self-archiving policy.
Institution: The University of Sheffield
Academic Units: The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield)
Depositing User: Mrs Megan Hobbs
Date Deposited: 25 Mar 2010 11:43
Last Modified: 17 Nov 2015 01:36
Published Version: http://dx.doi.org/10.1103/PhysRevE.79.016305
Status: Published
Publisher: American Physical Society
Refereed: Yes
Identification Number: 10.1103/PhysRevE.79.016305
Related URLs:
URI: http://eprints.whiterose.ac.uk/id/eprint/10562

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