Title

Analysis of Model Variance for Ensemble Based Turbulence Modeling

Abstract

This report develops an ensemble or statistical eddy viscosity model. The model is parameterized by an ensemble of solutions of an ensemble-Leray regularization. The combined approach of ensemble time stepping and ensemble eddy viscosity modeling allows direct parametrization of the turbulent viscosity coefficient. We prove unconditional stability and that the model's solution approaches statistical equilibrium as t → ∞ the model's variance converges to zero as t → ∞. The ensemble method is used to interrogate a rotating flow, testing its predictability by computing effective averaged Lyapunov exponents.

Department(s)

Mathematics and Statistics

Comments

Funding: Nan Jiang and William Layton were partially supported by NSF grants DMS 1216465 and AFOSR FA9550-12-1-0191. Songul Kaya was supported by TUBITAK.

Keywords and Phrases

Lyapunov methods; Turbulence; Turbulence models; Eddy viscosity; Eddy viscosity model; Ensemble; Leray Regularization; Solution approach; Statistical equilibrium; Turbulent viscosity; Unconditional stability; Viscosity; Turbulence Modeling

International Standard Serial Number (ISSN)

1609-4840; 1609-9389

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2015 De Gruyter, All rights reserved.

Publication Date

01 Apr 2015

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