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          Institute: MPI für Meteorologie     Collection: Ocean in the Earth System     Display Documents



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ID: 529118.0, MPI für Meteorologie / Ocean in the Earth System
On degrees of freedom of certain conservative turbulence models for the Navier-Stokes equations
Authors:Korn, P.
Language:English
Date of Publication (YYYY-MM-DD):2011
Title of Journal:Journal of Mathematical Analysis and Applications
Volume:378
Start Page:49
End Page:63
Review Status:Peer-review
Audience:Not Specified
Abstract / Description:We study the degrees of freedom of several conservative computational turbulence models that are derived via a non-dissipative regularizations of the Navier-Stokes equations. For the Navier-Stokes-α, the Leray-α and the Navier-Stokes-ω equations we prove that the longtime behavior of their respective solutions is completely determined by a finite set of grid values and by a finite set of Fourier modes. For each turbulence model the number of determining nodes and of determining modes is estimated in terms of flow parameters, such as viscosity, smoothing length, forcing and domain size. These estimates are global as they do not depend on an individual solution. © 2011 Elsevier Inc. All rights reserved.
External Publication Status:published
Document Type:Article
Communicated by:Carola Kauhs
Affiliations:MPI für Meteorologie/Ocean in the Earth System
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