On degrees of freedom of certain conservative turbulence models for the 
Navier-Stokes equations

Korn, P.

doi:10.1016/j.jmaa.2011.01.013

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On degrees of freedom of certain conservative turbulence models for the Navier-Stokes equations

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Korn, P.
Numerical Model Development and Data Assimilation, The Ocean in the Earth System, MPI for Meteorology, Max Planck Society;

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Korn, P. (2011). On degrees of freedom of certain conservative turbulence models for the Navier-Stokes equations. Journal of Mathematical Analysis and Applications, 378, 49-63. doi:10.1016/j.jmaa.2011.01.013.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0011-F505-5

Abstract

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.