Open Access Publications from the University of California

## Inertial manifolds for certain subgrid-scale $\alpha$ models of turbulence

• Author(s): Abu Hamed, M
• Guo, Y
• Titi, ES
• et al.

## Published Web Location

https://doi.org/10.1137/140987833
Abstract

Copyright © by SIAM. In this paper we prove the existence of an inertial manifold, i.e., a globally invariant, exponentially attracting, finite-dimensional smooth manifold, for two different subgrid-scale á-models of turbulence, the simplified Bardina model and the modified Leray-á model, in two-dimensional space. That is, we show the existence of an exact rule that parameterizes the dynamics of small spatial scales in terms of the dynamics of large ones. In particular, this implies that the long-time dynamics of these turbulence models is equivalent to that of a finite-dimensional system of ordinary differential equations.

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