Inertial Manifolds for Certain Subgrid-Scale alpha-Models of Turbulence Academic Article

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 -models of turbulence, the simplified Bardina model and the modified Leray- 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.

authors

• Titi, Edriss

published proceedings

• SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS

author list (cited authors)

• Abu Hamed, M., Guo, Y., & Titi, E. S.

citation count

• 8

complete list of authors

• Abu Hamed, Mohammad||Guo, Yanqiu||Titi, Edriss S

publication date

• January 2015

publisher

• Society for Industrial & Applied Mathematics (SIAM)  Publisher

published in

• SIAM Journal on Applied Dynamical Systems  Journal

keywords

• Inertial Manifold
• Modified Leray-alpha Model
• Navier-stokes Equations
• Simplified Bardina Model
• Subgrid-scale Models
• Turbulence Models

Digital Object Identifier (DOI)

• 10.1137/140987833

URI

• https://hdl.handle.net/1969.1/184231

start page

• 1308

end page

• 1325

volume

• 14

issue

• 3

URL

• http%3A%2F%2Fdx.doi.org%2F10.1137%2F140987833