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

Abu Hamed, M, Guo, Y, Titi, ES. (2015). Inertial manifolds for certain subgrid-scale $\alpha$ models of turbulence . SIAM Journal on Applied Dynamical Systems, 14(3), 1308-1325. 10.1137/140987833

cited authors

  • Abu Hamed, M; Guo, Y; Titi, ES

abstract

  • 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.

authors

publication date

  • January 1, 2015

published in

Digital Object Identifier (DOI)

start page

  • 1308

end page

  • 1325

volume

  • 14

issue

  • 3