Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Some physical considerations attendant to the approximate inertial manifolds for Navier-Stokes equations

Pages: 585 - 593, Volume 2, Issue 4, October 1996      doi:10.3934/dcds.1996.2.585

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Oscar P. Manley - U.S. Department of Energy, Washington, DC., United States (email)

Abstract: In contrast with the other papers presented at the 1995 Xian Workshop, this article explores some physical ideas evoked by the concept of approximate inertial manifolds. Notably, while there is no clear separation of scales, such as needed for the existence of an inertial manifold, in turbulent flows there is a separation of physical phenomena. Thus the behavior of the spectrum ranging from the energy containing modes, through the inertial range is unaffected by dissipation, while the low energy content modes in the dissipation range are dominated by dissipation. An iterative process is developed yielding an effective viscosity useful for large eddy simulation. Some conjectures about the spectrum resulting from such a simulation are explored.

Keywords:  Navier-Stokes equations, inertial manifolds.
Mathematics Subject Classification:  35Qxx.

Received: October 1995;      Revised: April 1996;      Published: July 1996.