Global attractor and determining modes for a hyperbolic MHD turbulence Model

Abstract

Magnetohydrodynamics (MHD)-α models are regularized systems used to study the turbulent flow of a magnetofluid, because of the impossibility to handle non-regularized models either analitically or numerically. In order to establish the validity of a model as a large eddy simulation model, one needs to test properties related to the number of degrees of freedom of long-time dynamics of the solutions. Preliminary information is provided by estimates concerning the number of determining modes. We consider the MHD–Voight model for an incompressible fluid and find estimates for a number of asymptotically determining modes and modes on global attractor.

Keywords:

• magnetohydrodynamics
• MHD-α models
• MHD–Voight model
• regularizing MHD
• damped hyperbolic system
• turbulence models
• incompressible fluid
• global attractor
• determining modes