Modelling of the interaction of lower and higher modes in two-dimensional MHD-equations

The problem of approximating the exact solution to the magnetohydrodynamic equations is considered. The behavior of a viscous, incompressible, and resistive fluid is examined for a long period of time. The strategy of approximating the solutions of the Navier-Stokes equations (NSE) is used. The exis...

Full description

Saved in:
Bibliographic Details
Published in:Nonlinear analysis 1996, Vol.26 (1), p.41-54
Main Author: Schmidtmann, Olaf
Format: Article
Language:English
Subjects:
approximate inertial manifolds
Mathematical models
MHD-equations
Q1
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The problem of approximating the exact solution to the magnetohydrodynamic equations is considered. The behavior of a viscous, incompressible, and resistive fluid is examined for a long period of time. The strategy of approximating the solutions of the Navier-Stokes equations (NSE) is used. The existence of a finite dimensional global attractor and a finite number of determining modes of the two-dimensional NSE shows that the long time behavior of these equations is determined by a finite number of parameters. In order to obtain a better approximation, it is pointed out that the long time behavior of 2D turbulent flows is mainly controlled by a finite number of modes related to the Stokes operator and that the higher modes remain small for a large time.
ISSN:0362-546X
1873-5215
DOI:10.1016/0362-546X(94)00207-X