Approximation of attractors, large eddy simulations and multiscale methods
Abstract
Recend advances in the mathematical theory of the NavierStokes equations have produced new insight in the mathematical theory of turbulence. In particular, the study of the attractor for the NavierStokes equations produced the first connection between two approaches to turbulence that seemed far apart, namely the conventional approach of Kolmogorov and the dynamical systems theory approach. Similarly the study of the approximation of the attractor in connection with the newly introduced concept of approximate inertial manifolds has produced a new approach to large eddy simulations and the study of the interaction of small and large eddies in turbulent flows. Some of the new results concerning the functional properties of the NavierStokes equations are surveyed, and their relevance to turbulence is discussed.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 July 1991
 DOI:
 10.1098/rspa.1991.0078
 Bibcode:
 1991RSPSA.434...23T
 Keywords:

 Kolmogoroff Theory;
 NavierStokes Equation;
 Turbulent Flow;
 Flow Theory;
 Fourier Series;
 Galerkin Method;
 Three Dimensional Flow;
 Fluid Mechanics and Heat Transfer