Multiple realization vs. one-path analysis of a strange attractor
Abstract
The statistical dynamics approach is a powerful tool for analyzing dynamical phenomena. It consists in calculating the evolution of a statistical distribution associated with a dynamical system. This distribution represents a canonical ensemble of initial conditions for the system. Under well known constraints the statistical distribution reaches a fixed point which corresponds to an attractor for the dynamical system. When the attractor is strange, the best way to find the stationary distribution is by numerical means. In this work some properties of the stationary distribution are compared with geometrical properties of the attractor for a well known system (Lorenz system). It is demonstrated that the stationary distribution corresponds well with the attractor. Finally it is proposed to extend this method in the calculation of turbulent flows. The proposal requires the development of two concepts: random functions and Galerkin projection for Navier Stokes equations. The first concept requires in turn the development of new computational tools; some of which are presented here.
- Publication:
-
APS Division of Fluid Dynamics Meeting Abstracts
- Pub Date:
- November 1999
- Bibcode:
- 1999APS..DFD..DF05R