CLARENCE ROWLEY
Control and Dynamical Systems
Mail Code 107-81
California Institute of Technology
Pasadena, CA 91125, USA
http://green.caltech.edu/~clancy
clancy@caltech.edu
Abstract:
We present a method for applying the Karhunen-Loeve decomposition to
systems with continuous symmetry. The method in effect removes
variables associated with the symmetry from the problem, and has been
used in previous works both to identify coherent structures in
solutions of PDEs, and to derive low-order models via Galerkin
projection. The main result of this work is to derive a simple and
easily implementable set of reconstruction equations which close
the system of ODEs produced by Galerkin projection. The geometric
interpretation of the method closely parallels techniques used in
geometric phases and reconstruction techniques in geometric
mechanics. We apply the method to the Kuramoto-Sivashinsky equation
and are able to derive models of much lower dimension than are
possible with the traditional Karhunen-Loeve expansion.