NUMERICAL COMPUTATION OF UNSTABLE PERIODIC SOLUTIONS TO A SYSTEM OF EQUATIONS FOR FLUID MOTION

摘要

In this paper we review a novel approach to the characterization of spatiotemporal coherence observed in the transition to turbulence or developed low-Reynolds-number turbulence. This approach is based upon reproducible dynamics of coherent structures extracted from turbulent flows as a simple invariant solution, such as an unstable periodic solution, to a system of equations for fluid motion, i.e., the Navier-Stokes equation. Unstable periodic motion embedded in turbulent flow is discussed with emphasis on numerical methods for computation of a corresponding unstable solution.