The taylor-green vortex : Fully developed turbulence and transition to spatial chaos

Abstract

A brief introduction to fully developed turbulence is given (cf. Refs. 1-2). We then report results obtained from numerical simulations of the Taylor-Green three dimensional vortex flow 3. This flow is perhaps the simplest system in which one can study the generation of small scales by three-dimensional vortex stretching and the resulting turbulence. The problem is studied by both direct spectral numerical solution of the Navier-Stokes equations (with up to 2563 modes) and by power series analysis in time.