Recurrent flows: The clockwork behind turbulence

Abstract

The understanding of chaotic dynamics in high-dimensional systems that has emerged in the last decade offers a promising dynamical framework to study turbulence. Here turbulence is viewed as a walk through a forest of exact solutions in the infinite-dimensional state space of the governing equations. Recently, Chandler & Kerswell (J. Fluid Mech., vol. 722, 2013, pp. 554-595) carry out the most exhaustive study of this programme undertaken so far in fluid dynamics, a feat that requires every tool in the dynamicist's toolbox: numerical searches for recurrent flows, computation of their stability, their symmetry classification, and estimating from these solutions statistical averages over the turbulent flow. In the long run this research promises to develop a quantitative, predictive description of moderate-Reynolds-number turbulence, and to use this description to control flows and explain their statistics. © 2013 Cambridge University Press.