Chaos, Coherence and Control

Abstract

In 1976, Werner Heisenberg lay dying. On his deathbed, he is reported to have said (Gleick, 1988) that he had two questions for God: why relativity, and why turbulence. "I really think," said Heisenberg, "He may have an answer to the first question." In this paper we focus on a tiny piece of the second question, "Why turbulence?" Specifically, we try to understand just enough of that question to be able to decide whether or how turbulence could possibly be controlled. This is an ambitious agenda, and to study it we break the problem into manageable topics. So here we discuss two things. First, we review progress over the past decade on the control of low-dimensional, temporally chaotic dynamics. Second, we explore recent work which demonstrates how the dynamics of spatially chaotic, but temporaRy regular, systems can be manipulated. We conclude by very briefly discussing the prognosis of this research for the control of truly turbulent problems, which are unpredictable both in space and in time.