Chaos, coherence, and turbulence

This paper is a personal overview of the efforts over the past half century to understand fluid turbulence in terms of simpler coherent units. The consequences of chaos and the concept of coherence are first reviewed, using examples from free-shear and wall-bounded shear flows, and including how the simplifications due to coherent structures have been useful in the conceptualization and control of turbulence. It is remarked that, even if this approach has revolutionized our understanding of the flow, most of turbulence cannot yet be described by structures. This includes cascades, both direct and inverse, and possibly junk turbulence, whose role, if any, is currently unknown. This part of the paper is mostly a catalog of questions, some of them answered and others still open. A second part of the paper examines which new techniques can be expected to help in attacking the open questions and which, in the opinion of the author, are the strengths and limitations of current approaches, such as data-driven science and causal inference.