Strange Attractors, Coherent Structures and Statistical Approaches

Abstract

All turbulent flows contain both order and disorder. The relative proportions depend on Reynolds number, geometry (type) and boundary and initial conditions. For example, axisymmetric jets appear to have much less well-defined structures than most other flows under the same circumstances. An axisymmetric jet at high Reynolds number, arising from disturbed initial conditions, has ordered structures that are almost imperceptable to the unaided eye, and must be extracted using statistical techniques. On the other hand, mixing layers appear to have a higher proportion of ordered structures than other flows under the same circumstances. A mixing layer at relatively low Reynolds number arising from undisturbed initial conditions has such strong order that it is almost difficult to find the disorder. Most flows are somewhere in between, depending on the circumstances of their formation. No turbulent flow is completely without disorder, nor is there any completely without structure.