I am honoured to present the Opening Lecture at this Symposium on the Geometry and Statistics of Turbulence. I vividly recall a previous IUTAM Symposium in Tokyo in 1983 on the subject Turbulence and Chaotic Phenomena in Fluids; at that Symposium, I contributed a lecture with the title "Simple topological aspects of turbulent vorticity dynamics". During the last two decades, increasing attention has been paid to characteristic structures detected in both experimental work and in direct numerical simulation (DNS); indeed, it is these developments that have provided the main motivation for the present Symposium, and that will be described in many of the lectures on the programme. In this introductory lecture, it may be appropriate to resume the theme of my 1983 lecture, but at a more basic level: I propose to consider the generic structure of scalar fields in both 2D and 3D turbulence, the topological description of these fields, and the manner in which the topology may change with time. I shall also seek to describe how, at the simplest level, the geometry of these fields may be related to the most basic statistical property - the field spectrum.
展开▼
