Analogies, Misconceptions and Ill-Defined Concepts

The above statement by Batchelor is true of far more than just what is called “small-scale” features of turbulence. In other words, analogies in turbulence research have a special status mainly due to unsatisfactory state of not only theory but also of hard evidence on the small-scale features/properties of turbulent flows. Most of these analogies are aimed to look at similarity between genuine turbulence and some “analogous” system such as evolution of some passive object (e.g., scalar, vector, etc.), polymers, and some other (see below) in a prescribed random (usually Gaussian) velocity field. This led in many cases to exaggerated and consequently misleading claims on analogous behaviour between the two and consequently to misconceptions even for systems with the same generic features, such as the same symmetries, conservation laws, etc., which do not guarantee similar behaviour, Kraichnan (1974). Hence the purpose of this chapter is twofold. First, the main emphasis is given to differences rather than similarities. The primary reason for this is that (at least some) understanding of differences is expected to aid better understanding of both systems and avoid misconceptions associated with extending the analogies too far. Second, dealing with conceptual aspects of turbulence research leads necessarily to addressing misconceptions which have arisen during more than a century of turbulence research attempting to achieve some physical understanding/picture of this enigmatic phenomenon. Apart from the critical aspects, the main constructive outcome from addressing a variety of misconceptions is the hope to achieve a deeper understanding of the problems to be encountered and coped with. This is the main aim and emphasis of this chapter.