COMMENT ON COHERENT STRUCTURES IN FLUIDS, FRACTALS, AND THE FRACTAL STRUCTURE OF FLOW SINGULARITIES.

Abstract

The most widely known of all coherent structures of fluid flow are clouds that seem made up of billows upon billows. These are clearly not spheres. In fact, none of the standard geometric shapes can represent their surface without undue artificiality. A radically different geometry is required. It is based on the shapes called fractals. The fact that there is a relation between coherent structures and fractals deserves being featured even in this brief Comment, because some students of coherent structure dismiss fractals by extending to them their disillusionment with 'statistical methods. ' It is true that the most useful fractals are random, and that the nonrandom fractals are often specifically tailored to share some desirable features of the random ones. But it is not true that structures generated by chance can only be purely chaotic, like random points in the plane. Quite to the contrary, structures that everyone views as coherent happen to be spontaneously present in the typical fractal shapes.