FRACTALS IN FLUID MECHANICS

The basic concepts of fractal geometry are relatively simple. Although they are not entirely new, the recognition that these simple notions form a unified language for a variety of disciplines in natural science is due to Mandelbrot.1 Our objective is to assess briefly the role of fractals and multifractal measures in fluid flows broadly, including turbulence and combustion. As applications have yet to mature, the report captures a snap-shot of the changing scene. We focus on activities that are common to both fluid dynamics and fractals and ignore some isolated aspects; we also omit comments on possible fractal structure obtained in chaotic mixing. Finally, we emphasize the question of how fractals enter physical problems, not the classical results. Much of the material to be covered below can be found in refererences cited in the bibliography2–7. Other references cited are not meant to be exhaustive.