Turbulence and Stochastic Processes: Kolmogorov's Ideas 50 Years on (Philosophical transactions of the Royal Society 1991)

It is 50 years since the publication of A.N. Kolmogorov's paper in 1941, probably the most famous paper ever written on turbulence. This volume commemorates this and other papers which established many of the key ideas of probability theory, stochastic processes and turbulence. These have since found application in many areas of research, including the theory of the turbulent motions of fluids, diffusion theory, the theory of automata, and communication theory. In putting together this volume the editors asked their colleagues to review, in the context of recent research, Kolmogorov's different contributions. And because his original papers are so important and not widely available, translations of two of his 1941 papers and one 1942 paper on turbulence have been included. Most of the fundamental problems in turbulence being investigated today were known to Kolmogorov, and he established lines of research which are still being followed and are attracting new methods of analysis. For example, Mandelbrot and Frisch here describe the recent ideas of multi-fractals and their use in understanding turbulence. Other contributions cover probability theory, small-scale turbulence, branching processes, fractal variables, general turbulent flows and turbulent combustion.