Most frequent particle paths in a plane

Abstract

A model of plane continuous random motions is developed. The most frequent paths among these orbits are evaluated. A simple arrangement of them is discussed. The loci of points which have moved the same arc length from an original straight line seem to describe the dissipation of a vertical smoke column or the currents at the influx of a river into a lake. This success suggests that the most frequent particle paths are new elementary units from which various types of turbulent motions might be built up,