A measure of form difference and its application to the study of turbulent motions
Article
English
OPEN
Groen, P.
(2011)
The aim of the present paper is twofold, viz., on one hand, to introduce a measure of form difference between two configurations of a given number of points as a tool for studying the effect of turbulent motions upon the deformation and spreading of point clusters, and, on the other hand, to derive a statistical relationship between the deformations of triangles of a given size, formed by triads of points in a field of random motions, and the properties of that field (eddy diffusivity as a function of size). As a geometrical by-product, a systemetics of triangle forms is found, which represents the set of all possible triangle forms by means of the points of a sphere. In this representation the form difference, as defined in this paper, appears to be equivalent with the angular distance on the sphere between the points representing the forms of the triangles.DOI: 10.1111/j.2153-3490.1965.tb00197.x