A measure of form difference and its application to the study of turbulent motions

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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
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