Measuring the Quantitative Characteristics of Local Vortices on a Plane of a Deformed Material

Abstract

A problem for determining the center, size, and spatial distribution of displacements of a vortex on the basis of a plane vector field is under consideration. A seed algorithm is proposed instead of typical contour scanning, and specific circulation is used as a criterion for determining the center of a vortex flow. In order to increase the stability of this algorithm, a parameter playing the role of a threshold is introduced. A Monte-Carlo method is used to study the influence of measurement errors on the accuracy in determining the coordinates of a hard rotation center, and the relationship between the false alarm probability and the threshold level is established. The use of the least squares method for calculating the spatial distribution of displacements is shown. This approach is demonstrated on the example of a real vector field measured in the vicinity of a main crack tip.