Uncertainty in calculating vorticity from 2D velocity fields using circulation and least-squares approaches

Abstract

The most common method for determining vorticity from planar velocity information is the circulation method. Its performance has been evaluated using a plane of velocity data obtained from a direct numerical simulation (DNS) of a three dimensional plane shear layer. Both the ability to reproduce the vorticity from the exact velocity field and one perturbed by a 5% random “uncertainty” were assessed. To minimize the sensitivity to velocity uncertainties, a new method was developed using a least-squares approach. The local velocity data is fit to a model velocity field consisting of uniform translation, rigid rotation, a point source, and plane shear. The least-squares method was evaluated in the same manner as the circulation method. The largest differences between the actual and calculated vorticity fields were due to the filter-like nature of the methods. The new method is less sensitive to experimental uncertainty. However the circulation method proved to be slightly better at reproducing the DNS field.

The least-squares method provides additional information beyond the circulation method results. Using the correlation $\overline {P\omega \omega }$ and a vorticity threshold criteria to identify regions of rigid rotation (or eddies), the rigid rotation component of the least-squares method indicates these same regions.