UNCERTAINTY IN CALCULATING VORTICITY FROM 2D VELOCITY-FIELDS USING CIRCULATION AND LEAST-SQUARES APPROACHES

The most common method for determining vorticity from planar velocity information is the circulation method. Its performance has been evalua ted using a plane of velocity data obtained from a direct numerical si mulation (DNS) of a three dimensional plane shear layer. Both the abil ity to reproduce the vorticity from the exact velocity field and one p erturbed by a 5% random ''uncertainty'' were assessed. To minimize the sensitivity to velocity uncertainties, a new method was developed usi ng a least-squares approach. The local velocity data is fit to a model velocity field consisting of uniform translation, rigid relation, a p oint source, and plane shear. The least-squares method was evaluated i n the same manner as the circulation method. The largest differences b etween the actual and calculated vorticity fields were due to the filt er-like nature of the methods. The new method is less sensitive to exp erimental uncertainty. However the circulation method proved to be sli ghtly better al reproducing the DNS field. The least-squares method pr ovides additional information beyond the circulation method results. U sing the correlation 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.