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 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 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.The authors thank Dr. Michael Rogers of NASA Ames Research Center for supplying the DNS fields. In addition, Professor Ellen Longmire at the University of Minnesota asked how else might one calculate vorticity other than the circulation method and prompted this investigation.