Scalar imaging velocimetry measurements of the velocity gradient tensor field in turbulent flows. I. Assessment of errors

The consept of flow field velocimetry based on scalar imaging measurements [Phys. Fluids A 4, 2191 (1992)] is here formulated in terms of an integral minimization implementation, where the velocity field u(x,t) is found by minimizing weighted residuals of the conserved scalar transport equation, along with the continuity condition and a smoothness condition. We apply this technique to direct numerical simulation (DNS) data for the limiting case of turbulent mixing of a Sc= 1 passive scalar field. The spatial velocity fields u(x,t) thus obtained demonstrate good correlation with the exact DNS fields, as do the statistics of the velocity and the velocity gradient fields. The results from this integral minimization implementation also show significant improvement over those from the direct inversion technique reported earlier. These results are shown to be largely insensitive to noise at levels characteristic of current fully resolved scalar field measurements.