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A frequency-based dual-plane stereoscopic particle image velocimetry (DSPIV) technique is presented that permits fully-resolved simultaneous measurement of all nine components of the instantaneous velocity gradient tensor field ∇u(x,t) at the small scales of a turbulent flow. The technique is based on two essentially independent stereo PIV systems that provide three-component velocity measurements in two differentially-spaced light sheets of different colors, in this case 532 nm and 635 nm. Differentiation of the resulting velocity components within each plane and between the two planes yields all nine velocity gradient tensor ∂u i /∂x j . Spatial scales relevant to the flow and the spatial resolution achievable with such measurements are discussed. Control of the light sheet thickness, separation, and parallelism over the field-of-view of the PIV cameras are essential for the technique. Methods to accurately measure and quantify these issues are presented, along with results for the present DSPIV configuration. A calibration method, error analysis, and system performance study using synthetic PIV data characterizes the accuracy of the DSPIV technique. Preliminary results show encouraging velocity vector fields in the two differentiallyspaced data planes. The resulting velocity gradient field ∇u(x,t) provides all three components of the vorticity vector field ω(x,t) and all six components of the strain rate tensor field e(x,t). These in turn permit access to fields of central relevance to the turbulence dynamics, including the kinetic energy dissipation rate field 2ν e :e(x,t), the enstrophy field ω :ω(x,t), and the enstrophy production rate field ω · e·ω(x,t).

Highly-resolved three-dimensional velocity measurements via dual-plane stereo particle image velocimetry (DSPIV) in turbulent flows