This paper presents an experimental technique for obtaining fully resolved measurements of the vector velocity field u(x,t) throughout a four-dimensional spatiotemporal region in a turbulent flow. The method uses fully resolved four-dimensional scalar field imaging measurements in turbulent flows [Phys. Fluids A 3, 1115 (1991)] to extract the underlying velocity field from the exact conserved scalar transport equation. A procedure for accomplishing this is described, and results from a series of test cases are presented. These involve synthetically generated scalar fields as well as actual measured turbulent flow scalar fields advected numerically by various imposed flow fields. The imposed velocity fields are exactly known, allowing a careful validation of the technique and its potential accuracy. Results obtained from a zeroth iteration of the technique are found to be very close to the exact underlying vector velocity field. Further results show that successive iterations bring the velocity field from the zeroth iteration even closer to the exact result. It is also shown that the comparatively dense velocity field information that this technique provides is well suited for accurate extraction of the more dynamically insightful strain rate and vorticity fields ∈(x,t) and ω(x,t).
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