Four-dimensional measurements of vector fields in turbulent flows

Experimental methods and results are presented for fully-resolved, three- and four-dimensional, spatio-temporal measurements of scalar gradient vector fields ∇ζ (x.1) and velocity vector fields U(X,I) in turbulent flows. Each three-dimensional spatial data volume is composed of up to 2563 spatial data points, with volumes acquired sequentially in time. The four-dimensional data sets are each comprised of over 3 billion individunl point measurements, and are simultaneously differentiable in x, y, z, and 1, allowing access to thc spatial structure and temporal dynamics in these fields. Space and time scales relevant to such nieasurenients are summarized. A method for assessing the resolution achieved by such measurements is presented, and as are criteria for over-resolution in digital measurernents. Results give the space- and time-varying conserved scalar field and vector velocity field simultaneously on a regular three-dimensional spatial grid. Direct differentiation of these fields yields the spatial structure in the full nine-component velocity gradient tensor field ∇u(x,l). From these, the vector vorticity field ωi(x,t) and tensor strain rate field εij(x.t)are extracted, as are the kinetic energy dissipation rate field 2v ε: ε (x,t), the enstrophy field, the enstrohy production rate field ½.ω.ω(x,t)and the pressure gradient field ∇p.(x,t). Extension of the scalar imaging velocinietry technique to whole-field measurements are described, and various limitingcases is described, which yields velocity vector fields that are filtered in space and time at the resolution scale A. Such whole-field SIV measurementsallow use of the full spatial and temporal dynamic range available to the measurements, and permits measurements in turbulent flows at arbitrarily high Reynolds numbers.