Scalar imaging velocimetry measurements of the velocity gradient tensor field in turbulent flows. II. Experimental results

Abstract

Scalar imaging velocimetry is here applied to experimental turbulent flow scalar field data to yield the first fully resolved, non‐intrusive laboratory measurements of the spatio‐temporal structure and dynamics of the full nine‐component velocity gradient tensor field ∇u(x,t), as well as the pressure gradient field ∇p(x,t), in a turbulent flow. Results are from turbulent flows at outer scale Reynolds numbers in the range 3,000≤Reδ≤4,200, with Taylor scale Reynolds numbers Reλ≊45. These give a previously inaccessible level of detailed experimental access to the spatial structure in the velocity gradient tensor field at the small scales of turbulent flows, and through the much longer temporal dimension of these four‐dimensional data spaces allow access to the inertial range of scales as well. Sample spatio‐temporal data planes and probability distributions spanning more than 75 advection time scales (λν/U) are presented for various dynamical fields of interest, including the three components of the velocity field u(x,t), the nine components of the velocity gradient tensor field ∇u(x,t) through the full vector vorticity field ωi(x,t) and tensor strain rate field εij(x,t), the kinetic energy dissipation rate field Φ(x,t)≡2νε:ε(x,t), the enstrophy field 1/2ω⋅ω(x,t), the enstrophy production rate field ω⋅ε⋅ω(x,t), and the pressure gradient field ∇p(x,t). Continuity tests show agreement with the zero divergence requirement that exceeds the highest values reported from single‐point, invasive, multi‐probe measurements. Distributions of strain rate eigenvalues as well as alignments of the strain rate eigenvectors with both the vorticity and scalar gradient vectors are in agreement with DNS results, as are distributions of the measured helicity density fields u⋅ω(x,t). Results obtained for the true kinetic energy dissipation rate field show good agreement, up to 14th‐order, with previous inertial range structure function exponents measured by Anselmet et al. [J. Fluid Mech. 140, 63 (1984)] at much higher Reynolds numbers. In addition, probability distributions scaled on inner variables show good agreement among buoyant and non‐buoyant turbulent flow cases, further suggesting that these results are largely indicative of the high Reynolds number state of the inner scales of fully developed turbulent flows. © 1996 American Institute of Physics.