Evolution of the velocity-gradient tensor in a spatially developing turbulent flow

An experimental study of turbulence generated by a low-blockage space-filling fractal square grid was performed using cinematographic stereoscopic particle image velocimetry in a water tunnel. All fluctuating velocity gradients were measured and their statistics were computed at three different stations along the streamwise direction downstream of the grid: in the production region, at the location of peak turbulence intensity and in the non-equilibrium decay region. The usual signatures of these statistics are only found in the decay region, where a well-defined $ #1{} #1{ {#1}} ≤ = ≤ = ≥ = ≥ = {Pr} {Fr} {Re}2/3$ power-law dependence of the second-order structure function on two-point distance is also present. However, this $2/3$ exponent is well defined over a wide range of scales even at the peak location, where the statistics of the fluctuating velocity-gradient tensor are very unusual. There, as at the production region station, the Q--R teardrop shape is not yet fully developed, vortex stretching only slightly dominates over compression and they both fluctuate very widely, reaching very high low-probability values. In these two stations, there is also only marginal preference between sheet-like and tube-like velocity-gradient structures as seen by the sign of the second eigenvalue of the strain-rate tensor. Yet, there are subregions of the flow in the production region where the $2/3$ exponent is present and where the Q--R teardrop shape is as undeveloped as for the entire data set at this station.