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

Abstract

AbstractAn 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$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}2/3$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$Q\text {--}R$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$Q\text {--}R$teardrop shape is as undeveloped as for the entire data set at this station.