Direct Numerical Simulations of Turbulence Subjected to a Straining and De-Straining Cycle

In many turbulent flows, significant interactions between fluctuations and mean velocity gradients occur in nonequilibrium conditions, i.e., the turbulence does not have sufficient time to adjust to changes in the velocity gradients applied by the large scales. The simplest flow that retains such physics is the time dependent homogeneous strain flow. A detailed experimental study of initially isotropic turbulence subjected to a straining and destraining cycle was reported by Chen et al. [“Scale interactions of turbulence subjected to a straining-relaxation-destraining cycle,” J. Fluid Mech. 562, 123 (2006)] . Direct numerical simulation (DNS) of the experiment of Chen et al. [“Scale interactions of turbulence subjected to a straining-relaxation-destraining cycle,” J. Fluid Mech. 562, 123 (2006)] is undertaken, applying the measured straining and destraining cycle in the DNS. By necessity, the Reynolds number in the DNS is lower. The DNS study provides a complement to the experimental one including time evolution of small-scale gradients and pressure terms that could not be measured in the experiments. The turbulence response is characterized in terms of velocity variances, and similarities and differences between the experimental data and the DNS results are discussed. Most of the differences can be attributed to the response of the largest eddies, which, even if are subjected to the same straining cycle, evolve under different conditions in the simulations and experiment. To explore this issue, the time evolution of different initial conditions parametrized in terms of the integral scale is analyzed in computational domains with different aspect ratios. This systematic analysis is necessary to minimize artifacts due to unphysical confinement effects of the flow. The evolution of turbulent kinetic energy production predicted by DNS, in agreement with experimental data, provides a significant backscatter of kinetic energy during the destraining phase. This behavior is explained in terms of Reynolds stress anisotropy and nonequilibrium conditions. From the DNS, a substantial persistency of anisotropy is observed up to small scales, i.e., at the level of velocity gradients. Due to the time dependent deformation, we find that the major contribution in the Reynolds stresses budget is provided by the production term and by the pressure/strain correlation, resulting in large time variation of velocity intensities. The DNS data are compared with predictions from the classical Launder–Reece–Rodi isoptropic production [ B. E. Launder et al., “Progress in the development of a Reynolds stress turbulence closure,” J. Fluid Mech. 68, 537 (1975) ] Reynolds stress model, showing good agreement with some differences for the redistribution term.