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A total of 11 grids in four families, including single- and multi-scale grids, are tested to investigate the development and decay characteristics of grid-generated turbulence. Special attention has been focused on dissipation and non-equilibrium characteristics in the decay region. A wide non-equilibrium region is observed for fractal square grids with three and four iterations. The distributions of the Taylor microscale λ, integral length scale Lu, and dissipation coefficient Cε show that a simple combination of large and small grids does not reproduce elongated non-equilibrium regions as realized by the fractal square grid. On the other hand, a new kind of grid, quasi-fractal grids, in which the region of the smaller fractal elements (N=2–4) of the fractal square grid is replaced by regular grids, successfully reproduce a similar flow field and non-equilibrium nature to that seen in the fractal square grid case. This suggests that the combination of large square grid and inhomogeneously arranged smaller grids produces an elongated non-equilibrium region. The dissipation coefficient Cε is better collapsed using Re0=t0U∞/ν (where t0 is the thickness of the largest grid bar, U∞ the inflow velocity, and ν the kinematic viscosity) as a global/inlet Reynolds number rather than ReM=MU∞/ν (where M is the mesh size) [P. C. Valente and J. C. Vassilicos, “Universal dissipation scaling for non-equilibrium turbulence,” Phys. Rev. Lett. 108, 214503 (2012)].

The geometry of turbulent/non-turbulent interfaces (TNTIs) arising from flows with and without mean shear is investigated using direct numerical simulations of turbulent planar jets (PJET) and shear free turbulence (SFT), respectively, with Taylor Reynolds number of about Reλ≈100. In both flows, the TNTI is preferentially aligned with the tangent to the TNTI displaying convex, where the turbulent fluid nearby tends to have a stronger enstrophy, more frequently than concave shapes. The different flow configurations are reflected in different orientations of the TNTI with respect to the flow direction (and its normal). While the interface orientation with respect to the mean flow direction in PJET has an influence on the velocity field near the TNTI and the enstrophy production in the turbulent sublayer, there is no particular discernible dependence on the interface orientation in SFT. Finally, the intense vorticity structures or “worms,” which are possibly associated with “nibbling” entrainment mechanism, “feel” the local geometry of the TNTI, and it is shown that in PJET, a smaller local radius of these structures arises in regions near the TNTI where the local TNTI faces the mean flow direction.

Response time of the post-shock wave (SW) overpressure modulation by turbulence is investigated in wind tunnel experiments. A peak-overpressure fluctuation, observed on a wall, is induced by turbulence around the SW ray, but away from the wall, demonstrating finite response time of the modulation. We propose a model of the modulation based on the SW deformation by a local flow disturbance, which yields the response time being proportional to the product of the large-eddy turnover time and (MT/MS0)0.5 (MT: turbulent Mach number and MS0: shock Mach number), in consistent with the experiments.

Implicit large eddy simulation (ILES) of passive scalar transfer in compressible turbulence is evaluated for subsonic and supersonic turbulent planar jets. The ILES used in this study relies on fully explicit numerical schemes for spatial and temporal discretization and low‐pass and shock‐capturing filters used as an implicit subgrid‐scale (SGS) model. The ILES results are compared with the direct numerical simulation (DNS) database of the same flows. The ILES results exhibit good agreements with the DNS for first‐ and second‐order statistics of velocity and passive scalar. The scalar transport by turbulent velocity fluctuations is well captured by the ILES. The temporal evolution of the jet strongly depends on the jet Mach number, where a higher Mach number results in the delay of jet development. The Mach number dependence of velocity and passive scalar fields is consistent between the ILES and DNS. The low‐pass filters used as the implicit SGS model contribute to the dissipation of turbulent kinetic energy and scalar variance. Under the present numerical conditions, the filters account for about 50% of the dissipation in a fully developed turbulent jet. The dissipation rate in the ILES, which is the sum of the grid‐scale and SGS dissipation rates, is very close to the dissipation rate in the DNS, and the amount of the SGS dissipation is well controlled by the low‐pass filters. The filters also dump numerical oscillations in the velocity field caused by strong pressure waves outside the supersonic jet at the high Mach number.

Multi-particle dispersion is studied using direct numerical simulations of temporally evolving mixing layers and planar jets for tetrahedra consisting of four fluid particles which are seeded in the turbulent regions or in the non-turbulent regions near the turbulent/non-turbulent interface (TNTI). The modified Richardson law for decaying turbulence is observed for particle pairs. The size dependence of the mean and relative motions of the entrained tetrahedra indicates that the characteristic length scale of the entrained lumps of fluid is approximately 10 times the Kolmogorov microscale. When the tetrahedra move within the TNTI layer they are flattened and elongated by vortex stretching at a deformation rate that is characterized by the Kolmogorov time scale. The shape evolutions of the tetrahedra show that in free-shear flows, thin-slab structures of advected scalars are generated within the TNTI layers.

Direct numerical simulations for compressible temporally evolving turbulent boundary layers (TBLs) at Mach numbers of M = 0.8 and 1.6 are preformed up to the Reynolds number based on the momentum thickness Reθ ≈ 2200 to investigate a passive scalar field near the turbulent/non-turbulent interface (TNTI) layer that is formed at the edge of the TBLs. The passive scalar is diffused from the wall in the TBLs developing on the moving wall at constant speed. The outer edge of the TNTI layer detected by an isosurface of vorticity magnitude and passive scalar are compared by visualization, and it is shown that the passive scalar can be used for detecting the TNTI layer in compressible boundary layers. Conditional statistics are calculated as a function of the distance from the outer edge of the TNTI layer. The mean thicknesses of the TNTI layer, viscous superlayer (VSL), and turbulent sublayer (TSL), is about 15ηI, 4ηI, and 11ηI, respectively (ηI: Kolmogorov length scale in the turbulent core region near the TNTI layer). The conditional mean profiles of scalar dissipation rate have a large peak near the boundary between the VSL and TSL, where the fluid with a low scalar value locally entrained from non-turbulent region encounters the turbulent fluid with a higher scalar value. The scalar dissipation rate near the TNTI depends on the TNTI orientation: it is larger near the TNTI facing the downstream direction with respective to the mean flow in the boundary layer (leading edge). This is partially explained by the dependence of the production rate of passive scalar gradient. The conditional mean production rate of the scalar dissipation rate near the leading edge is as large as in the turbulent core region while it is close to the non-turbulent value when the TNTI faces the upstream region (trailing edge).

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