We investigate experimentally wind tunnel turbulence generated by multiscale/fractal grids pertaining to the same class of low-blockage space-filling fractal square grids. These grids are not active and nevertheless produce very much higher turbulence intensities u ′ /U and Reynolds numbers Re λ than higher blockage regular grids. Our hot wire anemometry confirms the existence of a protracted production region where turbulence intensity grows followed by a decay region where it decreases, as first reported by Hurst & Vassilicos [15]. We introduce the wake-interaction length-scale x * and show that the peak of turbulence intensity demarcating these two regions along the centreline is positioned at about 0.5x * . The streamwise evolutions on the centreline of the streamwise mean flow and of various statistics of the streamwise fluctuating velocity all scale with x * . Mean flow and turbulence intensity profiles are inhomogeneous at streamwise distances from the fractal grid smaller than 0.5x * , but appear quite homogeneous beyond 0.5x * . The velocity fluctuations are highly non-gaussian in the production region but approximately gaussian in the decay region. Our results confirm the finding of Seoud & Vassilicos [31] that the ratio of the integral length-scale L u to the Taylor microscale λ remains constant even though the Reynolds number Re λ decreases during turbulence decay in the region beyond 0.5x * . As a result the scaling L u /λ ∼ Re λ which follows from the u ′3 /L u scaling of the dissipation rate in boundary-free shear flows and in usual grid-generated turbulence does not hold here. This extraordinary decoupling is consistent with a non-cascading and instead self-preserving single-length scale type of decaying homogeneous turbulence proposed by George & Wang [12], but we also show that L u /λ is nevertheless an increasing function of the inlet Reynolds number Re 0 . Finally, we offer a detailed comparison of the main assumption and consequences of the George & Wang theory against our fractal-generated turbulence data.

The dimensionless dissipation rate constant Cϵ of homogeneous isotropic turbulence is such that Cϵ=f(logReλ)Cs′3, where f(logReλ) is a dimensionless function of logReλ which tends to 0.26 (by extrapolation) in the limit where logReλ⪢1 (as opposed to just Reλ⪢1) if the assumption is made that a finite such limit exists. The dimensionless number Cs′ reflects the number of large-scale eddies and is therefore nonuniversal. The nonuniversal asymptotic values of Cϵ stem, therefore, from its universal dependence on Cs′. The Reynolds number dependence of Cϵ at values of logReλ close to and not much larger than 1 is primarily governed by the slow growth (with Reynolds number) of the range of viscous scales of the turbulence. An eventual Reynolds number independence of Cϵ can be achieved, in principle, by an eventual balance between this slow growth and the increasing non-Gaussianity of the small scales. The turbulence is characterized by five length-scales in the following order of increasing magnitude: the Kolmogorov microscale η, the inner cutoff scale η*≈η(7.8+9.1logReλ), the Taylor microscale λ∼Reλ1∕2η, the voids length scale λv∼Reλ1∕3λ, and the integral length scale L∼Reλ2∕3λv.

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We report an experimental investigation of the separating/reattaching flow over a descending ramp with a $25^{\circ }$ expansion angle. Emphasis is given to mass entrainment through the boundaries of the separated shear layer emanating from the upper edge of the ramp. For this purpose, the turbulent/non-turbulent interface and the separation line inferred from image-based analysis are used respectively to mark the upper and lower bounds of the separated shear layer. The main objective of this study is to identify the physical parameters that scale the development of the separated shear layer, by giving a specific emphasis to the investigation of mass entrainment. Our results emphasise the multiscale nature of mass entrainment through the separated shear layer. The recirculation length $L_{R}$, step height $h$ and free-stream velocity $U_{\infty }$ are the dominant scales that organise the separated flow (and related large-scale quantities as pressure distribution or shear layer growth rate) and set mean mass fluxes. However, local viscous mechanisms seem to be responsible for most of local mass entrainment. Furthermore, it is shown that large-scale mass entrainment is driven by incoming boundary layer properties, since $L_{R}$ scales with $Re_{\unicode[STIX]{x1D703}}$, and in particular by its turbulent state. Surprisingly, the relationships evidenced in this study suggest that these dependencies are established over a large distance upstream of separation and that they might also extend to small scales, at which viscous entrainment is dominant. If confirmed by additional studies, our findings would open new perspectives for designing effective separation control systems.

We experimentally perform open and closed-loop control of a separating turbulent boundary layer downstream from a sharp edge ramp. The turbulent boundary layer just above the separation point has a Reynolds number Re θ ≈ 3 500 based on momentum thickness. The goal of the control is to mitigate separation and early re-attachment. The forcing employs a spanwise array of active vortex generators. The flow state is monitored with skin-friction sensors downstream of the actuators. The feedback control law is obtained using model-free genetic programming control (GPC) (Gautier et al. 2015). The resulting flow is assessed using the momentum coefficient, pressure distribution and skin friction over the ramp and stereo PIV. The PIV yields vector field statistics, * antoine.debien@onera.fr † Kai.von.Krbek@krbek.de e.g. shear layer growth, the back-flow area and vortex region. GPC is benchmarked against the best periodic forcing. While open-loop control achieves separation reduction by locking-on the shedding mode, GPC gives rise to similar benefits by accelerating the shear layer growth. Moreover, GPC uses less actuation energy.

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This study focuses on the geometrical properties of turbulent flame fronts and other interfaces. Toward that end, we use an original tool based on proper orthogonal decomposition (POD), which is applied to the interface spatial coordinates. The focus is mainly on the degree of roughness of the flame front, which is quantified through the scale dependence of its coverage arclength. POD is first validated by comparing with the caliper technique. Fractal characteristics are extracted in an unambiguous fashion using a parametric expression which appears to be impressively well suited for representing Richardson plots. Then it is shown that, for the range of Reynolds numbers investigated here, the scale-by-scale contribution to the arclength does not comply with scale similarity, irrespectively of the type of similarity which is invoked. The finite ratios between large and small scales, referred to as finite Reynolds number effects, are likely to explain this observation. In this context, the Reynolds number that ought to be achieved for a proper inertial range to be discernible, and for scale similarity to be likely to apply, is calculated. Fractal characteristics of flame folding are compared to available predictions. It is confirmed that the inner cutoff satisfactorily correlates with the Kolmogorov scale while the outer cutoff appears to be proportional to the integral length scale. However, the scaling for the fractal dimension is much less obvious. It is argued that much higher Reynolds numbers have to be reached for drawing firm statements about the evolution (or constancy) of the fractal dimension with respect to flame and flow parameters. Finally, a heuristic phenomenology of corrugated interfaces is highlighted. The degree of generality of the latter phenomenology is confirmed by comparing the folding of different interfaces including a turbulent-nonturbulent interface, a liquid jet destabilized by a surrounding air jet, a cavitating flow, and an isoscalar evolving in a turbulent medium. The latter outcome is likely to have strong implications for modeling the corrugation of turbulent interfaces occurring in many physical situations.

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