The probability density function (PDF) of the instantaneous streamwise velocity has consistently been used to extract information on the formation of uniform momentum zones (UMZs) in wall-bounded flows. Its temporal evolution has previously revealed patterns associated with the geometry and amplitude of the underlying velocity fluctuations [Laskari and McKeon, J. Fluid Mech. 913, A6 (2021)0022-112010.1017/jfm.2020.1163]. In this paper, we examine the robustness of these patterns in a variety of data sets including experiments and wall-bounded flow models. Experimental data sets spanning a range of Reynolds numbers, with very long temporal and spatial domains, suggest that the rate of the observed temporal variations scales in inner units. The use of a convection velocity, uniform across heights, to transform space into time has a marginal effect on these features. Similarly, negligible effects are observed between internal and external geometries. Synthetic databases generated following the resolvent framework and the attached eddy model are employed to draw comparisons to the experimental databases. Our findings highlight the distinctive strengths of each: The broadband frequency input of the attached eddy model allows for a better statistical description as opposed to a narrow frequency input in the resolvent data sets; instantaneously, however, representative eddies are seen to lack some structural details leading to the observed temporal behavior, which is better replicated by resolvent modes. Overall, given the considerable variety of the input data tested, the agreement between the data sets highlights the robustness of the spatiotemporal characteristics of the examined UMZs. It also underpins the need for their proper inclusion in UMZ modeling from a statistical as well as an instantaneous viewpoint; the current analysis accentuates important performance indicators for both.

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The probability density function (p.d.f.) of the streamwise velocity has been shown to indicate the presence of uniform momentum zones in wall-bounded turbulent flows. Most studies on the topic have focused on the instantaneous characteristics of this p.d.f. In this work, we show how the use of time-resolved particle image velocimetry data highlights robust features in the temporal behaviour of the p.d.f. and how these patterns are associated with the change of the number of zones present in the flow over time. The use of a limited resolvent model provides a clear link between this experimentally observed behaviour and the underlying velocity structures and their phase characteristics. This link is further supported by an extended resolvent model consisting of self-similar hierarchies centred in the logarithmic region, with triadically consistent members, yielding much more complex patterns in the p.d.f. Results indicate that the geometric similarity of these members instantaneously, as well as their relative evolution in time (dictated by their wall-normal varying wave speed), both inherent to the model, can reproduce many experimentally identified features.@en

Small spatial perturbations grow into fingers along the unstable interface of a fluid displacing a more viscous fluid in a porous medium or a Hele-Shaw cell. Mitigating this Saffman-Taylor instability increases the efficiency of fluid displacement applications (e.g., oil recovery), whereas amplifying these perturbations is desirable in, e.g., mixing applications. In this work, we investigate the Saffman-Taylor instability through analysis and experiments in which air injected with an oscillatory flow rate outwardly displaces silicone oil in a radial Hele-Shaw cell. A solution for linear instability growth that shows the competing effects of radial growth and surface tension, including wetting effects, is defined given an arbitrary reference condition. We use this solution to define a condition for stability relative to the constant flow rate case and make initial numerical predictions of instability growth by wave number for a variety of oscillations. These solutions are then modified by incorporating reference conditions from experimental data. The morphological evolution of the interface is tracked as the air bubble expands and displaces oil between the plates. Using the resulting images, we analyze and compare the linear growth of perturbations about the mean interfacial radius for constant injection rates with and without superimposed oscillations. Three distinct types of flow rate oscillations are found to modulate experimental linear growth over a constant phase-averaged rate of fluid displacement. In particular, instability growth at the interface is mildly mitigated by adding to the base flow rate provided by a peristaltic pump a second flow with low-frequency oscillations of small magnitude and, to a lesser extent, high-frequency oscillations of large amplitude. In both cases, the increased stability results from the selective suppression of the growth of large wave numbers in the linear regime. Contrarily, intermediate oscillations consistently destabilize the interface and significantly amplify the growth of the most unstable wave numbers of the constant flow rate case. Numerical predictions of low-frequency oscillations of opposite sign (initially decreasing) show promise of even greater mitigation of linear instability growth than that observed in this investigation. Looking forward, proper characterization of the unsteady, wetting, and nonlinear dynamics of instability growth will give further insight into the efficacy of oscillatory injection rates.

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Velocity structures associated with large streamwise density gradients in an incompressible turbulent boundary layer (with air as the working fluid, ) are analysed experimentally using planar image velocimetry and aero-optic measurements. The resulting flow topologies for the velocity fluctuations associated with large negative and positive density gradients are in excellent agreement with results for coolings and heatings in time, respectively (Antonia & Fulachier, J. Fluid Mech., vol. 198, 1989, pp. 429-451). The current results are complimentary to those from Saxton-Fox et al. (AIAA J., vol. 57 (7), 2019, pp. 2828-2839), on the signature of the vertical velocity structures associated with large density gradients. In the present work, these structures are shown to exhibit a sign change, consistent with the scalar gradient, and are localised in the wall-normal direction with an average height of approximately , almost constant for increasing distance from the wall. The corresponding small-scale streamwise fluctuations also exhibit a consistent sign change, which is found to originate, on average, from upstream leaning structures. The emerging picture for the velocity field is then that of a multiscale phenomenon, where small-scale structures, responsible for large optical aberrations, are superimposed on the back of large-scale bulge-like structures that are known to populate the outer layers. The proposed conceptual model is consistent with early ideas of 'typical' eddies (Falco, Phys. Fluids, vol. 20 (10), 1977, pp. S124-S132), the hairpin vortex model and associated shear layers (Adrian et al., J. Fluid Mech., vol. 422, 2000, pp.1-54), as well as with notions of multiscale velocity organisation in shear layers (Klewicki & Hirschi, Phys. Fluids, vol. 16 (11), 2004, pp. 4163-4176; Saxton-Fox et al. 2019), and it provides new insight into the geometry of the small-scale velocity structures.

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Planar particle image velocimetry (PIV) measurements were performed in a thermal boundary layer with simultaneous measurements of the streamwise density gradient, averaged across the boundary layer height. Previous work on the topic (Saxton-Fox et al., 2019) revealed that large density gradients were associated with tall wall-normal velocity structures extending across the entire boundary layer height. The authors suggested that these structures were a result of a wall-normal average of smaller scales, which reside at different locations from the wall, and contribute to the same density gradient change. Results from the present work support this model and show that, if a second condition on the vertical location of the identified features is imposed, one can extract wall-normal velocity structures that are localized in the vertical direction. Their average wall-normal extent is found to be around 0.1δ, with no significant variation across the boundary layer height. The corresponding conditionally averaged streamwise velocity fluctuations also show a change in sign from the wall up to edge of the boundary layer, consistent with the underlying density gradient condition. This sign change is found to originate on average from upstream leaning structures of opposite signs, while the inferred flow topology is shown to agree with earlier results on the topic (Antonia and Fulachier, 1989).

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