The properties of the wake generated by a porous body fully immersed in a turbulent boundary layer are experimentally assessed. The body consists of an array of cylinders, with diameter $d$, covering a circular patch of diameter $D$. For fixed $d$ and $D$, by increasing the number of cylinders, $N_{c}$, within the patch, the wake properties are systematically tested under different levels of density ($\unicode[STIX]{x1D719}$ $=$ covered planar area per total surface) and compared to the flow past a solid body of equivalent diameter and height ($H$). Some insights on the complex flow developing in the wake are captured: $\unicode[STIX]{x1D719}$ varying in the range 2 %–24 % results in the flow meandering among the cylinders and bleeding from the top, the sides and the trailing edge of the patch. The interplay between trailing edge and top bleeding prevents wake entrainment, locking the wake longitudinal extent to 5–7 patch diameters, regardless of the density level. Due to the finite body vertical extent, a third shear layer develops from the top of the patch. The interaction between the top shear layer and the lateral ones leads to a mutual alteration, namely a nonlinear growth not captured by the classical mixing layer theory. Nevertheless, on the horizontal plane at the patch mid-height, the mean flow recovers, exhibiting a self-similar decay. Surprisingly, the recovery is well described by the classical planar wake theory and the characteristic scales, namely the maximum velocity deficit and the wake half-width, evolve linearly as proposed by Wygnanski et al. (J. Fluid Mech., vol. 168, 1986, pp. 31–71).

The Lagrangian approach is natural for studying issues of turbulent dispersion and mixing. We propose in this work a general Lagrangian stochastic model for inhomogeneous turbulent flows, using velocity and acceleration as dynamical variables. The model takes the form of a diffusion process, and the coefficients of the model are determined via Kolmogorov theory and the requirement of consistency with velocity-based models. We show that this model generalises both the acceleration-based models for homogeneous flows as well as velocity-based generalised Langevin models. The resulting closed model is applied to a channel flow at high Reynolds number, and compared to experiments as well as direct numerical simulations. A hybrid approach coupling the stochastic model with a Reynolds-averaged Navier–Stokes model is used to obtain a self-consistent model, as is commonly used in probability density function methods. Results highlight that most of the acceleration features are well represented, notably the anisotropy between streamwise and wall-normal components and the strong intermittency. These results are valuable, since the model improves on velocity-based models for boundary layers while remaining relatively simple. Our model also sheds some light on the statistical mechanisms at play in the near-wall region.

We present a combined experimental and theoretical investigation of the dynamics of water imbibition through paper with swelling. The Washburn equation has been widely used to describe the dynamics of the liquid absorption in paper, but its prediction of liquid imbibition speed has been reported to be inaccurate. Our recent study (Chang et al., J. Fluid Mech., vol. 845, 2018, pp. 36–50) demonstrated that the internal cavity of cellulose fibres composing the paper is partially responsible for the limited accuracy of the Washburn equation based on oil imbibition experiments. Here we extend the investigation to water absorption through paper with swelling. We demonstrate that the swelling of the cellulose fibre network in addition to the internal voids of the cellulose fibres crucially affects the imbibition dynamics. Based on the microscopic observation that paper swelling is caused by the expansion of inter-fibre space, we suggest a mathematical model for water imbibition which considers both intra-fibre voids and swelling. By introducing parameters that characterize the swelling speed and volume of paper, our model markedly improves prediction of the water imbibition speed. The results provide not only a theoretical background for designing paper-based microfluidic systems, but also new insights into capillary flow through expandable porous media.

The effects of large-scale motion (LSM) on the spatio-temporal dynamics of separated shear layers induced by a forward-facing step submerged in a thick turbulent boundary layer (TBL) are investigated using a time-resolved particle image velocimetry. The Reynolds number based on the free-stream velocity and step height was 13 200. The oncoming TBL was developed over a cube-roughened surface and the thickness was 6.5 times the step height. The step height was chosen to coincide with the elevation where the dominant frequency of streamwise fluctuating velocity in the TBL occurred. At this elevation, the local turbulence intensity was 14.5 %. Distinct regions of elevated Reynolds stresses were observed upstream and downstream of the leading edge of the step. The unsteady dynamics of the separation bubbles upstream and downstream of the step was investigated using the reverse flow area. Both separation bubbles exhibit low-frequency flapping motion, and the dominant frequency of the downstream separation bubble is identical to the dominant frequency of the streamwise fluctuating velocity in the oncoming TBL at the step height. As the low-velocity region of LSM passes over the step, the downstream separation bubble is enlarged and subsequently undergoes a high-frequency oscillation. Turbulence motions were partitioned into low-, medium- and high-frequency regimes based on spectral analysis of the Reynolds stresses. The contributions from these partitioned turbulence motions are used to elucidate the effects of LSM on the elevated Reynolds stresses in the shear layers upstream and downstream of the step.

We examine experimentally the influence of non-Darcy effects on convective dissolution in Hele-Shaw cells. We focus on buoyancy-driven convection, where the flow is controlled by the Rayleigh–Darcy number, $Ra$, which measures the strength of convection compared to diffusion. The Hele-Shaw cell is suitable to mimic Darcy flows only under certain geometrical constraints, and a recent theoretical work (Letelier et al., J. Fluid Mech., vol. 864, 2019, pp. 746–767) demonstrated that a precise limit exists for the parameter $\unicode[STIX]{x1D716}^{2}Ra$ – $\unicode[STIX]{x1D716}\sim$ thickness-to-height ratio – beyond which the flow exhibits non-Darcy effects. In this work, we run experiments for solute convection in Rayleigh–Bénard-like configuration. We examine a wide range of the parameters space $(Ra,\unicode[STIX]{x1D716})$ and we clearly identify the application limits of Darcy flow assumptions. Besides confirming previous theoretical predictions, current results are of relevance in the context of porous media flows – which are often studied experimentally with Hele-Shaw set-ups. Using our original datasets, we have been able to explain and reconcile the discrepancies observed between scaling laws previously proposed for Rayleigh–Bénard-like experiments and simulations in similar contexts. Specifically, we attribute an important role to the parameter $\unicode[STIX]{x1D716}^{2}Ra$, which clearly establishes thresholds beyond which Hele-Shaw experiment results are influenced by three-dimensional effects.