The present study offers a twofold contribution on counter-gradient transport (CGT) of turbulent scalar flux. First, by examining turbulent scalar mixing through synchronized particle image velocimetry and planar laser-induced fluorescence on an inclined jet in cross-flow, we clarify the previously unexplained phenomenon of CGT, revealing key flow structures, their spatial distribution and modelling implications. Statistical analysis identifies two distinct CGT regions: local cross-gradient transport in the windward shear layer and non-local effects near the wall after injection. These behaviours are driven by specific flow structures, namely Kelvin–Helmholtz vortices (local) and wake vortices (non-local), suggesting that scalar flux can be decomposed into a gradient-type term for gradient diffusion and a term for large-eddy stirring. Second, we propose a new approach for reconstruction of turbulent mean flow and scalar fields using continuous adjoint data assimilation (DA). By rectifying model-form errors through anisotropic correction under observational constraints, our DA model minimizes discrepancies between experimental measurements and numerical predictions. As expected, the introduced forcing term effectively identifies regions where traditional models fall short, particularly in the jet centreline and near-wall regions, thereby enhancing the accuracy of the mean scalar field. These enhancements occur not only within the observation region but also in unseen regions, underscoring present DA approach's reliability and practicality for reproducing mean flow behaviours from limited data. These findings lay a solid foundation for adjoint-based model-consistent data-driven methods, offering promising potential for accurately predicting complex flow scenarios like film cooling.

This paper demonstrates experimentally that imposed periodic forcing can significantly alter the global flow characteristics of the flow over a double backward-facing step. The geometry consists of two equal height steps spaced up to eight step heights apart. A periodic zero-mass flux jet located at the first step's top corner was issued at frequencies ranging from below the step-mode instability frequency up to approximately five times the shear-layer instability frequency. Reattachment of the flow onto the first step was achieved for step separations as low as three single-step heights with imposed forcing; significantly shorter than the five single-step heights that occurred without forcing. A significant reduction in mean base pressure on the first step, and increase on the second step, occurred for low forcing frequencies. Even for large step separations, the effect of forcing on the flow persisted sufficiently far downstream to appreciably influence the development of the second recirculation zone. Importantly, previous forced single and unforced double backward-facing step flows provide reference cases to examine and discuss similarities and differences. This study offers insight into possibilities and potential outcomes of flow control for applications ranging from the drag reduction of ground vehicles such as pickup trucks, to enhanced mixing in industrial processes.

The dynamics of the interaction of a system of two thin volatile liquid droplets resting on a soft viscoelastic solid substrate are investigated theoretically. The developed model fully considers the effect of evaporative cooling and the generated Marangoni stresses due to the induced thermal gradients, while also accounting for the effect of the gas phase composition and the diffusion of vapour in the atmosphere of the droplets. Using the framework of lubrication theory, we derive evolution equations for both the droplet profile and the displacement of the elastic solid, which are solved in combination with Laplace's equation for the vapour concentration in the gas phase. A disjoining-pressure/precursor-film approach is used to describe contact-line motion. The evolution equations are solved numerically, using the finite-element method, and we present a thorough parametric analysis to investigate the physical properties and mechanisms that affect the dynamics of droplet interactions. The results show that the droplets interact through both the soft substrate and the gas phase. In the absence of thermocapillary phenomena, the combined effect of non-uniform evaporation due to the increased vapour concentration between the two droplets and elastocapillary phenomena determines whether the drop–drop interaction is attractive or repulsive. The Marangoni stresses suppress droplet attraction at the early stages of the drying process and lead to longer droplet lifetimes. For substrates with intermediate stiffness, the emergence of spontaneous symmetry breaking at late stages of evaporation is found. The rich dynamics of this complex system is explored by constructing a detailed map of the dynamic regimes.

Simulating complex gas flows from turbulent to rarefied regimes is a long-standing challenge, since turbulence and rarefied flow represent contrasting extremes of computational aerodynamics. We propose a multiscale method to bridge this gap. Our method builds upon the general synthetic iterative scheme for the mesoscopic Boltzmann equation, and integrates the $k$–$\omega$ model in the macroscopic synthetic equation to address turbulent effects. Asymptotic analysis and numerical simulations show that the macroscopic–mesoscopic coupling adaptively selects the turbulence model and the laminar Boltzmann equation. The multiscale method is then applied to opposing jet problems in hypersonic flight surrounding by rarefied gas flows, showing that the turbulence could cause significant effects on the surface heat flux, which cannot be captured by the turbulent model nor the laminar Boltzmann solution alone. This study provides a viable framework for advancing understanding of the interaction between turbulent and rarefied gas flows.

We report experimental and theoretical results on how a fluid (homogeneous or continuously stratified) is spun up in a closed, semicircular cylinder. Experiments were performed for Rossby numbers $Ro=0.02$, 0.2 and 1 (the latter corresponding to the limiting case of spin-up from rest), with the Ekman number $E=O({10^{-5}})$, and the Burger number ($S$) varied between 0 and 10. There are two key processes: Ekman pumping that drives the core flow; and the formation and breakdown of the vertical-wall boundary layers, with respective characteristic time scales $t\sim E^{-1/2}$ and $Ro^{-1}$. When these time scales are comparable, the observed flow is dominated by the gradual spin-up of the initial anticyclone that forms when the rotation rate is increased, which fills the container's interior; vorticity generated adjacent to the vertical walls throughout remains confined to the neighbourhood of the container's walls and corners. Conversely, when ${E^{1/2}/Ro\ll 1}$, the vertical-wall boundary layers rapidly break down, resulting in the formation of cyclonic vortices in the container's vertical corners, which grow and interact with the initial anticyclone, leading to the formation of a three-cell flow pattern. For $Ro=0.02$, our theoretical description of the flow generally agrees well with experiments, and the computation of the eruption times for the unsteady boundary layers is consistent with the observations for both $Ro=0.02$ and $Ro=0.2$.

The hydrodynamic cavitation in semidilute solution flows of a flexible polymer additive in water was experimentally explored in a mesoscale converging–diverging nozzle to elucidate the cavitation reduction effects of polymer additives. Rheological measurements demonstrated that polymer solutions were shear-thinning, with infinite viscosities larger than pure water. The polymer additives significantly mitigated the intensity of cloud cavitation and the growth of violent cavity structures in the tested solution concentrations. Under conditions of supercavitation, the tested polymer solutions could not suppress the growth of large structures but showed a reduction in the population of cavitation bubbles. The temporal evolution and spatial variation of cavitation structures in different concentrations were captured using high-speed imaging. Statistical analysis of the images showed that polymers reduce cavitation via three main mechanisms. (1) The longitudinal expansion of cavities downstream is attenuated relative to the pure water. The streamwise distribution of vapour-ratio fluctuations was flattened, and its peak was shifted upstream in the solutions. (2) Mean collapse and growth rate of cavitating bubble pockets and their fluctuations were noticeably relaxed by polymer additives. For a 400 p.p.m. solution (parts per million (p.p.m.)), a reduction of 65 % was measured relative to pure water flow at the highest tested flow rate. (3) Spectral analysis of the downstream pressure indicated that the shedding frequency at the cavitation inception was reduced as the solution's concentration increased. This reduction was as high as 70 % for a 400 p.p.m. solution. These results highlight the strong interplay between polymer additives and the generation of cavitation-related structures.

Direct numerical simulations of turbulent non-rotating and rotating plane Couette flow with a periodically modulated plate velocity are conducted to study the effect of modulated forcing on turbulent shear flows. The time-averaged shear Reynolds number is fixed at $Re_S = 3 \times 10^4$, which results in a frictional Reynolds number of approximately $Re_\tau \approx 400$. The modulating frequency is varied in the range $Wo\in (20,200)$, while the modulating amplitude is kept fixed at $10\,\%$ of the shear velocity except to demonstrate that varying this parameter has minimal effect. The resulting shear at the plates is found to be independent of the forcing frequency, and equal to the non-modulated baseline. For the non-rotating simulations, two clear flow regions can be seen: a near-wall region that follows Stokes’ theoretical solution, and a bulk region that behaves similar to Stokes’ solutions but with an increased effective viscosity. For high driving frequencies, the amplitude response follows the scaling laws for modulated turbulence of von der Heydt et al. (Phys. Rev. E, vol. 67, 2003, 046308). Cyclonic rotation is not found to modify the system's behaviour in a substantial way, but anti-cyclonic rotation changes significantly the system's response to periodic forcing. We find that the persistent axial inhomogeneities introduced by mild anti-cyclonic rotation make it impossible to measure the propagation of the modulation adequately, while stronger anti-cyclonic rotation creates regions where the modulation travels instantaneously.

Vertical convection is the fluid motion that is induced by the heating and cooling of two opposed vertical boundaries of a rectangular cavity (see e.g. Wang et al., J. Fluid Mech., vol. 917, 2021, A6). We consider the linear stability of the steady two-dimensional flow reached at Rayleigh numbers of O($10^8$). As a function of the Prandtl number, $Pr$, and the height-to-width aspect ratio of the domain, $A$, the base flow of each case is computed numerically and linear simulations are used to obtain the properties of the leading linear instability mode. Flow regimes depend on the presence of a circulation in the entire cavity, detachment of the thermal layer from the boundary or the corner regions and on the oscillation frequency relative to the natural frequency of oscillation in the stably temperature-stratified interior, allowing for the presence of internal waves or not. Accordingly, the regime is called slow or fast, respectively. Either the global circulation or internal waves in the interior may couple the top and bottom buoyancy currents, while their absence implies asymmetry in their perturbation amplitude. Six flow regimes are found in the range of $0.1 \leq Pr \leq 4$ and $0.5 \leq A \leq 2$. For $Pr \lessapprox 0.4$ and $A>1$, the base flow is driven by a large circulation in the entire cavity. For $Pr \gtrapprox 0.7$, the thermal boundary layers are thin and the instability is driven by the motion along the wall and the detached boundary layer. A transition between these regimes is marked by a dramatic change in oscillation frequency at $Pr = 0.55 \pm 0.15$ and $A <2$.

Just as a solid object would, a liquid jet or a stream of droplets impacting a free surface deforms and perforates it. This generic flow interaction, met in everyday life but also in cutting edge industrial processes, has puzzled scientists for centuries. Lee et al. (J. Fluid Mech., vol. 921, 2021, A8) present an experimental study of a simple droplet train interacting with a liquid bath and identify two stages in the interaction: a first where a cavity elongates and finally bursts, and a second where the interface is steadily punched by the incoming stream. Each of these regimes is explained with elementary but effective models arising from first principles, thereby revealing a full and simple picture of the physics of making holes in liquids.

Using laboratory experiments and numerical simulations, we examine the transfer of soluble material from small, spherical particles sinking in homogeneous turbulence at large Péclet number. A theoretical analysis predicts two distinct mechanisms of convective mass transfer: strain due to turbulence and slip due to gravitational settling. Their relative strength is parametrised by the sinking ratio, ${Sr} = w_0 \tau _\eta /a$, where $w_0$ is the quiescent settling velocity, $a$ is the particle radius and $\tau _\eta$ is the Kolmogorov time scale. This analysis predicts that the topology of the concentration wake changes from a symmetric topology at ${Sr} \ll 1$ to an asymmetric topology at ${Sr} \gg 1$ as the dominant mechanism of mass transfer changes. Particle tracking flow visualisations of small spheres releasing dye in turbulence confirm the existence of this change in mechanism at ${Sr} = O(1)$. We complement these experiments with numerical simulations of the mass transfer from sinking particles. The transfer rate predicted by the simulation is found to be in good agreement with literature data for mass transfer to turbulent suspensions of solid particles and is consistent with asymptotic expressions for mass transfer in uniform flow when ${Sr} \gg 1$. A decomposition of the convective fluxes confirms the transition in the transfer mechanism. At ${Sr} = O(1)$, both mechanisms provide comparable contributions to the transfer rate. Cross-correlation analysis reveals that particle-scale knowledge of both the recent strain and velocity history is required to predict the instantaneous transfer rate. Turbulence-induced particle rotation has a modest suppression effect upon convective transfer by sinking.

The effect of single perforations and their location on the drag and reconfiguration of flexible plates was explored through laboratory experiments and direct numerical simulations. The plates were subjected to uniform flows with negligible turbulence, and the perforations had a square cross-section resulting in a low porosity ratio of $\gamma \approx 0.028$. Rigid plates with and without perforations and flexible plates without perforations served as the baseline cases. The perforated plates exhibited distinct jets through the openings in the wake, significantly impacting the aerodynamic force and plate deformation. The velocity and position of the centre jet velocity in relation to downwind distance were influenced by both the incoming flow and the location of the perforations. The centre jet velocity profiles were normalized using an effective velocity and corrected perforation half-width, revealing their dependence on these factors. A simple first-order formulation was developed to predict the change in drag for various perforated plates under a wide range of incoming velocities. This formulation was supported by numerical simulations across a wider range of Cauchy number to confirm the proposed model and separate the effect of the Cauchy and Reynolds numbers. The results of this study may inform the design of flexible structures, define effective porosity and serve as an initial step towards modelling the complex interaction between flow and structures with low porosity.