We investigate drop break-up morphology, occurrence, time and size distribution, through large ensembles of high-fidelity direct-numerical simulations of drops in homogeneous isotropic turbulence, spanning a wide range of parameters in terms of the Weber number $We$, viscosity ratio between the drop and the carrier flow $\mu _r=\mu _d/\mu _l$, where d is the drop diameter, and Reynolds ($Re$) number. For $\mu _r \leq 20$, we find a nearly constant critical $We$, while it increases with $\mu _r$ (and $Re$) when $\mu _r > 20$, and the transition can be described in terms of a drop Reynolds number. The break-up time is delayed when $\mu _r$ increases and is a function of distance to criticality. The first break-up child-size distributions for $\mu _r \leq 20$ transition from M to U shape when the distance to criticality is increased. At high $\mu _r$, the shape of the distribution is modified. The first break-up child-size distribution gives only limited information on the fragmentation dynamics, as the subsequent break-up sequence is controlled by the drop geometry and viscosity. At high $We$, a $d^{-3/2}$ size distribution is observed for $\mu _r \leq 20$, which can be explained by capillary-driven processes, while for $\mu _r > 20$, almost all drops formed by the fragmentation process are at the smallest scale, controlled by the diameter of the very extended filament, which exhibits a snake-like shape prior to break-up.

The vortex dynamics and the structural load in a step cylinder (consisting of a small, d, and a large, D, cylinder) flow are investigated numerically at Reynolds number ($Re_D$) 150 for diameter ratios $D/d=2.0, 2.4$ and 2.8. First, the formation mechanism of a non-uniform oblique vortex shedding (the vortex shedding frequency remains unchanged as the oblique shedding angle varies) behind the small cylinder is explained: an increase in the production rate of the vortex strength and a farther downstream movement of the vortex formation position occur simultaneously as the vicinity of the step is approached along the small cylinder. Second, the structural load (the drag and lift) along the step cylinder is investigated, where four local extremes (two local minima and two local maxima) are observed. An in-depth investigation of the vortex dislocation effects on the structural load is provided, showing that the decreased circulation in the near wake and the weakened staggered Kármán vortex shedding pattern cause a major reduction (90 %) of the sectional lift amplitude and a relatively modest reduction (5.7 %) of the sectional drag amplitude, compared with the corresponding sectional force when no vortex dislocation occurs. This new knowledge combined with the three-dimensional effect of the step cylinder wake (caused by the blending of the small and larger cylinder wakes around the step) explain the formation of the four local extremes and the distribution of the structural load between them. Finally, it is found that the increasing $D/d$ amplifies the structural load variation along the step cylinder.

Understanding particle motion in narrow channels can guide progress in numerous applications, from filtration to vascular transport. Thermal or active fluctuations of fluid-filled channel walls can slow down or increase the dispersion of tracer particles via entropic trapping in the wall bulges or hydrodynamic flows induced by wall fluctuations, respectively. Previous studies concentrated primarily on the case of a single Brownian tracer. Here, we address what happens when there is a large ensemble of interacting Brownian tracers – a common situation in applications. Introducing repulsive interactions between tracer particles, while ignoring the presence of a background fluid, leads to an effective flow field. This flow field enhances tracer dispersion, a phenomenon reminiscent of that seen for single tracers in incompressible background fluid. We characterise the dispersion by the long-time diffusion coefficient of tracers numerically and analytically with a mean-field density functional analysis. We find a surprising effect where an increased particle density enhances the diffusion coefficient, challenging the notion that crowding effects tend to reduce diffusion. Here, inter-particle interactions push particles closer to the fluctuating channel walls. Interactions between the fluctuating wall and the now-nearby particles then drive particle mixing. Our mechanism is sufficiently general that we expect it to apply to various systems. In addition, our perturbation theory quantifies dispersion in generic advection–diffusion systems.

A highly compressive effect would suppress the mixing of the shear layer in a convex wall jet. The spanwise distributed protrusions at the nozzle lip are employed to achieve mixing enhancement in this study. The mixing characteristics and enhancement mechanisms are numerically investigated by the delayed detached-eddy simulation method based on the two-equation shear-stress transport model. A widely applicable flow spatiotemporal analysis method, called proper orthogonal decomposition (POD), is used to gain further insight into the dynamical behaviours of the flow instability mode. The results reveal that the centrifugal effect maintains and amplifies the initial perturbations induced by the spanwise distributed heterogeneities, resulting in forced streamwise vortices. The instabilities induced by the streamwise vortices significantly increase the growth rate of the jet half-width and the shear layer vorticity thickness. The spanwise wavelength of the streamwise vortices is consistent with the spanwise distributed forced excitation. In addition, the spanwise meandering motion of the streamwise vortices is observed, which is usually associated with the streamwise travelling wave. This is further confirmed by the POD analysis of the spanwise velocity fluctuation in both stream-radial and stream-span sections. Also, the spatial distributions of the POD modes with the highest energy provide information on the secondary instability modes. Both sinuous and varicose types of disturbances are observed in the unforced jet, whereas the forced jet seems to be dominated by the sinuous type instability, which is more easily excited than the varicose type instability. Moreover, the turbulence intensity in the forced jet is also significantly enhanced as expected due to the earlier and stronger streamwise vortices and associated instabilities. The enhanced turbulent characteristics of the highly compressible condition tend to be isotropic, whereas in the unforced jet, it is anisotropic due to the strong compressibility suppressing the spanwise turbulent fluctuations.

Separation induced by impinging shock is a fundamental feature in supersonic and hypersonic flows; however, it is difficult to predict the pressure plateau due to a limited theoretical understanding of the effect of impinging shock strength. In this study, the evolution of the separation configuration and pressure distribution with changes in impinging shock angle is examined, and a theoretical equation for predicting the pressure plateau based on minimum entropy production is proposed. For validation, an experimental device that can measure wall pressure in the separation region at high spatiotemporal resolution is developed, and schlieren visualization is employed to capture the flow structure. Accordingly, the fine characteristics of pressure distributions along the centreline of the separation region as well as the reattachment region induced by shock impingement at various angles ($8.5^\circ$ to $30.5^\circ$) are obtained in a flow of Mach number 5 and Reynolds number ${\approx }1.4\times 10^7\ {\rm m}^{-1}$. The experimental results agree well with the theoretical results; both indicate that the pressure distribution is strongly related to the impinging shock strength and that there is a critical flow deflection angle $\alpha ^\ast$ (${\approx }20.8^\circ$ for Mach 5). The pressure in the separation region grows nearly linearly with increasing impinging shock strength when the flow deflection angle of the impinging shock is less than $\alpha ^\ast$; the pressure stops growing and resides in a small range when the flow deflection angle is larger than $\alpha ^\ast$. Therefore, the impinging shock strength should be considered a main factor when predicting the pressure plateau.

The present study uses Galinstan as a test fluid to investigate the shock-induced atomisation of a liquid metal droplet in a high-Weber-number regime $(We \sim 400\unicode{x2013}8000)$. Atomisation dynamics is examined for three test environments: oxidizing (Galinstan–air), inert (Galinstan–nitrogen) and conventional fluids (deionised water–air). Due to the readily oxidizing nature of liquid metals, their atomisation in an industrial scale system is generally carried out in inert atmosphere conditions. However, no previous study has considered gas-induced secondary atomisation of liquid metals in inert conditions. Due to experimental challenges associated with molten metals, laboratory scale models are generally tested for conventional fluids like deionised water, liquid fuels, etc. The translation of results obtained from conventional fluid to liquid metal atomisation is rarely explored. Here a direct multiscale spatial and temporal comparison is provided between the atomisation dynamics of conventional fluid and liquid metals under oxidizing and inert conditions. The liquid metal droplet undergoes breakup through the shear-induced entrainment mode for the studied range of Weber number values. The prevailing mechanism is explained based on the relative dominance of droplet deformation and Kelvin–Helmholtz wave formation. The study provides quantitative and qualitative similarities for the three test cases and explains the differences in morphology of fragmenting secondary droplets in the oxidizing test case (Galinstan–air) due to rapid oxidation of the fragmenting ligaments. A phenomenological framework is postulated for predicting the morphology of secondary droplets. The formation of flake-like secondary droplets in the Galinstan air test case is based on the oxidation rate of liquid metals and the properties of the oxide layer formed on the atomizing ligament surface.

We present theoretical results related to the experimental findings of Matsubara & Alfredsson (J. Fluid Mech., vol. 430, 2001, pp. 149–168) on the scaling of the energy spectra of the Klebanoff modes, i.e. streamwise-elongated vortical disturbances generated by free-stream turbulence in a flat-plate transitional boundary layer. The scaling is explained by a model that describes the streamwise evolution of the streamwise and spanwise energy spectra. The theoretical framework is based on the quasi-steady asymptotic solution of the boundary-region equations, on an axial-symmetric model of the free-stream spectrum, and on the spectral response of the boundary layer to the external perturbations.

We investigate the role of inter-scale interactions in the high-Reynolds-number skin-friction drag reduction strategy reported by Marusic et al. (Nat. Commun., vol. 12, 2021). The strategy involves imposing relatively low-frequency streamwise travelling waves of spanwise velocity at the wall to actuate the drag generating outer scales. This approach has proven to be more energy efficient than the conventional method of directly targeting the drag producing inner scales, which typically requires actuation at higher frequencies. Notably, it is observed that actuating the outer scales at low frequencies leads to a substantial attenuation of the major drag producing inner scales, suggesting that the actuations affect the nonlinear inner–outer coupling inherently existing in wall-bounded flows. In the present study, we find that increased drag reduction, through imposition of spanwise wall oscillations, is always associated with an increased coupling between the inner and outer scales. This enhanced coupling emerges through manipulation of the phase relationships between these triadically linked scales, with the actuation forcing the entire range of energy-containing scales, from the inner (viscous) to the outer (inertial) scales, to be more in phase. We also find that a similar enhancement of this nonlinear coupling, via manipulation of the inter-scale phase relationships, occurs with increasing Reynolds number for canonical turbulent boundary layers. This indicates improved efficacy of the energy-efficient drag reduction strategy at very high Reynolds numbers, where the energised outer scales are known to more strongly superimpose and modulate the inner scales. Leveraging the inter-scale interactions, therefore, offers a plausible mechanism for achieving energy-efficient drag reduction at high Reynolds numbers.

We present experimental evidence of multifractality and scale-free network topology in a noise-perturbed laminar jet operated in a globally stable regime, prior to the critical point of a supercritical Hopf bifurcation and prior to the saddle-node point of a subcritical Hopf bifurcation. For both types of bifurcation, we find that (i) the degree of multifractality peaks at intermediate noise intensities, (ii) the conditions for peak multifractality produce a complex network whose node degree distribution obeys an inverse power-law scaling with an exponent of $2 < \gamma < 3$, indicating scale-free topology and (iii) the Hurst exponent and the global clustering coefficient can serve as early warning indicators of global instability under specific operating and forcing conditions. By characterising the noise-induced dynamics of a canonical shear flow, we demonstrate that the multifractal and scale-free network dynamics commonly observed in turbulent flows can also be observed in laminar flows under certain stochastic forcing conditions.

The detailed energy sources that sustain the eigenmodal exponential growth in boundary layers are currently unclear. In the present study, the phase of each term in the linear stability equation is examined to identify the significant physical sources for a wide range of Mach numbers and wall temperature ratios. The Tollmien–Schlichting mode for incompressible flows, the oblique first mode for supersonic flows and the Mack second mode and supersonic mode for hypersonic flows share some similar features. The unique appearance of obliqueness for the most unstable first mode is accompanied by the enhancement of Reynolds shear stress. By contrast, the weakened Reynolds thermal stress prevents the oblique second mode from being the most unstable state. Wall cooling stabilises the oblique first mode by rendering Reynolds thermal stress and dilatation fluctuations out of phase with the internal energy fluctuation. It destabilises the second mode by a newly generated pronounced region of wall-normal internal energy transport beneath the second generalised inflection point. In comparison, the porous coating destabilises the oblique first mode by significantly enhancing the mean-shear production while it stabilises the second mode similarly to wall heating. Finally, the relatively weak supersonic mode has the feature that the phase destruction of wall-normal transport near the critical layer results in a low contribution to the internal energy growth. Connections and consistencies are also highlighted with the previous inviscid thermoacoustic interpretation for the second mode (Kuehl, AIAA J., vol. 56, 2018, pp. 3585–3592) and for the supersonic mode. The pronounced sources along the critical layer and near-wall regions provide a unified understanding of the local energy amplification mechanisms of the inviscid modes in hypersonic boundary layers.

Through boundary integral simulations and asymptotic analysis, we investigate the effect of a finite Navier slip length on the rheological proprieties of a dilute two-dimensional suspension of plate-like particles in the creeping flow limit. Specifically, we study the effects of Navier slip, particle thickness and Péclet number on the effective shear viscosity and average normal stress difference of an isolated two-dimensional plate-like particle in an unbounded shear flow field. We find that Navier slip induces a significant reduction in the effective viscosity and increases the average normal stress difference. The effect of slip becomes more enhanced as the thickness of the particle decreases and as the Péclet number increases. Remarkably, the analysis suggests that it is theoretically possible for a dilute suspension of slip plate-like particles at high Péclet numbers to have a shear viscosity smaller than that of the suspending fluid.

Self-excited oscillations of flags attached at the leading edge of aerofoils have been investigated at post-stall angles of attack at a chord Reynolds number of 100 000. Significant increases in the time-averaged lift coefficient and stall angle have been observed for three aerofoils: one symmetric, one cambered and one with a sharp leading edge. The aerodynamic improvement is due to the periodic formation of vortices caused by the flag oscillations. When the flag is near the aerofoil surface, it is lifted upwards by the induced velocity of the growing vortex. As the flag moves up, the vortex grows in strength and reaches maximum circulation when the flag is furthest from the aerofoil surface and subsequently sheds. Flags with large stiffness exhibit better spatial and temporal coherence of flag oscillations than the compliant flags, resulting in a larger maximum lift coefficient and higher stall angle. For all aerofoils tested, the best lift enhancement with respect to the clean aerofoils is found when the angle of attack is 6° to 10° above the stall angle of the clean aerofoil. High lift is observed when the flags are locked in with the wake instability in a narrow frequency band, depending on the flag mass ratio and length.

We study the effect of a confined turbulent counter-current gas flow on the waviness of a weakly inclined falling liquid film. Our study is centred on experiments in a channel of 13 mm height, using water and air, where we have successively increased the counter-current gas flow rate until flooding. Computations with a new low-dimensional model and linear stability calculations are used to elucidate the linear and nonlinear wave dynamics. We find that the gas pressure gradient plays an important role in countering the stabilizing effect of the tangential gas shear stress at the liquid–gas interface. At very low inclination angles, the latter effect dominates and can suppress the long-wave Kapitza instability unconditionally. By contrast, for non-negligible inclination, the gas effect is linearly destabilizing, amplifies the height of nonlinear Kapitza waves, and exacerbates coalescence-induced formation of large-amplitude tsunami waves. Kapitza waves do not undergo any catastrophic transformation when the counter-current gas flow rate is increased beyond the absolute instability (AI) limit. On the contrary, we find that AI is an effective linear wave selection mechanism in a noise-driven wave evolution scenario, leading to highly regular downward-travelling nonlinear wave trains, which preclude coalescence events. In our experiments, where Kapitza waves develop in a protected region before coming into contact with the gas, flooding is eventually caused far beyond the AI limit by upward-travelling short-wave ripples. Based on our linear stability calculations for arbitrary wavenumbers, we have uncovered a new short-wave interfacial instability mode with negative linear wave speed, causing these ripples.

An experimental study on the aerobreakup of a wall-attached droplet induced by a shock wave is carried out in this work. The shock wave and the post-wave air stream are generated by a shock tube facility, and the dynamics of droplet breakup are captured through high-speed imaging from the side, the oblique front and the back views, respectively. The wall-attached droplets with different wettabilities are considered, including the hydrophobic, hemispherical and hydrophilic ones. For the convenience of analysis, droplets with different wettabilities are unified with the same equivalent radius and, thus, the same Weber number and Reynolds number. Different from the evolution of a free spherical droplet, it is observed that the hydrophobic droplet can develop ‘peak’ structures on the windward and leeward sides, respectively; while the hemispherical and hydrophilic droplets leave a liquid film on the wall. The occurrence of ‘peak’ structures is caused by the local standing vortex on the droplet windward and leeward sides, and the residual of a liquid film on a solid wall is related to the boundary layer near the wall. Through comparing the height, width and advancing distance of droplet deformation between the spherical droplet and the wall-attached droplets with different wettabilities, it is found that the wall will inhibit the deformation and fragmentation of droplets on the flow direction. The ‘peak’ and film structures are responsible for the deviation of the dimensionless width between spherical and wall-attached droplets. The ‘lip’ structure is related to the recirculation flow at the rear of the droplet, which causes the reverse of velocity on the surface. The radius of the ‘lip’ decreases with the decrease of contact angle. The Rayleigh–Taylor (R–T) and Kelvin–Helmholtz (K–H) instabilities of wall-attached and spherical droplets are also studied by experiments and theoretical analysis. With the decrease of contact angle, the development of the K–H instability hardly changes, while the R–T instability results in a smaller wavelength of perturbation on the windward side. This study is expected to give some guidance for regulating the aerodynamic fragmentation of droplets in engineering applications.

Correct prediction of particle transport by surface waves is crucial in many practical applications such as search and rescue or salvage operations and pollution tracking and clean-up efforts. Recent results by Deike et al. (J. Fluid Mech., vol. 829, 2017, pp. 364–391) and Pizzo et al. (J. Phys. Oceanogr., vol. 49, no. 4, 2019, pp. 983–992) have indicated transport by deep-water breaking waves is enhanced compared with non-breaking waves. To model particle transport in irregular waves, some of which break, we develop a stochastic differential equation describing both mean particle transport and its uncertainty. The equation combines a Brownian motion, which captures non-breaking drift-diffusion effects, and a compound Poisson process, which captures jumps in particle positions due to breaking. From the corresponding Fokker–Planck equation for the evolution of the probability density function for particle position, we obtain closed-form expressions for its first three moments. We corroborate these predictions with new experiments, in which we track large numbers of particles in irregular breaking waves. For breaking and non-breaking wave fields, our experiments confirm that the variance of the particle position grows linearly with time, in accordance with Taylor's single-particle dispersion theory. For wave fields that include breaking, the compound Poisson process increases the linear growth rate of the mean and variance and introduces a finite skewness of the particle position distribution.