Slender sheets of viscous liquid can show features characteristic of elastic materials, such as buckling under compression. Likewise, thin sheets of solid material subject to sufficiently high stress can deform plastically, i.e. flow. In this volume, Hewitt & Balmforth (J. Fluid Mech., vol. 908, 2021, A5) explore the territory between these regimes, by developing asymptotic theories for thin viscoelastic and elasto-viscoplastic sheets, focusing primarily on regimes in which bending deformations dominate stretching. Their results reveal a rich phenomenology and provide new theoretical tools with which to probe thin layers of soft materials.

Leading-edge-vortex (LEV) formation often characterizes the unsteady flows past airfoils and wings. Recent research showed that initiation of LEV formation on airfoils in two-dimensional flow is closely tied to the criticality of the so-called leading-edge suction parameter (LESP). To characterize the LEV initiation on wings in three-dimensional flow, a large set of pitching wings was studied using Reynolds-averaged Navier–Stokes computations (computational fluid dynamics, CFD). The CFD results showed that the pitch angle and spanwise location for LEV initiation varied widely between the different wings. The same cases were also analysed using an unsteady vortex-lattice method (UVLM), which assumes attached flow. Low-order prediction of LEV initiation is assumed to occur at the pitch angle when the UVLM-calculated LESP at any point on the wing span first becomes equal to the pre-determined critical LESP for the airfoil. For all the cases, the predicted pitch angles and spanwise locations for LEV initiation from the low-order method agreed excellently with the corresponding CFD predictions. These observations show that LEV initiation on finite wings is governed by criticality of leading-edge suction, enabling the prediction of LEV initiation on an unsteady finite wing using attached-flow wing theory and the critical LESP values for the airfoil sections.

Flow structure inside and around a rectangular array of emerged cylinders located adjacent to the sidewall of an open channel is investigated using eddy-resolving numerical simulations. This configuration is particularly relevant for understanding how patches of aquatic vegetation developing near a river's banks affect flow and transport. The array of width W = 1.6D and length L = 33D–35D (D is the flow depth) contains rigid cylinders. Simulations with incoming, fully developed turbulent flow (channel Reynolds number, ReD = 12 500) are conducted with different values of the solid volume fraction (0.02 < ϕ < 0.1), frontal area per unit volume of the array, a (0.41 < aW < 1.63), diameter of the solid cylinders (d = 0.1D and 0.2D) and cylinder shape (circular and square). The paper focuses on investigating flow and turbulence structure inside and downstream of the array and the role played by coherent structures (e.g. vortices forming in the horizontal shear layer at the lateral face of the array, vortices shed in the wake of the solid cylinders) in sediment entrainment and transport. Simulation results show that significant upwelling and downwelling motions are generated near the front and lateral faces of the array and inside the shear layer. Moreover, some distance from the front face of the array, the shear layer vortices generate successive regions of high and low streamwise velocity inside the patch. The frequency associated with these wave-like oscillations is approximately half of the frequency associated with the advection of vortices in the downstream part of the shear layer. These streamwise velocity oscillations induce spanwise patches of high and low bed friction velocity that extend over the regions occupied by the array and the horizontal shear layer. For sufficiently high array resistance, horseshoe vortices form around the upstream corner of the array and provide an additional mechanism for sediment entrainment. For aW > 0.5, mean-flow recirculation bubbles form behind the array. For constant aW, the total size of the region containing recirculation bubbles decreases with increasing d/D. Simulations results are used to quantify the effect of varying ϕ, aW, d/D and the cylinders’ shape on the streamwise decay of the mean streamwise velocity inside the array, turbulent kinetic energy distribution, mean streamwise drag forces acting on the cylinders and mean streamwise drag coefficients.

Miniature shock tubes are finding growing importance in a variety of interdisciplinary applications. There is a lack of experimental data to validate the existing shock tube flow models that explain the shockwave attenuation in pressure-driven miniature shock tubes. This paper gives insights into the shock formation and shock propagation phenomena in miniature shock tubes of 2, 6 and 10 mm square cross-sections operated at diaphragm rupture pressure ratios in the range 5–25 and driven section initially at ambient conditions. Pressure measurements and visualization studies are carried out in a new miniature table-top shock tube system using nitrogen and helium as driver gases. The experimental findings are validated using a shock tube model explained in terms of two regions: (i) the shock formation region, dominated by wave interactions due to the diaphragm's finite rupture time; and (ii) the shock propagation region, where the shockwave attenuation occurs mainly due to wall effects and boundary layer growth. Correlations to predict the variation of shock Mach number in the shock formation region and shock propagation region work well for the present findings and experimental data reported in the literature. Similar flow features are observed in the shock tubes at the same dimensionless time stamps. The formation of the planar shock front scales proportionally with the diameter of the shock tube. The peak Mach number attained by the shockwave is higher as the shock tube diameter increases.

In this work we investigate the effects of two distinct actuation methods on the hydrodynamics of elastic rectangular plates oscillating at resonance. Plates are driven by plunging motion at the root or actuated by a distributed internal bending moment at Reynolds numbers between 500 and 4000. The latter actuation method represents internally actuated smart materials and emulates the natural ability of swimming animals to continuously change their shapes with muscles. We conduct experiments with plunging elastic plates and piezoelectric plate actuators that are simulated using a fully coupled three-dimensional computational model based on the lattice Boltzmann method. After experimental validation the computational model is employed to probe plate hydrodynamics for a wide range of parameters, including large oscillation amplitudes which prompts nonlinear effects. The comparison between the two actuation methods reveals that, for the same level of tip deflection, externally actuated plates significantly outperform internally actuated plates in terms of thrust production and hydrodynamic efficiency. The reduced performance of internally actuated plates is associated with their suboptimal bending shapes which leads to a trailing edge geometry with enhanced vorticity generation and viscous dissipation. Furthermore, the difference in actuation methods impacts the inertia coefficient characterizing the plate oscillations, especially for large amplitudes. It is found that the inertia coefficient strongly depends on the tip deflection amplitude and the Reynolds number, and actuation method, especially for larger amplitudes.

Indirect noise generated by the acceleration of synthetic compositional and entropic perturbations through non-isentropic nozzles is measured experimentally. A physics-based analytical low-order model to evaluate the indirect noise generated by non-isentropic compact nozzles is developed and validated with experimental measurements. A one-dimensional model for describing the waves generated by the addition of mass, momentum, energy and species to a steady flow in an entropy and composition wave generator is presented. The transfer functions describing the multiple reflections of acoustic waves in an enclosed environment are derived. This analytical framework allows unambiguous identification and isolation of the experimental direct and indirect noise generated by the injection of helium, methane, argon or carbon dioxide into a flow duct. Experimental data show that entropic and compositional noise make a significant contribution to the overall pressure traces acquired in the entropy generator. Moreover, it is demonstrated that the isentropic modelling assumption is inadequate to capture the experimental behaviour, while the analytical model for non-isentropic nozzles successfully describes the direct and indirect noise transfer functions. The disregard for the compositional contribution and the unjustified use of the isentropic assumption can provide significantly inaccurate noise predictions. This work shows that compositional noise, as well as non-isentropicity in the system, should be considered in future thermoacoustic and combustion noise models.

In the fields of microgripping and microassembly, the self-alignment motion of a solid micro-object linked by a liquid meniscus to a substrate or a tool is an inexpensive way to overcome the current limitations of the assembly processes at microscale by getting rid of the positioning actuators. Original models providing a dynamical description of the capillary self-alignment of an $L\times D \times d$ chip are reported, as well as experimental results as evidence of their validity. The first two models describe the liquid and the solid physics in two dimensions. Both include nonlinearities and describe the coupling between a laminar flow and a solid structure. The fluid–solid coupling is ensured by the boundary conditions at their surface of contact and by the forces the liquid and the solid apply on each other. Both models yield the shift, lift and tilt modes of deformation of the liquid meniscus. Equations are first numerically solved by using a finite element method (model 1). By approximating the menisci with spherical caps, a geometrical model is then presented (model 2). Next, for small oscillations and thin liquid layers, the equations are linearised. The solution to the semianalytical three degrees of freedom (3-DOF) modal analysis is thus obtained (model 3). Finally, a semianalytical 1-DOF model is presented and numerically solved by considering a one-dimensional motion for the solid object (model 4). Solutions for models 1, 3 and 4 are computed and show good agreement with the experimental measurements. Yet, the remaining deviations are investigated to identify their origin.

The canopy-related terms in the transport equations for momentum, Reynolds stresses, turbulent kinetic energy and its dissipation rate were described by a perturbative expansion around a velocity scale based on the mean total kinetic energy. The quality of the series and the relative magnitude of the first orders were analysed through comparison with the results of large-eddy simulation of three canopy flows representative of real-life applications. The flows in question were those over a horizontally homogeneous forest, a sequence of forest stands and clearings, and a forested hill. The analysis gave both the highest order required for an accurate evaluation of the canopy effects and a mathematical formulation for the canopy-related terms in a Reynolds-averaged Navier–Stokes formulation. This offers a sounder basis and assured consistency for the turbulence modelling of canopy flows between Reynolds-averaged Navier–Stokes and large-eddy simulation frameworks.

Gas-fluidized beds of flexible fibres, which have been rarely studied before, are investigated in this work using the coupled approach of the discrete element method and computational fluid dynamics. In the present numerical method, gas–fibre interaction is modelled by calculating the interaction force for each constituent element in the fibre, and the composition of the interaction forces on the constituent elements generates a resultant hydrodynamic force and a resultant hydrodynamic torque on the fibre. Pressure drops and fibre orientation results from the present simulations with various fibre aspect ratios are in good agreement with previous experimental and simulation results. Some novel results are obtained for the effects of fibre flexibility. Larger hydrodynamic forces on fibres (before the bed is fluidized) and smaller minimum fluidization velocities (MFVs) are observed for more flexible fibre beds due to the smaller porosities, while smaller hydrodynamic forces are obtained for the more flexible fibres when the beds are fluidized with significant fibre motion. By scaling the superficial gas velocity using the MFVs, the data of pressure drop can collapse onto the Ergun correlation for stiff fibres of various aspect ratios; however, the pressure drop curves deviate from the Ergun correlation for very flexible fibres, due to the significant fibre bed expansion before the MFV is reached. The fibre aspect ratio and flexibility both have an impact on the solids mixing rate, and it is found that the solids mixing rates are essentially determined by the ratio of the superficial gas velocity to MFV.

The compressibility effects on energy exchange mechanisms in a three-dimensional, spatially developing plane free shear layer are investigated via data produced by direct numerical simulation. The compressible shear layer is simulated using a high-order discontinuous spectral element method for convective Mach numbers $M_c = 0.3$, 0.5 and 0.7. The energy exchange mechanisms in the flow are examined by analysing the budget terms of mean kinetic, internal and turbulent kinetic energy transport equations, in both transition and turbulent regions. The results show that turbulent production, turbulent viscous dissipation, mean viscous dissipation, pressure dilatation and enthalpic production are the main mechanisms responsible for energy exchange among different forms of energy. The effects of compressibility on energy transfer mechanisms are studied based on the analyses of those five budget terms. The primary budget terms evolve differently in the transition and turbulent regions and change significantly for varying compressibility. In the transition region, a double-peak variation becomes a single peak in the streamwise profile of the turbulent production as $M_c$ increases from 0.3 to 0.7, due to significant changes in the vortex pairing structures. The shear layer centre slightly shifts to the high-speed side due to the appearance of the velocity deficit. The velocity deficit presence distance (VDPD) becomes longer as compressibility increases. However, in the turbulent region, the cross-stream profiles of the main budget terms significantly shift to the low-speed side because of the asymmetric mass entrainment and shift even further as $M_c$ increases.

Collisions in a dilute polydisperse suspension of spheres of negligible inertia interacting through non-continuum hydrodynamics and settling in a slow uniaxial compressional flow are studied. The ideal collision rate is evaluated as a function of the relative strength of gravity and uniaxial compressional flow and it deviates significantly from a linear superposition of these driving terms. This non-trivial behaviour is exacerbated by interparticle interactions based on uniformly valid non-continuum hydrodynamics, that capture non-continuum lubrication at small separations and full continuum hydrodynamic interactions at larger separations, retarding collisions driven purely by sedimentation significantly more than those driven purely by the linear flow. While the ideal collision rate is weakly dependent on the orientation of gravity with the axis of compression, the rate including hydrodynamic interactions varies by more than $100\,\%$ with orientation. This dramatic shift can be attributed to complex trajectories driven by interparticle interactions that prevent particle pairs from colliding or enable a circuitous path to collision. These and other important features of the collision process are studied in detail using trajectory analysis at near unity and significantly smaller than unity size ratios of the interacting spheres. For each case analysis is carried for a large range of relative strengths and orientations of gravity to the uniaxial compressional flow, and Knudsen numbers (ratio of mean free path of the media to mean radius).

Single fuel droplet vaporization, with special attention to the case of ethanol, is considered in this study. First, we showed, using an order-of-magnitude analysis and detailed unsteady simulations, that the commonly used quasi-steady assumption is not suitable for an accurate description of the liquid phase during the evaporation process. Second, we demonstrated that an increase in the relative importance of radiation explains the departures of the evaporation rate from the $d^{2}$-law observed experimentally when sufficiently large droplets – initial radius above 0.25 mm – evaporated in ambient temperatures around 800 K. The multicomponent formulation included here, in which the physical properties of both liquid and gas phases depend on the concentration of the different species involved, was validated by comparing our numerical results with experimental data of ethanol, $n$-heptane, ethanol–water and $n$-dodecane–$n$-hexadecane droplets available in the literature. Because of its technological relevance, we dedicated special attention to the effect of the droplet water content and ambient humidity on the evaporation time of ethanol droplets. Our computations showed higher vaporization rates with increasing ambient humidity as a consequence of the extra heat generated during the condensation of moisture on the droplet surface.

The spatial distribution of a scalar undergoing advection and diffusion is impacted by the velocity variability sampled by tracer particles. In spatially structured velocity fields, such as porous medium flows, Lagrangian velocities along streamlines are often characterized by a well-defined correlation length and can thus be described by spatial-Markov processes. Diffusion, on the other hand, is generally modelled as a temporal process, making it challenging to capture advective and diffusive dynamics in a single framework. We develop a description of transport based on a spatial-Markov velocity process along Lagrangian particle trajectories, incorporating the effect of diffusion as a local averaging process in velocity space. The impact of flow structure on this diffusive averaging is quantified through an effective shear rate. The latter is fully determined by the point statistics of velocity magnitudes together with characteristic longitudinal and transverse length scales associated with the flow field. For infinite longitudinal correlation length, our framework recovers Taylor dispersion, and in the absence of diffusion it reduces to a standard spatial-Markov velocity model. We derive dynamical equations governing the evolution of particle position and velocity and obtain scaling laws for the dependence of longitudinal dispersion on Péclet number. These results provide new insights into the role of shear and diffusion on dispersion processes in heterogeneous media.

We study the structure of the thermal boundary layer (BL) in Rayleigh–Bénard convection for Prandtl number ($Pr$) 0.021 by conducting direct numerical simulations in a two-dimensional square box for Rayleigh numbers ($Ra$) up to $10^9$. The large-scale circulation in the flow divides the horizontal plates into three distinct regions, and we observe that the local thermal BL thicknesses in the plume-ejection region are larger than those in the plume-impact and shear-dominated regions. Moreover, the local BL width decreases as $Ra^{-\beta (x)}$, with $\beta (x)$ depending on the position at the plate. We find that the values of $\beta (x)$ are nearly the same in the impact and shear regions, and are larger in the ejection region. Thus, the local BL width decreases faster in the ejection region than in the shear and impact regions, and we estimate that the thermal BL structure would be uniform throughout the horizontal plate for $Ra \geq 8 \times 10^{12}$ in our low-$Pr$ convection. We compare the thermal BL profiles measured at various positions at the plate with the Prandtl–Blasius–Pohlhausen (PBP) profile and find deviations everywhere for all the Rayleigh numbers. However, the dynamically rescaled profiles, as suggested by Zhou & Xia (Phys. Rev. Lett., vol. 104, 2010, 104301), agree well with the PBP profile in the shear and impact regions for all the Rayleigh numbers, whereas they still deviate in the ejection region. We also find that, despite the growing fluctuations with increasing $Ra$, thermal boundary layers in our low-$Pr$ convection are transitional and not yet fully turbulent.

The presence of elongated streaks of high and low streamwise velocity in the shear layer of circular jets breaks the axisymmetry of their steady-state solution. If the streaks are considered to be part of the base flow, for the purpose of linear instability analysis, the instability eigenmodes are thus affected by their presence. The resulting changes of growth rate and spatial shapes of eigenmodes, related to the shear instability in jets, are investigated here for parallel base flows. Optimal streamwise vortices (‘rolls’) with prescribed azimuthal periodicity are computed, such that the transient temporal growth of the streaks that they produce is maximal. The presence of finite-amplitude streaks requires the formulation of eigenvalue problems in a two-dimensional cross-plane. Sinuous rolls and streaks are found to have a stabilising effect on the Kelvin–Helmholtz instability, whereas the varicose rolls and streaks have a destabilising effect. Absolute instability is not found to occur. This work shows that the effects of rolls and streaks need to be taken into account for more precise modelling of jet instability.

We present a network-based modal analysis technique that identifies key dynamical paths along which perturbations amplify over a time-varying base flow. This analysis is built upon the Katz centrality, which reveals the flow structures that can effectively spread perturbations over a time-evolving network of vortical interactions on the base flow. Motivated by the resolvent form of the Katz function, we take the singular value decomposition of the resulting communicability matrix, complementing the resolvent analysis for fluid flows. The right-singular vectors, referred to as the broadcast modes, give insights into the sensitive regions where introduced perturbations can be effectively spread and amplified over the entire fluid-flow network that evolves in time. We apply this analysis to a two-dimensional decaying isotropic turbulence. The broadcast mode reveals that vortex dipoles are important structures in spreading perturbations. By perturbing the flow with the principal broadcast mode, we demonstrate the utility of the insights gained from the present analysis for effectively modifying the evolution of turbulent flows. The current network-inspired work presents a novel use of network analysis to guide flow control efforts, in particular for time-varying base flows.

A relation between the ensemble average and the nearest particle statistics is derived. The relation accounts for interactions among all the particles, not only the nearest one, and can be used to study long-range particle interactions without the difficulty of a divergent integral. As an example, this relation is applied to calculate the particle sedimentation velocity to the first order of the particle volume fraction. Using the relation, an important particle–fluid–particle stress is introduced for general multiphase flows.

Numerous field observations of tsunami-induced eddies in ports and harbours have been reported for recent tsunami events. We examine the evolution of a turbulent shallow-water monopolar vortex generated by a long wave through a series of large-scale experiments in a rectangular wave basin. A leading-elevation asymmetric wave is guided through a narrow channel to form a flow separation region on the lee side of a straight vertical breakwater, which coupled with the transient flow leads to the formation of a monopolar turbulent coherent structure (TCS). The vortex flow after detachment from the trailing jet is fully turbulent ($Re_h \sim O(10^{4}\text {--}10^{5}$)) for the remainder of the experimental duration. The free surface velocity field was extracted through particle tracking velocimetry over several experimental trials. The first-order model proposed by Seol & Jirka (J. Fluid Mech., vol. 665, 2010, pp. 274–299) to predict the decay and spatial growth of shallow-water vortices fits the experimental data well. Bottom friction is predicted to induce a $t^{-1}$ azimuthal velocity decay and turbulent viscous diffusion results in a $\sqrt {t}$ bulk vortex radial growth, where $t$ represents time. The azimuthal velocity, vorticity and free surface elevation profiles are well described through an idealised geophysical vortex. Kinematic free surface boundary conditions predict weak upwelling in the TCS-centre, followed by a zone of downwelling in a recirculation pattern along the water column. The vertical confinement of the flow is quantified through the ratio of kinetic energy contained in the secondary and primary surface velocity fields and a transition point towards a quasi-two-dimensional flow is identified.

The dynamics, structure and stability of zonal jets in planetary flows are still poorly understood, especially in terms of coupling with the small-scale turbulent flow. Here, we use an experimental approach to address the questions of zonal jets formation and long-term evolution. A strong and uniform topographic $\beta$-effect is obtained inside a water-filled rotating tank thanks to the paraboloidal fluid free upper surface combined with a specifically designed bottom plate. A small-scale turbulent forcing is performed by circulating water through the base of the tank. Time-resolving particle image velocimetry measurements reveal the self-organization of the flow into multiple zonal jets with a strong instantaneous signature. We identify a subcritical bifurcation between two regimes of jets depending on the forcing intensity. In the first regime, the jets are steady, weak in amplitude, and directly forced by the local Reynolds stresses due to our forcing. In the second one, we observe highly energetic and dynamic jets of width larger than the forcing scale. An analytical modelling based on the quasi-geostrophic approximation reveals that this subcritical bifurcation results from the resonance between the directly forced Rossby waves and the background zonal flow.

Starting from an alternative decomposition of the turbulent field, a multi-dimensional statistical formalism for the description and understanding of turbulence in free-shear flows is proposed and applied to the symmetries of planar temporal jets. The theoretical framework is based on the exact equation for the second-order moment of the two-point velocity increment and allows us to trace, for the first time, the spatially evolving cascade processes at the basis of turbulence mixing and entrainment. Fascinating reverse energy cascade mechanisms are found to be responsible for the generation of long and wide structures in the interface region. Analogously to two-dimensional turbulence, the energy provided by these spatially ascending reverse cascades is found to be eventually dissipated by viscosity at large scales through friction shearing processes involving a thin cross-flow layer of these large-scale structures. Finally, the external non-turbulent region of the jet is also found to be active from an energetic point of view. It is found that pressure-mediated non-local phenomena of displacement of almost quiescent fluid give rise to non-turbulent fluctuations that in time, through transitional mechanisms, would contribute to the growth of the turbulent jet. Overall, the unexpected paths taken by the scale-energy flux in the combined physical/scale space, which are a substantial novelty with respect to known descriptions of turbulent mixing and entrainment, may have major repercussions on our theoretical understanding and modelling, as anticipated here by reduced equations capable of giving a simple scale-dependent description of the rich dynamics of the flow.