In this paper, we study the aeroacoustic instability which occurs in a deep axisymmetric cavity in a turbulent pipe flow. This phenomenon is the axisymmetric counterpart of the classical whistling of a rectangular deep cavity subject to a grazing flow. The whistling of such axisymmetric cavity originates from the interaction of the coherent fluctuations of the vorticity at the cavity's opening with one of its trapped azimuthal or radial acoustic modes. We focus here on the situation involving the first pure azimuthal mode, which is trapped in the cavity. As a consequence of the rotational symmetry of the configuration, azimuthal modes are actually pairs of degenerate eigenmodes, or almost degenerate in the presence of small asymmetries. Therefore, the aeroacoustic instabilities exhibit more complex mechanisms than in the case of a rectangular deep cavity. In particular, we show that self-sustained spinning modes induce a symmetry breaking of the mean flow and we will elucidate the details of this phenomenon. To that end, simultaneous acoustic and time-resolved stereoscopic particle image velocimetry (PIV) measurements are performed. They reveal that when large-amplitude aeroacoustic waves spin around the cavity, a quasi-steady mean flow starts whirling slowly in the opposite direction to the wave propagation. A linear perturbation analysis around an axisymmetric mean flow confirms the experimental observations: although the incoming pipe flow is not swirling, the hydrodynamic component of the aeroacoustic wave induces such whirling motion of the mean flow because of the forcing from the steady part of the coherent Reynolds stress tensor.

To assess how the presence of surfactant in lung airways alters the flow of mucus that leads to plug formation and airway closure, we investigate the effect of insoluble surfactant on the instability of a viscoplastic liquid coating the interior of a cylindrical tube. Evolution equations for the layer thickness using thin-film and long-wave approximations are derived that incorporate yield-stress effects and capillary and Marangoni forces. Using numerical simulations and asymptotic analysis of the thin-film system, we quantify how the presence of surfactant slows growth of the Rayleigh–Plateau instability, increases the size of initial perturbation required to trigger instability and decreases the final peak height of the layer. When the surfactant strength is large, the thin-film dynamics coincide with the dynamics of a surfactant-free layer but with time slowed by a factor of four and the capillary Bingham number, a parameter proportional to the yield stress, exactly doubled. By solving the long-wave equations numerically, we quantify how increasing surfactant strength can increase the critical layer thickness for plug formation to occur and delay plugging. The previously established effect of the yield stress in suppressing plug formation (Shemilt et al., J. Fluid Mech., vol. 944, 2022, A22) is shown to be amplified by introducing surfactant. We discuss the implications of these results for understanding the impact of surfactant deficiency and increased mucus yield stress in obstructive lung diseases.

The whistling induced by a low-Mach turbulent flow through a deep axisymmetric cavity in a duct is investigated theoretically and experimentally. The experiments include acoustic measurements and stereoscopic particle image velocimetry (PIV). The paper focuses on the effect of a mean swirl on the dynamics of the azimuthal aeroacoustic modes. The mean swirl in the cavity has two origins: one component is imposed by a controlled tangential air injection upstream of the cavity, and the other component spontaneously arises under the action of the self-sustained azimuthal aeroacoustic mode, as explained in the companion paper, Part 1 (Faure-Beaulieu, Xiong, Pedergnana & Noiray, J. Fluid Mech., vol. 971, 2023, A21). Experiments show that the dynamics of the aeroacoustic wave is influenced by the imposed swirl. In particular, the spinning wave propagating against the swirl is promoted. To explain this, a linear perturbation analysis is performed around an incompressible mean swirling flow obtained from RANS simulations. It reveals that the dominant shear layer modes of azimuthal order 1 and −1 involved in the whistling phenomenon are helical modes winding respectively with and against the swirl, and spinning respectively in counterswirl and co-swirl directions. The counterswirl hydrodynamic mode is the least damped of the two, which is in agreement with the experimental observations. Finally, a low-order model based on the wave equation is derived. With only a few parameters, it fully reproduces the experimental observations for a wide range of imposed swirl intensity in the duct flow, and it allows us to disentangle the mechanisms responsible for this complex aeroacoustic instability.

Pore-resolved direct numerical simulations are performed to investigate the interactions between streamflow turbulence and groundwater flow through a randomly packed porous sediment bed for three permeability Reynolds numbers, $Re_K=2.56$, 5.17 and 8.94, representative of natural stream or river systems. Time–space averaging is used to quantify the Reynolds stress, form-induced stress, mean flow and shear penetration depths, and mixing length at the sediment–water interface (SWI). The mean flow and shear penetration depths increase with $Re_K$ and are found to be nonlinear functions of non-dimensional permeability. The peaks and significant values of the Reynolds stresses, form-induced stresses, and pressure variations are shown to occur in the top layer of the bed, which is also confirmed by conducting simulations of just the top layer as roughness elements over an impermeable wall. The probability distribution functions (p.d.f.s) of normalized local bed stress are found to collapse for all Reynolds numbers, and their root-mean-square fluctuations are assumed to follow logarithmic correlations. The fluctuations in local bed stress and resultant drag and lift forces on sediment grains are mainly a result of the top layer; their p.d.f.s are symmetric with heavy tails, and can be well represented by a non-Gaussian model fit. The bed stress statistics and the pressure data at the SWI potentially can be used in providing better boundary conditions in modelling of incipient motion and reach-scale transport in the hyporheic zone.

The shock wave–turbulent boundary layer interaction over a compression corner is studied using global stability analysis (GSA) and resolvent analysis based on a separation of scales between the low-frequency, large-scale motions and the turbulent fluctuations. The GSA identifies a leading stationary mode, which becomes globally unstable as the ramp angle is beyond a critical value. For globally stable flows, the resolvent analysis captures two-dimensional and three-dimensional local maxima in optimal gain, both of which are due to modal resonance between the forcing and the leading global mode. Notably, the frequency-premultiplied optimal gain associated with two-dimensional disturbances peaks at a low frequency. For different interaction strengths, the peak frequencies collapse onto a universal value of 0.015 when non-dimensionalized using the length of the separation region and the free-stream velocity. A numerical simulation perturbed with the corresponding optimal forcing reveals that the response is in the form of a back-and-forth shock motion.

We present a statistical characterization of the interaction between a planar shock and a finite-diameter, cylindrical column of dense gas based on three-dimensional, large-eddy simulation results. In the simulation, the column of gas is initially inclined at an angle $\alpha _0$ with respect to the shock plane. Effects of the initial column angle on the mixing characteristics are examined at Mach number 2.0 for column incline angles $1^\circ$, $5^\circ$, $10^\circ$ and $30^\circ$. Mean velocity profiles show that the column angle affects the gas velocity components in the vertical plane, but not in the spanwise direction. The gas undergoes higher initial upward acceleration at larger initial column incline angles. With time, the gas motion tends to become one-dimensional in the streamwise direction. Initially, velocity fluctuations are most intense within the interior of the column, but concentrate near the column leading edge over time. At high wavenumbers $\kappa$, the turbulent kinetic energy spectra follow a power-law scaling of $\kappa ^{-1}$. The structure functions of the mass fraction do not clearly demonstrate power-law scaling except at early times for $\alpha _0=30^\circ$, manifesting overall trends very similar to those observed in earlier experiments. Probability distributions of the mass fraction show independence of the mean and the standard deviation of the mixed gas on $\alpha _0$. The column angle was also found to have little effect on the mixing efficiency characterized by the molecular mixedness. Velocity components in the streamwise and transverse directions tend towards a bimodal distribution for larger $\alpha _{0}$.

We report an experimental study of the motion of a clapping body consisting of two flat plates pivoted at the leading edge by a torsion spring. Clapping motion and forward propulsion of the body are initiated by the sudden release of the plates, initially held apart at an angle $2\theta _o$. Results are presented for the clapping and forward motions, and for the wake flow field for 24 cases, where depth-to-length ratio ($d^* = 1.5,1\text { and }0.5$), spring stiffness per unit depth ($Kt$), body mass ($m_b$) and initial separation angle ($2\theta _o = 45^{\circ }\text { and }60^{\circ }$) are varied. The body initially accelerates rapidly forward, then slowly retards to nearly zero velocity. Whereas the acceleration phase involves a complex interaction between plate and fluid motions, the retardation phase is simply fluid dynamic drag slowing the body. The wake consists of either a single axis-switching elliptical vortex loop (for $d^* = 1\text { and }1.5$) or multiple vortex loops (for $d^* = 0.5$). The body motion is nearly independent of $d^*$ and most affected by variation in $\theta _o$ and $Kt$. Using conservation of linear momentum and conversion of spring strain energy into kinetic energy in the fluid and body, we obtain a relation for the translation velocity of the body in terms of the various parameters. Approximately 80 % of the initial stored energy is transferred to the fluid, only 20 % to the body. The experimentally obtained cost of transport lies between 2 and $8\ \mathrm {J}\ \mathrm {kg}^{-1}\ \mathrm {m}^{-1}$.

We carry out direct numerical simulations of flow in a plane open channel at friction Reynolds number up to ${{Re}}_{\tau } \approx 6000$. We find solid evidence for the presence of universal large-scale organization in the outer layer, with eddies that are larger and stronger than in the closed channel flow. As a result, velocity fluctuations are found to be stronger than in closed channels, throughout the depth. The inner-layer peak of the streamwise velocity variance is observed to grow logarithmically, as in Townsend's attached-eddy model (Townsend, The Structure of Turbulent Shear Flow, 2nd edn, Cambridge University Press, 1976), but saturation of the growth cannot be discarded based on the present data. Although we do not observe a clear outer peak of the streamwise velocity variance, we present substantial evidence that such a peak should emerge at a Reynolds number barely higher than achieved herein. The most striking feature of the flow is the presence of an extended logarithmic layer, with associated Kármán constant asymptoting to $k \approx 0.375$, in line with observations made in shear-free Couette–Poiseuille flow (Coleman et al., Flow Turbul. Combust., vol. 99, issue 3, 2017, pp. 553–564). The virtual absence of a wake region and of corrective terms to the log law in the present flow leads us to conclude that deviations from the log law observed in internal flows are likely due to the effects of the opposing walls, rather than the presence of a driving pressure gradient.

Direct numerical simulation of a compressible round jet is carried out at Mach number of 0.9 and Reynolds number of 3600 and the data are used to perform velocity gradient tensor (VGT) analysis for different regions of the spatially developing jet. For the developed portion of the jet, the classical teardrop shape is observed for the joint probability density function (p.d.f.) of Q and R (second and third invariants of the VGT). In the region just after the potential core, between $X = 10$ and 15 $r_0$ ($r_0$ is the jet inlet radius), an inclination towards the third quadrant is observed in the Q–R joint p.d.f. which represents the presence of tube-like structures. It is also shown that this inclination in the turbulent/non-turbulent (T/NT) boundary and interface towards the third quadrant is mainly a contribution of points that lie in regions with negative dilatation. Regions with weak expansion also show this third quadrant inclination to some extent. Points that lie in regions with relatively higher positive dilatation show no such inclination towards the third quadrant but are inclined towards the fourth quadrant which indicates the presence of sheet-like structures. Similarly for the domain segment $X = 15$ to 20 $r_0$, it is observed that points that lie in the regions with positive dilatation have a joint p.d.f. with an inclination towards fourth quadrant, which suggests the presence of sheet-like structures at the T/NT boundary and interface. Points that lie in regions with negative dilatation show the appearance of a third quadrant lobe.

Mass transport in suspensions of swimming microorganisms is one of the most important factors for the colonisation and growth of microorganisms. Hydrodynamic interactions among swimming microorganisms play an important role in mass transport, especially in highly concentrated suspensions. To elucidate the influence of highly concentrated cells on mass transport, we numerically simulated mass transport in lattices of squirmers that were fixed in space and oriented in the same direction. The effects of different volume fractions, Péclet numbers ($Pe$) and lattice configurations on mass transport were quantified by tracking Lagrangian material points that move with background flow with Brownian diffusivity. Although the flow field became periodic in space and each streamline basically extended in one direction, the motion of tracer particles became diffusive over long durations due to Brownian motion and cross-flows. Flow-induced diffusion was anisotropic and significantly enhanced over Brownian diffusion in the longitudinal direction. We also investigated mass transport in random configurations of squirmers to reproduce more general conditions. Similar enhanced diffusion was also observed in the random configurations, indicating that the flow-induced diffusion appears regardless of the configurations. The present flow-induced diffusion did not follow $Pe$ dependency of the conventional Taylor dispersion due to the cross-flows. The time and velocity scales were proposed, which enabled us to predict the flow-induced diffusivity from the data of the flow field and Brownian diffusivity without solving the mass conservation equation. The findings reported here improve our understanding of the transport phenomena in packed suspensions of swimming microorganisms.

The classical model of evaporation of liquids hinges on Maxwell's assumption that the air near the liquid's surface is saturated. It allows one to find the evaporative flux without considering the interface separating liquid and air. Maxwell's hypothesis is based on an implicit assumption that the vapour-emission capacity of the interface exceeds the throughput of air (i.e. its ability to pass the vapour on to infinity). If this is indeed so, then the air adjacent to the liquid would get quickly saturated, justifying Maxwell's hypothesis. In the present paper, the so-called diffuse-interface model is used to account for the interfacial physics and thus derive a generalised version of Maxwell's boundary condition for the near-interface vapour density. It is then applied to a spherical drop floating in air. It turns out that the vapour-emission capacity of the interface exceeds the throughput of air only if the drop's radius is $r_{d}\gtrsim 10\ \mathrm {\mu } \mathrm {m}$, but for $r_{d}\approx 2\ \mathrm {\mu } {\rm m}$, the two are comparable. For $r_{d} \lesssim 1\ \mathrm {\mu } {\rm m}$, evaporation is interface-driven, and the resulting evaporation rate is noticeably smaller than that predicted by the classical model.

Multigrain/polydispersity has a significant impact on turbidity current (TC). Despite the fact that several researches have looked into this effect, the impact of the fluid–particle interactions is not fully understood. Motivated by this, we employ the Eulerian–Lagrangian computational fluid dynamics–discrete element method model to investigate the dynamics of the bidisperse lock-exchange TC. Results show that, because the coarse particles will settle faster and stop moving forward, the two phases of bidisperse transport and fine component transport can be distinguished in the evolution of the bidisperse TC. During the bidisperse transport stage, the upper interface of each component is primarily determined by their own settling and transport characteristics and does not strongly depend on the relative fine particle volume fraction $\phi _F$. Fine particles are primarily responsible for the vortical structures near the upper interface of the TC head, and the increase of $\phi _F$ promotes their streamwise development. In comparison, fragmented vortical coherent structures are closely related to the presence of coarse particles, which can be seen in the lower layers. Bidisperse segregation alters the collision process between dispersed phases, which differs from monodisperse TC. The collisions and segregation-induced flow establish interconnections between the two dispersed phases. In the latter stage, the transport of fine particles is inhibited by both the lift force and the contact force produced by the collision with the deposited materials. As $\phi _F$ rises, the negative contact force weakens, and its change is essentially balanced by the rise in negative lift force.

Lean hydrogen/air premixed flame flashback in a turbulent boundary layer over a flat plate is investigated using three-dimensional direct numerical simulation with detailed chemical kinetics. The upstream propagation of the flame takes place in near-wall turbulence and the interaction between the flame and the approaching reactant flow is studied. It is found that backflow regions are always present immediately upstream of flame bulges that are convex towards the reactants, confirming earlier observations. A flashback speed, including the effects of flame displacement speed and flow velocity, is introduced to quantify the flame flashback behaviour. This analysis indicates that the flashback speed is overall positive and it is considerably affected by the presence of the backflow regions. A budget analysis of the pressure transport equation is performed to explain the presence of the backflow regions. It is suggested that the positive dilatation and thermal diffusion terms near the leading edge of flame bulges are the main reasons for the pressure increase, leading to an adverse pressure gradient. The effects of the flame-induced adverse pressure gradient on the structures of the turbulent boundary layer are also investigated. It is revealed that the near-wall mean velocity and skin-friction coefficient are reduced due to the adverse pressure gradient. The coherent vortical structures of the boundary layer turbulence are lifted by the adverse pressure gradient. The analysis of the Reynolds stress component showed that the ejection event is augmented by combustion while the sweep event is attenuated, which facilitates the occurrence of flame flashback.