Bioconvection is the prototypical active matter system for hydrodynamic instabilities and pattern formation in suspensions of biased swimming microorganisms, particularly at the dilute end of the concentration spectrum where direct cell–cell interactions are less relevant. Confinement is an inherent characteristic of such systems, including those that are naturally occurring or industrially exploited, so it is important to understand the impact of boundaries on the hydrodynamic instabilities. Despite recent interest in this area, we note that commonly adopted symmetry assumptions in the literature, such as for a vertical channel or pipe, are uncorroborated and potentially unjustified. Therefore, by employing a combination of analytical and numerical techniques, we investigate whether confinement itself can drive asymmetric plume formation in a suspension of bottom-heavy swimming microorganisms (gyrotactic cells). For a class of solutions in a vertical channel, we establish the existence of a first integral of motion, and reveal that asymptotic asymmetry is plausible. Furthermore, numerical simulations from both Lagrangian and Eulerian perspectives demonstrate with remarkable agreement that asymmetric solutions can indeed be more stable than symmetric; asymmetric solutions are, in fact, dominant for a large, practically important region of parameter space. In addition, we verify the presence of blip and varicose instabilities for an experimentally accessible parameter range. Finally, we extend our study to a vertical Hele-Shaw geometry to explore whether a simple linear drag approximation can be justified. We find that although two-dimensional bioconvective structures and associated bulk properties have some similarities with experimental observations, approximating near-wall physics in even the simplest confined systems remains challenging.

Direct numerical simulations of temporally developing compressible mixing layers have been performed to investigate the effects of large-scale structures (LSSs) on turbulent kinetic energy (TKE) budgets at convective Mach numbers ranging from $M_c=0.2$ to $1.8$ and at Taylor Reynolds numbers up to 290. In the core region of mixing layers, the volume fraction of low-speed LSSs decreases linearly with respect to the vertical distance at a Mach-number-independent rate. The contributions of low-speed LSSs to TKE, and its budget, including production, dissipation, pressure-strain and spatial diffusion terms, are primarily concentrated in the upper region of mixing layer. The streamwise and vertical mass flux coupling terms mainly transport TKE downwards in low-speed LSSs, and their magnitudes are comparable to the other dominant terms. Near the edges of LSSs, the sources and losses of all three components of TKE are completely different to each other, and dominated by turbulent diffusion, pressure diffusion, pressure-strain and dissipation terms. The TKE, their total variation and dissipation are significantly amplified at edges of low-speed LSSs, especially at the upper edge. This observation supports the existence of amplitude modulation exerted by the LSSs onto the near-edge small-scale structures in mixing layers. The level of amplitude modulation is strongest for the vertical velocity, followed by the streamwise velocity, and weakest for the spanwise velocity. Additionally, the amplitude modulation effect decreases significantly with increasing convective Mach number. The results on the amplitude modulation effect is helpful for developing predictive models of budget terms of TKE in mixing layers.

Poiseuille flow is a fundamental flow in fluid mechanics and is driven by a pressure gradient in a channel. Although the rheology of active particle suspensions has been investigated extensively, knowledge of the Poiseuille flow of such suspensions is lacking. In this study, dynamic simulations of a suspension of active particles in Poiseuille flow, situated between two parallel walls, were conducted by Stokesian dynamics assuming negligible inertia. Active particles were modelled as spherical squirmers. In the case of inert spheres in Poiseuille flow, the distribution of spheres between the walls was layered. In the case of non-bottom-heavy squirmers, on the other hand, the layers collapsed and the distribution became more uniform. This led to a much larger pressure drop for the squirmers than for the inert spheres. The effects of volume fraction, swimming mode, swimming speed and the wall separation on the pressure drop were investigated. When the squirmers were bottom heavy, they accumulated at the channel centre in downflow, whereas they accumulated near the walls in upflow, as observed in former experiments. The difference in squirmer configuration alters the hydrodynamic force on the wall and hence the pressure drop and effective viscosity. In upflow, pusher squirmers induced a considerably larger pressure drop, while neutral and puller squirmers could even generate negative pressure drops, i.e. spontaneous flow could occur. While previous studies have reported negative viscosity of pusher suspensions, this study shows that the effective viscosity of bottom-heavy puller suspensions can be negative for Poiseuille upflow, which is a new finding. The knowledge obtained is important for understanding channel flow of active suspensions.

We seek the conditions in which Alfvén waves (AW) can be produced in laboratory-scale liquid metal experiments, i.e. at low magnetic Reynolds Number ($Rm$). Alfvén waves are incompressible waves propagating along magnetic fields typically found in geophysical and astrophysical systems. Despite the high values of $Rm$ in these flows, AW can undergo high dissipation in thin regions, for example in the solar corona where anomalous heating occurs (Davila, Astrophys. J., vol. 317, 1987, p. 514; Singh & Subramanian, Sol. Phys., vol. 243, 2007, pp. 163–169). Understanding how AW dissipate energy and studying their nonlinear regime in controlled laboratory conditions may thus offer a convenient alternative to observations to understand these mechanisms at a fundamental level. Until now, however, only linear waves have been experimentally produced in liquid metals because of the large magnetic dissipation they undergo when $Rm\ll 1$ and the conditions of their existence at low $Rm$ are not understood. To address these questions, we force AW with an alternating electric current in a liquid metal in a transverse magnetic field. We provide the first mathematical derivation of a wave-bearing extension of the usual low-$Rm$ magnetohydrodynamics (MHD) approximation to identify two linear regimes: the purely diffusive regime exists when $N_{\omega }$, the ratio of the oscillation period to the time scale of diffusive two-dimensionalisation by the Lorentz force, is small; the propagative regime is governed by the ratio of the forcing period to the AW propagation time scale, which we call the Jameson number $Ja$ after (Jameson, J. Fluid Mech., vol. 19, issue 4, 1964, pp. 513–527). In this regime, AW are dissipative and dispersive as they propagate more slowly where transverse velocity gradients are higher. Both regimes are recovered in the FlowCube experiment (Pothérat & Klein, J. Fluid Mech., vol. 761, 2014, pp. 168–205), in excellent agreement with the model up to $Ja \lesssim 0.85$ but near the $Ja=1$ resonance, high amplitude waves become clearly nonlinear. Hence, in electrically driving AW, we identified the purely diffusive MHD regime, the regime where linear, dispersive AW propagate, and the regime of nonlinear propagation.

A phenomenological description is presented to explain the intermediate and low-frequency/large-scale contributions to the wall-shear-stress (${\tau }_w$) and wall-pressure ($\,{p}_w$) spectra of canonical turbulent boundary layers, both of which are well known to increase with Reynolds number, albeit in a distinct manner. The explanation is based on the concept of active and inactive motions (Townsend, J. Fluid Mech., vol. 11, issue 1, 1961, pp. 97–120) associated with the attached-eddy hypothesis. Unique data sets of simultaneously acquired ${\tau }_w$, ${p}_w$ and velocity-fluctuation time series in the log region are considered, across a friction-Reynolds-number ($Re_{\tau }$) range of $ {O}(10^3) \lesssim Re_{\tau } \lesssim {O}(10^6)$. A recently proposed energy-decomposition methodology (Deshpande et al., J. Fluid Mech., vol. 914, 2021, A5) is implemented to reveal the active and inactive contributions to the ${\tau }_w$- and $p_w$-spectra. Empirical evidence is provided in support of Bradshaw's (J. Fluid Mech., vol. 30, issue 2, 1967, pp. 241–258) hypothesis that the inactive motions are responsible for the non-local wall-ward transport of the large-scale inertia-dominated energy, which is produced in the log region by active motions. This explains the large-scale signatures in the ${\tau }_w$-spectrum, which grow with $Re_{\tau }$ despite the statistically weak signature of large-scale turbulence production, in the near-wall region. For wall pressure, active and inactive motions respectively contribute to the intermediate and large scales of the $p_w$-spectrum. Both these contributions are found to increase with increasing $Re_{\tau }$ owing to the broadening and energization of the wall-scaled (attached) eddy hierarchy. This potentially explains the rapid $Re_{\tau }$-growth of the $p_w$-spectra relative to ${\tau }_w$, given the dependence of the latter only on the inactive contributions.

Even though liquid foams are ubiquitous in everyday life and industrial processes, their ageing and eventual destruction remain a puzzling problem. Soap films are known to drain through marginal regeneration, which depends upon periodic patterns of film thickness along the rim of the film. The origin of these patterns in horizontal films (i.e. neglecting gravity) still resists theoretical modelling. In this work, we theoretically address the case of a flat horizontal film with a thickness perturbation, either positive (a bump) or negative (a groove), which is initially invariant under translation along one direction. This pattern relaxes towards a flat film by capillarity. By performing a linear stability analysis on this evolving pattern, we demonstrate that the invariance is spontaneously broken, causing the elongated thickness perturbation pattern to destabilise into a necklace of circular spots. The unstable and stable modes are derived analytically in well-defined limits, and the full evolution of the thickness profile is characterised. The original destabilisation process we identify may be relevant to explain the appearance of the marginal regeneration patterns near a meniscus and thus shed new light on soap-film drainage.

Large-eddy simulations (LES) of a hypersonic boundary layer on a $7^\circ$-half-angle cone are performed to investigate the effects of highly cooled walls (wall-to-recovery temperature ratio of $T_w / T_r \sim 0.1$) on fully developed turbulence and to validate a newly developed rescaling method based on volumetric flow extraction. Two Reynolds numbers are considered, $Re_m = 4.1 \times 10^6\ \text {m}^{-1}$ and $6.4 \times 10^6\ \text {m}^{-1}$, at free-stream Mach numbers of $M_\infty = 7.4$. A comparison with a reference laminar-to-turbulent simulation, capturing the full history of the transitional flow dynamics, reveals that the volumetric rescaling method can generate a synthetic turbulent inflow that preserves the structure of the fluctuations. Equilibrium conditions are recovered after approximately 40 inlet boundary layer thicknesses. Numerical trials show that a longer streamwise extent of the rescaling box increases numerical stability. Analyses of turbulent statistics and flow visualizations reveal strong pressure oscillations, up to $50\,\%$ of local mean pressure near the wall, and two-dimensional longitudinal wave structures resembling second-mode waves, with wavelengths up to 50 % of the boundary layer thickness, and convective Mach numbers of $M_c \simeq 4.5$. It is shown that their quasi-periodic recurrence in the flow is not an artefact of the rescaling method. Strong and localized temperature fluctuations and spikes in the wall-heat flux are associated with such waves. Very high values of temperature variance near the wall result in oscillations of the wall-heat flux exceeding its average. Instances of near-wall temperature falling below the imposed wall temperature of $T_w=300$ K result in pockets of instantaneous heat flux oriented against the statistical mean direction.

Ciliated microorganisms near the base of the aquatic food chain either swim to encounter prey or attach at a substrate and generate feeding currents to capture passing particles. Here, we represent attached and swimming ciliates using a popular spherical model in viscous fluid with slip surface velocity that affords analytical expressions of ciliary flows. We solve an advection–diffusion equation for the concentration of dissolved nutrients, where the Péclet number ($Pe$) reflects the ratio of diffusive to advective time scales. For a fixed hydrodynamic power expenditure, we ask what ciliary surface velocities maximize nutrient flux at the microorganism's surface. We find that surface motions that optimize feeding depend on $Pe$. For freely swimming microorganisms at finite $Pe$, it is optimal to swim by employing a ‘treadmill’ surface motion, but in the limit of large $Pe$, there is no difference between this treadmill solution and a symmetric dipolar surface velocity that keeps the organism stationary. For attached microorganisms, the treadmill solution is optimal for feeding at $Pe$ below a critical value, but at larger $Pe$ values, the dipolar surface motion is optimal. We verified these results in open-loop numerical simulations and asymptotic analysis, and using an adjoint-based optimization method. Our findings challenge existing claims that optimal feeding is optimal swimming across all Péclet numbers, and provide new insights into the prevalence of both attached and swimming solutions in oceanic microorganisms.

In this contribution, we develop a versatile formalism to derive unified two-phase models describing both the separated and disperse regimes as introduced by Loison et al. (Intl J. Multiphase Flow, vol. 177, 2024, 104857). It relies on the stationary action principle and interface geometric variables. This contribution provides a novel method to derive small-scale models for the dynamics of the interface geometry. They are introduced here on a simplified case where all the scales and phases have the same velocity and that does not take into account large-scale capillary forces. The derivation tools yield a proper mathematical framework through hyperbolicity and signed entropy evolution. The formalism encompasses a hierarchy of small-scale reduced-order models based on a statistical description at a mesoscopic kinetic level and is naturally able to include the description of a disperse phase with polydispersity in size. This hierarchy includes both a cloud of spherical droplets and non-spherical droplets experiencing a dynamical behaviour through incompressible oscillations. The associated small-scale variables are moments of a number density function resulting from the geometric method of moments (GeoMOM). This method selects moments as small-scale geometric variables compatible with the structure and dynamics of the interface; they are defined independently of the flow topology and, therefore, this model allows the coupling of the two-scale flow with an inter-scale transfer. It is shown, in particular, that the resulting dynamics provides partial closures for the interface area density equation obtained from the averaging approach.

The continental plates of Earth are known to drift over a geophysical time scale, and their interactions have led to some of the most spectacular geoformations of our planet while also causing natural disasters such as earthquakes and volcanic activity. Understanding the dynamics of interacting continental plates is thus significant. In this work, we present a fluid mechanical investigation of the plate motion, interaction and dynamics. Through numerical experiments, we examine the coupling between a convective fluid and plates floating on top of it. With physical modelling, we show the coupling is both mechanical and thermal, leading to the thermal blanket effect: the floating plate is not only transported by the fluid flow beneath, it also prevents the heat from leaving the fluid, leading to a convective flow that further affects the plate motion. By adding several plates to such a coupled fluid–structure interaction, we also investigate how floating plates interact with each other, and show that under proper conditions, small plates can converge into a supercontinent.

We identify forcing mechanisms that separately amplify subsonic and supersonic features obtained from a linearised Navier–Stokes based model for compressible parallel boundary layers. Resolvent analysis is used to analyse the linear model, where the nonlinear terms of the linearised equations act as a forcing to the linear terms. Considering subsonic modes, only the solenoidal component of the forcing to the momentum equations amplify these modes. When considering supersonic modes, we find that these are pressure fluctuations that radiate into the free stream. Within the free stream, these modes closely follow the trends of inviscid Mach waves. There are two distinct forcing mechanisms that amplify the supersonic modes: (i) the ‘direct route’, where the forcing to the continuity and energy equations and the dilatational component of the forcing to the momentum equations directly force the mode; and (ii) the ‘indirect route’, where the solenoidal component of the forcing to the momentum equations force a response in wall-normal velocity, and this wall-normal velocity in turn forces the supersonic mode. A majority of the supersonic modes considered are dominantly forced by the direct route. However, when considering Mach waves that are, like in direct numerical simulations, forced from the buffer layer of the flow, the indirect route of forcing becomes significant. We find that these observations are also valid for a streamwise developing boundary layer. These results are consistent with, and extend, the observations in the literature regarding the solenoidal and dilatational components of velocity in compressible turbulent wall-bounded flows.

Premixed hydrogen flames are prone to thermodiffusive instabilities due to strong differential diffusion effects. Reproducing these instabilities in large eddy simulations (LES), where their effects are only partially resolved, is challenging. Combustion models that account for differential diffusion effects have been developed for laminar flames, but to use them in LES, models for the turbulence/flame subfilter interactions are required. Modelling of the subfilter interactions is particularly challenging as instabilities synergistically interact with turbulence resulting in a strong enhancement of the turbulent flame speed. In this work, a combustion model for LES, which accounts for thermodiffusive instabilities and their interactions with turbulence, is presented. In the first part, an a priori analysis based on a direct numerical simulation (DNS) of a turbulent hydrogen/air jet flame is discussed. Progress variable, progress variable variance and mixture fraction are rigorously identified as suitable model input parameters, and an LES combustion model based on pre-tabulated unstretched premixed flamelets with varying equivalence ratio is formulated. Subfilter closure is achieved via a presumed probability density function and a significant reduction of modelling errors is achieved with the presented model. In the second part, LES of the DNS configuration are performed for an a posteriori analysis. The presented combustion model shows significant improvements in predicting the flame length and local phenomena, such as super-adiabatic temperature, compared with combustion models that either neglect differential diffusion effects or consider these effects but neglect the subfilter closure. Two variants of the model formulation with a water- or hydrogen-based progress variable have been tested, yielding overall similar predictions.

The current study characterizes the attenuation of instabilities in steady and unsteady shear layers by investigating shear-thinning flows downstream of a confined axisymmetric sudden expansion. Flow fields were captured using particle image velocimetry. Tested fluids exhibited approximate power-law indices of 1, 0.81, 0.61 and 0.47 and measurements were performed at mean throat-based Reynolds numbers of ${Re_m} = 4800$ and 14 400. Unsteady flows were tested at a Strouhal number and amplitude-to-mean velocity ratio of $St = 0.15$ and $\lambda = 0.95$, respectively. For unsteady shear layers, shear-layer roll-up regardless of shear-thinning strength was evidenced by collapse of average circulation over time. For steady shear layers, consistent shear-layer behaviour regardless of shear-thinning strength was evidenced by similar shear-layer trajectories and by growth rates in vorticity thickness. However, vorticity fields of the unsteady and steady shear layers, standard deviations of shear-layer trajectory, thickness of steady shear layers and Reynolds shear-stress spectra of the steady shear layers reveal an attenuation of shear-layer instabilities not captured by Reynolds number. Specifically, shear-layer instabilities exhibit increased diffusion with increasing shear-thinning strength and, in the case of steady shear layers, shear-thinning strength is shown to promote shear-layer stabilization. Also, evidenced by vorticity fields and through Reynolds shear-stress spectra, instabilities frequently coalesce into large rollers, a result that would suggest the presence of an inverse eddy cascade. The behaviour of shear-thinning fluids is shown to stabilize shear layers through attenuating shear-layer instabilities, complementing observations from previous studies showing how shear-thinning fluids promote turbulence in the dominant flow direction.

The bevelled nozzle is a promising noise control approach and has been tested to suppress the noise levels in supersonic circular jets, but not in rectangular jets so far. In this study, implicit large-eddy simulations are performed to analyse the noise control of supersonic rectangular jets with single- and double-bevelled nozzles. Three nozzle pressure ratios ($NPR = 2.3$, 3.0 and 5.0) are considered to form two over-expanded cold jets and one under-expanded cold jet, exhausted from a baseline convergent–divergent rectangular nozzle with an aspect ratio of 2.0. Results show that, with the increase of $NPR$, the oscillation of the jet plume is switched from a symmetrical mode to a flapping mode (preferential in the minor-axis plane), then to a helical mode, together with a reduction of the screech frequency. The amplitude of the screech tone is the strongest in the flapping jet, and the turbulent mixing noise is the most prominent in the helically oscillating jet. The single-bevelled nozzle induces asymmetric shock-cell structures and deflects the jet plumes, and the double-bevelled nozzle primarily enables the enhancement of the shear-layer mixing and shortens the lengths of the jet potential cores. With the bevelled nozzles, the gross thrusts of the baseline nozzle are increased by $0.05 \sim 7.38$ %. Details on the characteristics of far-field noise in the jets with/without the bevel cuts and their noise control mechanisms are discussed using the Ffowcs Williams–Hawkings acoustic analogy, dynamic mode decomposition and spatio-temporal Fourier transformation. Results suggest that the noise control has a close relationship with the destruction of well-organized coherent structures and the suppression of upstream-propagating guided-jet modes, which interrupt the feedback mechanism accounting for the generation of screech tones in the supersonic rectangular jets.

We report a comprehensive study of the wake of a porous disc, the design of which has been modified to incorporate a swirling motion at an inexpensive cost. The swirl intensity is passively controlled by varying the internal disc geometry, i.e. the pitch angle of the blades. A swirl number is introduced to characterise the competition between the linear (drag) and the azimuthal (swirl) momenta on the wake recovery. Assuming that swirl dominates the near wake and non-equilibrium turbulence theory applies, new scaling laws of the mean wake properties are derived. To assess these theoretical predictions, an in-depth analysis of the aerodynamics of these original porous discs has been conducted experimentally. It is found that, at the early stage of wake recovery, the swirling motion induces a low-pressure core, which controls the mean velocity deficit properties and the onset of self-similarity. The measurements collected in the swirling wake of the porous discs support the new scaling laws proposed in this work. Finally, it is shown that, as far as swirl is injected in the wake, the characteristics of the mean velocity deficit profiles match very well those of both laboratory-scale and real-scale wind-turbine data extracted from the literature. Overall, our results emphasise that, by setting the initial conditions of the wake recovery, swirl is a key ingredient to be taken into account in order to faithfully replicate the mean wake of wind turbines.

Topological properties of the spectrum of shallow-water waves on a rotating spherical body are established. Particular attention is paid to spectral flow, i.e. the modes whose frequencies transit between the Rossby and inertia–gravity wavebands as the zonal wavenumber is varied. Organising the modes according to the number of zeros of their meridional velocity, we conclude that the net number of modes transiting between the shallow-water wavebands on the sphere is null, in contrast to the Matsuno spectrum. This difference can be explained by a miscount of zeros under the $\beta$-plane approximation. We corroborate this result with the analysis of Delplace et al. (Science, vol. 358, 2017, pp. 1075–1077) by showing that the curved metric discloses a pair of degeneracy points in the Weyl symbol of the wave operator, non-existent under the $\beta$-plane approximation, each of them bearing a Chern number of $-1$.

In this paper, we study the rapid transition in Richtmyer–Meshkov instability (RMI) with reshock through three-dimensional double-layer swirling vortex rings. The rapid transition in RMI with reshock has an essential influence on the evolution of supernovas and the ignition of inertial confinement fusion, which has been confirmed in numerical simulations and experiments in shock-tube and high-energy-density facilities over the past few years. Vortex evolution has been confirmed to dominate the late-time nonlinear development of the perturbed interface. However, few studies have investigated the three-dimensional characteristics and nonlinear interactions among vortex structures during the transition to turbulent flows. The coexistence of co-rotating and counter-rotating vortices is hypothesized to induce successive large-scale strain fields, which are the main driving sources for rapid development. The three-dimensional effect is reflected in the presence of local swirling motion in the azimuthal direction, and it decreases the translation velocity of a vortex ring. Large-, middle- and small-scale strain fields are employed to describe the development process of RMI with reshock, e.g. vorticity deposited by the reshock, formation of the coexistence of the co-rotating and counter-rotating vortices, iterative cascade under the amplification of the strain fields and viscous dissipation to internal energy. This provides theoretical suggestions for designing practical applications, such as the estimation of the hydrodynamic instability and mixing during the late-time acceleration phase of the inertial confinement fusion.