The dynamic behaviours of an axisymmetric ferrofluid jet, surrounded by a non-magnetisable and immiscible fluid of equal density, are investigated from both asymptotic and numerical perspectives. This two-layer system consists of incompressible, inviscid fluids that flow irrotationally within each layer. Based on the expansions of the axisymmetric Dirichlet–Neumann operators developed by Xu & Wang (2025 J. Fluid Mech., vol. 1002, p. A23), strongly nonlinear longwave models – without assuming small wave amplitudes – are derived in various limits from the magnetised Euler equations within the Hamiltonian framework. In the supercritical regime, where the magnetic field is strong enough to completely suppress the Rayleigh–Plateau instability, these models show good agreement with the full Euler equations for monotonic solitary waves. This is particularly true concerning wave profiles and speed–energy bifurcations, even when the wave trough approaches the rigid bottom. Thus, these models overcome the limitations of the cubic full-dispersion model proposed in previous studies. An analytic criterion related to wave energy for the stability exchange of axisymmetric interfacial solitary waves under longitudinal perturbations is established for the full Euler equations. Guided by this criterion, the dynamic evolution of unstable solitary waves is then numerically solved using the derived strongly nonlinear equations. In the subcritical regime, the flow experiences the Rayleigh–Plateau instability. The phenomenon of singularity is examined in a configuration where the thickness of the outer layer is infinite, employing a newly proposed model that incorporates a non-local operator. It is demonstrated that infinite-slope singularities arise before pinching for most initial conditions; however, pinching may occur for sufficiently small initial amplitudes.

The flat plate transitional boundary layer response to the acceleration induced by the shock wave propagation is studied using large-eddy simulations. The steady boundary layer global behaviour is first investigated before focusing on the transient response of a turbulent region following the shock wave propagation. It is shown that the transient response of the turbulent region exhibits strong similarities with the spatial transition process to turbulence induced by free-stream turbulence, the so-called bypass transition. The boundary layer does not evolve gradually from the initial turbulence intensity to the final turbulence intensity but undergoes a temporal transition process composed of three distinct phases. These three different phases are comparable with the three stages of a bypass transition (i.e. buffeted laminar flow, transition and fully turbulent) because they are governed by the same physical processes. On the other hand, it is highlighted that this temporal response is identical to that described by He & Seddighi (J. Fluid Mech., vol. 715, 2013, pp. 60–102) during the study of an incompressible boundary layer undergoing an increase of mass flow rate. The boundary layer compression by the shock propagation does not contribute to any significant change in the turbulence dynamic after an unsteady acceleration.

An analytical theory is developed that describes acoustic microstreaming produced by the interaction of an oscillating gas bubble with a viscoelastic particle. The bubble is assumed to undergo axisymmetric oscillation modes, which can include radial oscillation, translation and shape modes. The oscillations of the particle are excited by the oscillations of the bubble. No restrictions are imposed on the ratio of the bubble and the particle radii to the viscous penetration depth and the separation distance, as well as on the ratio of the viscous penetration depth to the separation distance. Capabilities of the developed theory are illustrated by computational examples. The shear stress produced by the acoustic microstreaming on the particle’s surface is calculated. It is shown that this stress is much higher than the stress predicted by Nyborg’s formula (1958 J. Acoust. Soc. Am. 30, 329–339), which is commonly used to evaluate the time-averaged shear stress produced by a bubble on a rigid wall.

Active colloidal particles create flow around them due to non-equilibrium processes on their surfaces. In this paper, we infer the activity of such colloidal particles from the flow field created by them via deep learning. We first explain our method for one active particle, inferring the $2s$ mode (or the stresslet) and the $3t$ mode (or the source dipole) from the flow field data, along with the position and orientation of the particle. We then apply the method to a system of many active particles. We find excellent agreements between the predictions and the true values of activity. Our method presents a principled way to predict arbitrary activity from the flow field created by active particles.

The acoustic receptivity of Tollmien–Schlichting (TS) waves due to two-dimensional sharp-edged rectangular bumps and gaps in a compressible boundary layer was investigated by direct numerical simulations. The conclusions were based on a new procedure proposed for obtaining the receptivity amplitudes which appeared to be more robust and accurate than previous ones. The procedure is particularly important for the correct evaluation of the receptivity of gaps. The receptivity amplitudes for gaps were smaller than those for bumps, except for the nominally zero height/depth roughness element, where, consistent with a linear behaviour, they had the same absolute value. The procedure also revealed in detail the behaviour in the region downstream of the roughness element where the TS wave is formed (the formation region). This region extends for approximately $50\delta ^*_{b}$, regardless of bump height or gap depth. For bumps, the receptivity scaled superlinearly with bump height while for the gaps it scaled sublinear with depth. This behaviour is associated with the different velocity profiles caused by bumps and gaps in the formation region. We also discussed issues regarding comparison with experiments. Investigation of the effect of compressibility confirmed that, in the subsonic regime, the receptivity reduces with Mach number. Finally, we addressed the receptivity scaling with the acoustic wave amplitude. It was found that the receptivity scales linearly with the acoustic wave amplitude in a range for which experiments available in the literature indicated a superlinearly scaling. Reasons for these conflicting results are discussed.

The convection velocity in high-Reynolds-number pipe flow was investigated using two-point correlations obtained from two laser Doppler velocimetry systems. The Reynolds number ranged from ${\textit{Re}}_{{\tau}}=3000$ to 20 800, and profiles were obtained from $y/R=0.002$ up to the pipe centre, where $R$ is the pipe radius. This study examines the scaling behaviour of convection velocity profiles derived from raw velocity signals, and the convection characteristics of very large-scale motions (VLSMs) and large-scale motions extracted via scale-separated or time-resolved velocity signals. The profiles show that convection velocities from raw signals exceed the local mean velocity near the wall and gradually approach it toward the centre. These profiles can be scaled using inner variables, namely $y^+$ and $\Delta x^+$, where $\Delta x^+$ represents the measurement distance. Scale-separated convection velocities for VLSM-scale structures – defined as those larger than $5R$ – were higher than the unfiltered values and remained nearly constant up to $y^+ \leq 2000$ at ${\textit{Re}}_{{\tau}} \approx 20\,000$. In this constant region, the convection velocity of VLSMs scaled well with the bulk velocity $U_{\textit{b}}$, taking values of approximately $0.85U_{\textit{b}}$. Furthermore, analysis of the time-resolved data highlights that, when applying Taylor’s frozen turbulence hypothesis, it is essential to consider both the scale dependence and the temporal fluctuations of the convection velocity, which reflect the underlying spatio-temporal dynamics of the flow structures. The present study provides valuable data for discussions on converting frequency-domain measurements into wavenumber space using Taylor’s hypothesis.

A new mode of flame propagation from a wall in a mixture below the flammability limit is described. We consider a simple chemistry model in which the reaction rate vanishes for temperatures below some critical cutoff value. Two models for flame initiation by the wall are considered. The first model assumes heat release by the wall over a finite time, after which it becomes adiabatic. The second model assumes that the wall temperature changes according to a given law. Unlike the standard flame propagation mode, in which the flame propagates at a constant velocity through the unburned mixture, and which is not possible under the considered conditions, in the new mode the flame moves at a speed inversely proportional to the square root of time. It is found that the value of the fuel Lewis number, $\textit{Le}$, is determinant: the new mode of propagation exists only if $\textit{Le}\lt 1$. The influence of thermal expansion on the existence of this new propagation regime is investigated. It is interesting to note that the flame structure resembles the classical Stefan solution for phase-transition front propagation. However, the fundamental difference is that in the classical phase-transition front propagation problem the Lewis number is infinite, in our nomenclature, while the new flame propagation regime arises at $\textit{Le}\lt 1$.

The performance of the wavy leading edge (WLE) on the self-noise from a cambered NACA 65(12)-10 airfoil at a Reynolds number of 100 000 is investigated in this paper. The self-noise from the airfoils is measured in an anechoic wind tunnel while the flow details are obtained from both planar particle image velocimetry measurements and the wall-resolved large eddy simulations. It turns out that the WLE is effective in reducing both the tonal and the broadband separation noise in the mid-to-low-frequency range from the baseline airfoil. The underlying mechanisms of the noise reduction are also examined carefully from both the tonal and the broadband aspects. By introducing the WLE, the generated streamwise vortices can modify the boundary-layer development and reduce the spanwise coherence of the flow structures. As a consequence, the acoustic feedback loop responsible for the tonal noise from the baseline airfoil is disturbed. Additionally, the WLE decreases the convection velocity and generates less coherent wall pressure fluctuations in the low-to-mid-frequency range, leading to broadband separation noise reduction.

An important problem in passive scalar transport is to parametrize the effect of a fluctuating component of the flow, in order to overcome a limited resolution. A local effective diffusivity is one such parametrization, and over the years there have been many different suggestions for ‘closures’ that relate the advective flux to gradients of the mean concentration. Souza et al. (J. Fluid Mech., 2023, in press) introduce a stochastic framework where the local effective diffusivity is replaced by an exact effective diffusivity operator. By computing this operator for various examples, they quantify deviations from the local approximation, which can suggest areas of improvement and novel closure models.

The rheology of bubble suspensions is critical for the prediction and control of bubbly flows in various industrial processes. It is well known that bubble suspensions exhibit shear-thinning behaviour due to bubble shape deformation under pure shear, but the shear rheological response to dilatation under time-varying pressure remains unexplored. Here, we propose a constitutive equation for dilute bubble suspensions that accounts for both shear and dilatational effects, demonstrating that bubble compressibility can significantly influence the shear viscosity under time-varying pressures. Under constant-rate pressure variations, compression leads to a progressive reduction in viscosity, whereas decompression induces an increase. This peculiar compression-thinning behaviour arises microscopically from the fact that a shrinking bubble surface effectively weakens the flow resistance of the surrounding liquid. Under oscillatory pressure, the amplitude of the dilatation-induced viscosity grows with frequency, and the phase shift of the shear stress response transitions from $-\pi /2$ to $-\pi$. Notably, viscosity troughs emerge during oscillation cycles, leading to transient flow resistance lower than that in pure shear, indicating a potential route for drag reduction when combined with shear-thinning. These findings highlight bubble compressibility as a controllable factor for tuning bubbly flow rheology, with potential for enhanced flow efficiency in practical applications.

We study the collective behaviour of clusters of cylinders placed in the wake of a fixed cylinder and free to move in a direction perpendicular to that of the incoming flow, with no structural damping or stiffness. We keep the Reynolds number, defined based on the cylinder diameter, at 100 and consider five different configurations for the initial positions of the cluster cylinders: linear, rectangular, V-shaped, triangular and circular. In each configuration, we consider progressively increasing numbers of cylinders in the cluster. We show that overall, the cylinders tend to form final linear configurations, in which, after their transition, the cylinders form one or more lines. Some free-to-move cylinders might take the lead position in some of these linear formations depending on the initial configuration. These steady-state positions are achieved when the mean value of lift that acts on the cylinders becomes negligible. As a byproduct of these reconfigurations, the overall drag force that acts on the collection of cylinders reduces at their final steady-state locations in comparison with their original configurations. The complicated wakes that are observed in the fixed counterparts of these configurations are replaced by a series of vortex rows in the wake of separate lines of cylinders. Reducing the mass ratio allows the cylinders to oscillate about their mean displacement paths, but their transient paths and their final steady-state positions are not affected significantly by the decrease in the mass ratio.

We use the entropy method to analyse the nonlinear dynamics and stability of a continuum kinetic model of an active nematic suspension. From the time evolution of the relative entropy, an energy-like quantity in the kinetic model, we derive a variational bound on relative entropy fluctuations that can be expressed in terms of orientational order parameters. From this bound we show isotropic suspensions are nonlinearly stable for sufficiently low activity, and derive upper bounds on spatiotemporal averages in the unstable regime that are consistent with fully nonlinear simulations. This work highlights the self-organising role of activity in particle suspensions, and places limits on how organised such systems can be.

We recently lost a valuable colleague and friend, Paul Steen, and the text below is a brief overview of his life.

We have performed numerical simulations to investigate the phenomenon of axial pattern formation exhibited by a non-neutrally buoyant concentrated suspension. Continuum modelling of the concentrated suspension is done using the suspension balance model to identify the underlying mechanism of the phenomenon. We demonstrate that axial concentration variations become amplified to axial bands owing to the influence of the second normal stress difference ($N_2$), and the first normal difference ($N_1$) accentuates the effect of $N_2$. We demonstrate that the end walls of the rotating cylinder are necessary to prevent the smearing out of axial bands but are not a direct cause of the phenomenon.

We present three-dimensional direct numerical simulations of turbulent Rayleigh–Bénard convection in a closed rectangular box whose width $L_y$ and length $L_x$ are 0.8 and 2.4 times the height $H$, respectively. The Rayleigh number $\textit{Ra}$ varies from $10^5$ to $10^{10}$, and the Prandtl number is unity. The advantages of the present configuration are: (a) a relatively stable unidirectional large-scale circulation, consisting of two counter-rotating rolls, fills the cell and fixes the thermal plume ejection- and shear-dominated regions, in contrast to those in closed cylindrical cells. (b) The regions of plume ejection are essentially independent of the sidewalls so that their autonomous existence can be studied. This is because there is some space, or ‘fetch’, for the velocity and thermal boundary layers to develop along the length. (c) This geometry allows one to study the influence of locally thin and thick boundary layers (which follow larger or smaller plume activity) on the scaling of convection properties. In regions of larger plume activity (defined by an incessant movement of plumes), the temperature fluctuation as well as the normalised thermal and viscous dissipation rates decay more slowly with $\textit{Ra}$ than in regions of lower activity. Both viscous and thermal boundary layers thin down rapidly with increasing distance from the plume ejection region. The local thicknesses of both boundary layers decline more rapidly with $\textit{Ra}$ in the ejection region than in regions of impact and shear, where they are similar to each other. Despite these details, the global heat transport laws are practically the same as those in other configurations of low to moderate aspect ratios.