We investigate solute dispersion in a two-phase system comprising a Casson fluid flowing in a tube and its surrounding wall phase that allows interphase solute exchange to mimic solute transport in blood and tissue phases. A pulsatile pressure gradient is imposed, and Gill’s classical methodology is extended to two-phase flows to analyse solute transport. The key parameters are the diffusivity ratio between wall and fluid phases ($\lambda$), the partition coefficient ($\beta _p$), the Womersley number ($\alpha$), the yield stress ($\tau _y$), the wall thickness ($\delta _h$) and the initial dimensionless radius of the solute source ($a$). In the long-time limit, increasing $\lambda$, $\beta _p$ and $\delta _h$ reduces the phase-averaged convection ($K_1$) and dispersion ($K_2$) coefficients, owing to solute accumulation in the wall where convective and shear-induced transport are absent. Short-time behaviour is dictated by the rate of solute transfer to the wall. Larger $\alpha$ enhances both $K_1$ and $K_2$, while larger $\tau _y$ suppresses them. The presence of a wall phase permits $K_2$ to reach $O(10^{0})$, compared with $K_2 \sim O(10^{-3})$ without a wall, and can delay the onset of steady state to dimensionless time $t \sim O(10^{2})$. Strong solute exchange and increasing wall thickness diminish downstream solute penetration, while non-Newtonian effects promote interphase transfer. These results provide mechanistic insight into solute exchange across fluid–wall interfaces, relevant to solute transport in blood flow and engineered permeable systems.

This study investigates finite-wall effects in vortex ring–wall interactions on flat circular plates with diameters $1.5D_n \leqslant D \leqslant 10D_n$, where $D_n$ is the nozzle diameter. Flow visualisation experiments were conducted across a broad range of vortex Reynolds numbers, ${\textit{Re}}_{\varGamma } \approx 600$–$2800$, while particle image velocimetry measurements were performed over a focused range of ${\textit{Re}}_{\varGamma } \approx 1300$–$1900$. The formation length was fixed at $L/D_n = 2$, where $L$ is the length of the ejected fluid slug. The plate sizes examined span from those reproducing the canonical infinite-wall behaviour to plates smaller than the vortex ring’s diameter. Three distinct regimes are identified based on the relative plate size: (i) ‘infinite’ plates where edge effects are negligible; (ii) ‘quasi-infinite’ plates where boundary-layer separation dominates but weak edge-generated vorticity emerges; and (iii) ‘finite’ plates where boundary-layer roll-up over the edge replaces surface separation, yielding strong edge effects. These regimes are established through vorticity contour analysis and flow visualisation, supported by quantitative measurements of circulation, trajectory, vortex-core velocity, eccentricity and boundary-layer separation. Within the explored range, geometric extent rather than Reynolds number governs the interaction dynamics. Finite-edge effects manifest through enhanced and earlier secondary vorticity formation, stronger primary vortex decay and elongated rebound trajectories with larger orbital periods. When the plate diameter becomes smaller than the vortex ring diameter, edge clipping rapidly disrupts the coherent vortex structures. The results provide a canonical framework for understanding finite-surface interactions and for distinguishing edge-induced dynamics from curvature or confinement effects observed in previous studies.

This paper describes a high-order strongly nonlinear (SNL) model for long waves in the presence of a variable bottom, which is a generalisation of the model for a flat bottom (Choi 2022a, J. Fluid Mech. vol. 945, A15). This asymptotic model written in terms of the bottom velocity is obtained using systematic expansion with a single small parameter measuring the ratio of the water depth to the characteristic wavelength and is found linearly stable at any order of approximation. To test the high-order SNL model with a variable bottom, we solve numerically the first- and second-order models using a pseudo-spectral method to study the deformation or generation of long waves over a variable bottom. Specifically, we consider two examples: (i) the propagation of cnoidal waves over a fixed bottom topography, and (ii) the forced generation of solitary waves by a submerged topography moving steadily with a transcritical speed. The computed results are then compared with the fully nonlinear computation using a boundary integral method as well as the numerical solutions of the weakly nonlinear long wave model. It is found that the second-order SNL model for the bottom velocity is suitable for stable numerical computations and produces accurate solutions even for a relatively large-amplitude initial wave or submerged topography.

The proposed study aims to optimise a real-time opposition control strategy to reduce the intensity of near-wall sweep events by applying a Bayesian optimisation algorithm. The experiments were conducted in a fully turbulent channel flow characterised by a friction Reynolds number of $350$. Sweep events were identified using a gradient-based detection technique and controlled via a wall-normal jet. An open-loop control logic was implemented and the control parameters (frequency, voltage amplitude and delay time) were optimised, within the bounds imposed by the experimental set-up, to bring the maximum sweep events intensity reduction up to $54\,\%$, with a robust cost function. The effects of the control were observed by analysing the conditionally averaged sweep events at various streamwise locations downstream of the actuation point. Moreover, the conditional analysis was applied to the cross-correlation function of velocity signals highlighting the large reduction of the sweep event convection velocity during the blowing phase of the jet. An overall energy increase has been found in the conditionally averaged energy spectra for the controlled case. The analysis of conditionally averaged wavelet spectra revealed that the control, by interrupting the natural evolution of the sweep event, initially leads to a reduction in the energy associated with it, followed by a subsequent increase during the development of the jet-blowing phase.

Direct numerical simulations are performed to investigate the receptivity and subsequent evolution of free-stream acoustic disturbances, including the associated instability mechanisms in a Mach 6 flow over a cone–cylinder–flare configuration. The geometry and flow parameters replicate an experimental study at the Purdue BAMQ6T facility (Benitez et al., AIAA Aviation 2020 Forum, 2020, p. 3072). The results are analysed to reveal new physical insights into boundary-layer separation, instability growth and nonlinear processes. The effects of changing wall thermal conditions from the experimental cold isothermal ($T_w = 30\,\text{K}$) to adiabatic (hot) are also examined. The basic state exhibits an attached boundary layer over the cone, followed by the formation of a separation bubble over the cylinder and flare, and reattachment over the aft section of the flare. In the case of a hot wall, the separation bubble size increases significantly compared with the isothermal case, leading to altered shear-layer dynamics and delayed reattachment with steeper gradients. Stability investigation reveals first- and second-mode disturbances as distinct spectral bands. Direct numerical simulation spectra and linear analysis indicate enhanced amplification of low-frequency first-mode disturbances for the adiabatic wall compared with the isothermal case. Bispectral analysis over the cone, centred at a second-mode wave, reveals weak subharmonic–fundamental coupling, but strong fundamental–fundamental coupling near the nosetip. The rapidly distorted mean flow within the separation bubble supports amplification of low-frequency disturbances, exhibiting an irregular spatial distribution, making it difficult to distinctly separate mutually exclusive modes (e.g. shear-layer or boundary-layer modes) due to their coexistence and influence on each other. Further downstream, the reattachment zone over the flare exhibits the combined effect of boundary layer and shear-generated waves, where distinct boundary-layer modes are evident at higher frequencies. Bispectral mode decomposition indicates strong phase-locked interaction along the leading-edge shock and within the separated and reattachment zones. These interactions are further amplified with increasing inflow forcing amplitude, leading to the formation of localised hotspots indicative of strong nonlinear amplification.

This study implements blowing/suction control for aerofoil trailing-edge noise and systematically optimises blowing/suction angles and control locations within a Bayesian framework. Two distinct rounds were conducted for direct and sound-source-oriented coarse-grained Bayesian optimisations. In the direct optimisation, the mean overall sound pressure level of far-field noise is selected as the objective function. Optimal control parameters were obtained after 15 iterations, requiring 80 three-dimensional implicit large eddy simulations, and achieved a noise reduction of up to 3.7 dB. To reduce the substantial computational cost, a Gaussian process surrogate model was constructed using the sound source defined by multi-process acoustic theory. This enabled a second round of optimisation, termed sound-source-oriented coarse-grained Bayesian optimisation, which yielded comparable noise reduction. This refined approach exhibited low signal delay and rapid statistical convergence, which can significantly reduce both the computational cost per sampling and the iteration number. Consequently, the total computational cost was reduced to approximately one-sixth of the initial direct optimisation. Moreover, physical insights into noise reduction mechanisms were elucidated through dynamic mode decomposition (DMD), anisotropic invariant mapping and the analysis of source terms within the TNO model across several typical cases. The results indicate that the blowing-control case induces large-scale vortex shedding and enhances DMD mode energy and low-frequency noise emission. Furthermore, the suction control tends to disrupt coherent structures, reduce DMD mode energy and suppress radiated noise. Crucially, the suction control significantly decreases mean velocity gradients within the logarithmic layer and suppresses wall-normal Reynolds stresses, thereby considerably reducing TNO source intensity in this critical region. The optimal case exhibits superior performance across all metrics above, thus laying the foundation for the optimal control strategy. Additionally, the suction control facilitates attenuating the footprint of turbulent motions in wall-pressure fluctuations through pressure-velocity coherence analysis, hence promoting noise reduction. This work introduces a novel framework that integrates Bayesian optimisation with advanced noise diagnostic theory, and provides actionable insights for effective trailing-edge noise mitigation.

The Earth’s quasi-biennial oscillation (QBO) is a natural example of wave–mean flow interaction and corresponds to the alternating directions of winds in the equatorial stratosphere. It is due to internal gravity waves (IGWs) generated in the underlying convective troposphere. In stars, a similar situation is predicted to occur, with the interaction of a stably stratified radiative zone and a convective zone. In this context, we investigate the dynamics of this reversing mean flow by modelling a stably stratified envelope and a convectively unstable core in polar geometry. Here, the coupling between the two zones is achieved self-consistently, and IGWs generated through convection lead to the formation of a reversing azimuthal mean flow in the upper layer. We characterise the mean flow oscillations by their periods, velocity amplitudes and regularity. Despite a continuous broad spectrum of IGWs, our work shows good qualitative agreement with the monochromatic model of Plumb & McEwan (1978, J. Atmos. Sci. vol. 35, no. 10, pp. 1827–1839). While the latter was originally developed in the context of the Earth’s QBO, then our study could prove relevant for its stellar counterpart in massive stars, which host convective cores and radiative envelopes.

A combined experimental and numerical investigation was conducted to examine the mechanisms of aerodynamic noise reduction for twisted hexagonal cylinders at Reynolds numbers ($ \textit{Re} = 2\times 10^4$–$10^5$) and twist angles per unit span $\gamma ^*\in \mathbb{R}[0,1/3]$. It reveals a non-monotonic dependence of noise reduction on $\gamma ^*$, optimised for $\gamma ^* = 1/6$, where a tonal noise reduction of 15 dB and a total sound reduction of 11 dB at $ \textit{Re} = 2\times 10^4$ were achieved. This was consistent across all Reynolds numbers tested. Additionally, dual tones were observed in the noise spectra for cases with $1/18\leqslant \gamma ^* \lt 1/6$, leading to the identification of two distinct flow patterns (Pattern I and II) based on the number of tones in the spectrum. Large-eddy simulations were performed at $ \textit{Re} = 2\times 10^4$ to support the acoustic measurements. Spanwise variations in flow separation gave rise to two distinct regimes: separation (RI) and reattachment (RII). For Pattern I ($1/5.4 \leqslant \gamma ^* \leqslant 1/3$), the spanwise variation of shear layer separation induced wavy vortex shedding, contributing to a moderate noise reduction. For Pattern II ($1/18 \leqslant \gamma ^* \leqslant 1/7.2$), differences in vortex shedding frequencies between RI and RII regimes led to vortex dislocation, forming C- or X-type vortex structures. The $\gamma ^* = 1/6$ configuration leads to a transitional pattern between Pattern I and II, where modulation was predominantly observed in the RI regime. The superior noise reduction of $\gamma ^* = 1/6$ stems from the combined effects of frequent vortex dislocation and modulation, which reduces spanwise coherency and increases wake three-dimensionality.

This study investigates the heat-flux enhancement of convection flows inside a fluid layer bounded from the top and bottom by two inhomogeneous porous layers. The porous matrix is made of solid materials with very high diffusivity. The numerical results reveal that, compared with the traditional convection system, the heat flux is greatly increased when the thickness of porous layer is large enough. At small Rayleigh numbers, the enhancement is the result of the increase in effective diffusivity in the fluid-saturated porous layers and the reduction in flow friction at the porous interface. For large Rayleigh numbers, the permeable motions across the interfaces generate strong convective flux, which greatly increases the total heat flux. For the latter parameter range, the exponent of the power-law scaling between the Nusselt number and the Rayleigh number exceeds 1/2, which is the value of the ultimate scaling. Our findings are not only of great potential in heat management in various industrial applications but also imply that, in many natural systems with imperfect boundaries, the global heat flux may be much stronger than the prediction by using a convection system with perfect boundaries.

This paper explores dispersive shock waves (DSWs) of gravity-capillary waves within the framework of the two-dimensional, fully nonlinear Euler equations. In this system, initial wave profiles characterised by a smooth step function evolve into modulated wavetrains that connect different constant states, a phenomenon arising from the interplay between nonlinear and dispersive effects. The Bond number, which quantifies the relative significance of gravity compared to surface tension, is crucial in determining the behaviour of the DSW solution. As the Bond number increases from zero, solutions traverse four distinct zones: the radiating DSW region, an unstable crossover region, the travelling DSW region, and the inverse radiating DSW region. The propagation velocities of DSWs can be estimated using the DSW fitting method alongside numerical results from travelling waves. Particular attention is given to travelling DSWs, which are characterised by a uniform wavetrain followed by an oscillatory decaying wavepacket. Notably, the high platform and its extended periodic wavetrain can be part of a specific type of gravity-capillary solitary wave that features an oscillatory pulse, with the number of oscillations at the core potentially increasing indefinitely. The Whitham modulation theory for the Euler equations is employed to describe the modulation parameters – such as wavenumber, amplitude and wave mean – in the travelling DSW region. Finally, we discuss the bifurcation mechanism of solitary waves with oscillatory pulses in the Euler equations, along with analyses of their stability. It is also demonstrated that for relatively small Bond numbers, a series of trapped bubbles can occur along the bifurcation curves, representing the limiting configuration of this type of solitary wave.

We report an experimental study on the effects of polymer additives in the dissipative-scale flow field properties in turbulent Rayleigh–Bénard convection. The experiments were conducted in a cylindrical convection cell with a minute amount of polyacrylamide long-chain polymer. The local velocity gradient tensor was measured using an integrated home-made measurement system (J. Fluid Mech., 2024, vol. 984, p. A8). Although the single-roll large-scale circulation persists (owing to the slight tilt of the convection cell), polymers induce an anisotropic suppression of the dissipative-scale flow properties. The normal velocity gradient components are suppressed more than the shear components. The mean energy dissipation rate in both centre and side regions decreases, then levels off with increasing polymer concentration and the final reduction ratio exceeds 50 % in each region. In the side region, adding polymers has a stronger stabilising effect on the strain rate than the rotation. The anisotropic suppression of the velocity gradient tensor affects dissipation-rotation co-occurrence probability, velocity gradient triple decomposition and local streamline topology. Adding polymers also induces a deceleration effect and increases the contribution of local buoyancy in driving the flow. These results reveal that the addition of polymers can non-trivially manipulate dissipative-scale turbulence fields and energy cascades.

Predicting unsteady loads on plate-like objects during unsteady motion is important in many applications, such as ship manoeuvring, flight and biological propulsion. The drag force on a starting plate that moves normal to its surface can be severely underestimated during the acceleration phase when conventional methods are used to incorporate the effects of acceleration. These methods often introduce an inviscid added mass force that has its origin in potential flow. However, the flow field around a starting plate quickly diverges from potential flow after the start of the motion due to the continuous creation of vorticity at the plate surface. Following the concept of drag by Burgers (1921 Proc. K. Ned. Akad. Wet. 23, 774–782), we propose a model to predict the creation of vorticity on the plate surface and its advection into the vortex loop at the plate edges, based on Stokes’ first problem. This model shows that the acceleration drag force is a history force, in contrast to the inviscid added mass force that is proportional to the instantaneous acceleration of the plate. We perform experiments on starting plates over a large range of accelerations, velocities, fluid viscosities and plate geometries for which the model gives accurate predictions for the drag force during acceleration and during the relaxation phase immediately after the acceleration ceases. This model is extended to also predict the drag forces on accelerating plates during a starting motion with a non-constant acceleration.

Dynamics of spheroidal particle migration within the elasto-inertial square duct flow of Giesekus viscoelastic fluids were studied by using the direct forcing/fictitious domain method. The results show rich migration behaviours, a spheroidal particle gradually transitions from the corner (CO), channel centreline (CC), inertial rotational (IR), diagonal line and cross-section midline equilibrium positions with a decrease in the elastic number, depending on the initial particle position, initial particle orientation and fluid elasticity. From the effect of secondary flow, the IR equilibrium position is reported when the fluid inertia is relatively strong. Six (five) kinds of rotational behaviours are observed for the elasto-inertial migration of prolate (oblate) spheroids. Moreover, the critical elastic number is determined for the migration of spheroidal particles in Giesekus fluids. Near the critical elastic number, oblate and prolate spheroids can simultaneously maintain the CC, CO and IR equilibrium positions, and the initial orientation of particles affects their final rotational modes and equilibrium positions. Through comprehensive analysis, empirical formulas governing the ability of oblate and prolate spheroids to maintain the CC equilibrium position are proposed as $\textit{Wi} = 0.055\,\textit{Re}{-0.1}$ and Wi = 0.045 Re−0.35 when n = 0.5, 0.01 ≤ Wi ≤ 1. Due to the different directions of the pressure forces acting on the particles and the forces from the first normal stress difference and the second normal stress difference, the equilibrium position in Giesekus fluids is rapidly increased by increasing the secondary flow at higher elastic numbers, which is contrary to the phenomenon observed in the Oldroyd-B fluid.

Rough walls are commonly encountered in engineering applications. However, existing understanding of combustion in the turbulent boundary layer over rough walls is lacking. This study investigates turbulent boundary layer premixed flame flashback over rough walls using direct numerical simulations for the first time. The features of boundary layer flashback over walls with various roughness are explored in terms of flame morphology and flashback speed. It is found that the flame in rough-wall cases is more wrinkled compared with the smooth-wall case, particularly in the near-wall region, due to the presence of more small-scale vortical structures. Wall roughness reduces the flame flashback speed, which is attributed to the higher flow velocity at the leading edge of the flame front in rough-wall cases. The effects of wall roughness and combustion on boundary layer turbulence are revealed through two-point correlations of fluctuating velocity and wall resistance. The results show that, under non-reacting conditions, wall roughness reduces the streamwise and wall-normal extents of near-wall hairpin packets of boundary layer turbulence while increasing their inclination angles. Under reacting conditions, combustion further increases the inclination angle, with a more pronounced effect in rough-wall cases. Wall roughness influences wall resistance, primarily through its pressure component. Flame/wall interactions are also scrutinised, revealing higher wall heat loss in rough-wall cases, which is is mainly attributed to the increased wall surface area. A negative correlation between the quenching distance and the alignment of flame normal and wall normal is observed in rough-wall cases, which is weaker in smooth-wall cases.

The mixing mechanism within a single vortex has been a theoretical focus for decades, while it remains unclear especially under the variable-density (VD) scenario. This study investigates canonical single-vortex VD mixing in shock–bubble interactions (SBI) through high-resolution numerical simulations. Special attention is paid to examining the stretching dynamics and its impact on VD mixing within a single vortex, and this problem is investigated by quantitatively characterising the scalar dissipation rate (SDR), namely the mixing rate, and its time integral, referred to as mixedness. To study VD mixing, we first examine single-vortex passive-scalar (PS) mixing with the absence of a density difference. Mixing originates from diffusion and is further enhanced by the stretching dynamics. Under the axisymmetry and zero diffusion assumptions, the single-vortex stretching rate illustrates an algebraic growth of the length of scalar strips over time. By incorporating the diffusion process through the solution of the advection–diffusion equation along these stretched scalar strips, a PS mixing model for SDR is proposed based on the single-vortex algebraic stretching characteristic. Within this framework, density-gradient effects from two perspectives of the stretching dynamics and diffusion process are discovered to challenge the extension of the PS mixing model to VD mixing. First, the secondary baroclinic effect increases the VD stretching rate by the additional secondary baroclinic principal strain, while the algebraic stretching characteristic is still retained. Second, the density source effect, originating from the intrinsic nature of the density difference in the multi-component transport equation, suppresses the diffusion process. By accounting for both the secondary baroclinic effect on stretching and the density source effect on diffusion, a VD mixing model for SBI is further modified. This model establishes a quantitative relationship between the stretching dynamics and the evolution of the mixing rate and mixedness for single-vortex VD mixing over a broad range of Mach numbers. Furthermore, the essential role of the stretching dynamics on the mixing rate is demonstrated by the derived dependence of the time-averaged mixing rate $\overline {\langle \chi \rangle }$ on the Péclet number ${\textit{Pe}}$, which scales as $\overline {\langle \chi \rangle } \sim {\textit{Pe}}^{{2}/{3}}$.

In the fully developed region of a plane turbulent wall jet, the key jet parameters, including the jet velocity Um, jet half-width z1/2 and wall shear stress $ \tau_{0}$, follow the classical power-law scaling with the streamwise distance x: Um$v$/M0 ∼ (xM0/$v$2)−α, z1/2M0/$v$2 ∼ (xM0/$v$2)β and $ \tau_{0}$$v$2/(ρ$M_{0}^{2}$) ∼ (xM0/$v$2)−χ, where M0 is the source kinematic momentum flux, $v$ is the coefficient of kinematic viscosity of fluid, ρ is the mass density of fluid and α, β and χ are the positive scaling exponents. We present a theoretical framework to determine these exponents. Our framework reveals that each jet parameter exhibits a scaling transition. This transition is driven by a shift in the scaling law of the skin-friction coefficient as the Reynolds number Rem = Umzm/$v$ changes over from Rem < 8000 to Rem > 10 000, where zm is the wall-normal location corresponding to the jet velocity. Specifically, α transitions from 4(1 + γ)/(9 − γ) to 13(1 + γ)/[2(14 − γ)], β from 8/(9 − γ) to 13/(14 − γ) and χ from (9 + 7γ)/(9 − γ) to (14 + 12γ)/(14 − γ), where γ ≈ 0.05 is a parameter determined from experiments. We validate the theoretical predictions against extensive experimental datasets from the literature.

The dynamics of a fluid flow about its limit cycle can be analysed through phase reduction analysis – an approach that distils a high-dimensional dynamical system to its scalar phase dynamics. This technique provides insights into phase sensitivity, revealing the mechanisms that advance or delay phase dynamics. The phase-based reduced-order model derived from this approach serves as a foundation for identifying lock-on conditions and designing flow control techniques. Recent work by Sumanasiri et al. (J. Fluid Mech. vol. 1020, 2025, R4) applied phase reduction analysis to the fluid–structure interaction problem of aerofoil flutter in a free stream. Their analysis systematically changed the stiffness of the structural dynamics to decipher the phase dynamics mechanism of flutter. Moreover, they considered the use of optimised heaving motion to suppress the emergence of flutter. Their approach opens new avenues for modifying flow physics through innovative modifications of material properties and structural dynamics.