The coupling between Rayleigh–Taylor (R–T) and Saffman–Taylor (S–T) instabilities, when a gas displaces a high-viscosity liquid, remains challenging to elucidate due to the unclear roles of density and viscosity contrasts. Counterintuitively, our radial Hele-Shaw cell experiments revealed that viscosity contrast – typically considered a damping factor – serves as the primary driver of instability. We observed that the glycerin–air interface, despite its higher viscosity, exhibits significantly greater instability than the water–air interface. This anomalous behaviour arises from the S–T mechanism, which accelerates the onset of nonlinearity and induces an early transition to fingering. We applied a unified model to decouple the competing influences of surface tension oscillation and viscous damping on R–T instability and the S–T destabilisation. Moreover, we proposed criteria for either mostly enhancing or completely freezing the instability. These findings offer valuable insights into manipulating hydrodynamic instabilities in contracting/expanding geometries through surface tension and viscosity.

High-intensity focused ultrasound (HIFU) is a non-invasive alternative to traditional surgery for detection and treatment. When HIFU targets a specific area, ultrasonic cavitation occurs with mechanical stress, causing tissue damage, a process that is significantly influenced by the surroundings. This paper presents a numerical study on the cavitation initiation and evolution mechanisms under focused ultrasonic waves considering the influence of a solid surface. Firstly, the dynamic property of focused ultrasonic waves and the generation of diffraction waves is explained based on the Huygens–Fresnel principle, and the prefocused phenomenon is analysed. Notably, the scenario considering the existence of a solid wall is discussed, with the corresponding cavitation clouds in a ‘tree-like’ pattern that can be generally divided into three or four subregions. The different initiation mechanisms of the near-wall cavitation clouds under a different relative distance between the theoretical focal point and the solid wall are discussed in detail. Finally, by considering the effects of the incident waves, scattered waves and their reflected waves on the solid wall, a wave superposition model is established that can clearly explain the distribution characteristics of the near-wall cavitation clouds with different modes. The understanding of the ultrasonic cavitation mechanism may support precise control in future HIFU applications.

This paper presents the first experimental measurement of the Prandtl–Meyer function in the non-ideal compressible flow regime. Planar contoured nozzle profiles expand the flow to the supersonic regime, providing a uniform parallel flow of siloxane MM (hexamethyldisiloxane, $\textrm{C}_{6}\textrm{H}_{18}\textrm{OSi}_{2}$). Prandtl–Meyer expansions are then generated at sharp convex corners, for discrete flow deflection angles from 5$^\circ$ to 30$^\circ$. Stagnation pressures and temperatures are measured in the settling chamber, immediately upstream of the test section, to estimate the level of non-ideality of the investigated flows, ranging from mild non-ideal conditions to dilute ideal-gas states. Non-ideal thermodynamic effects through the expansions are characterised by means of independent measurements of Mach number by schlieren visualisations, and static pressure. Experimental comparisons across different thermodynamic states confirm the role of the compressibility factor evaluated at total conditions as a similarity parameter for moderately high non-ideal flows. To extract values of the Prandtl–Meyer function from the measurements, a simplified analytical model for the Prandtl–Meyer function dependency on the Mach number is formulated. The recovered values agree with Prandtl–Meyer theory, complemented with state-of-the-art thermodynamic models, for all the examined operating conditions.

The effect of a smooth surface hump on laminar–turbulent transition over a swept wing is investigated using direct numerical simulation (DNS), and results are compared with wind tunnel measurements. When the amplitude of incoming crossflow (CF) perturbation is relatively low, transition in the reference (without hump) case occurs near $53\,\%$ chord, triggered by the breakdown of type I secondary instability. Under the same conditions, no transition is observed in the hump case within the DNS domain, which extends to $69\,\%$ chord. The analysis reveals a reversal in the CF velocity component downstream of the hump’s apex. Within this region, the structure and orientation of CF perturbations are linearly altered, particularly near the wall. These perturbations gradually recover their original state further downstream. During this recovery phase, the lift-up mechanism is weakened, reducing linear production, which stabilises the stationary CF perturbations and weakens spanwise gradients. Consequently, the neutral point of high-frequency secondary CF instability modes shifts downstream relative to the reference case, leading to laminar–turbulent transition delay in the presence of the surface hump. In contrast, when the amplitude of the incoming CF perturbation is relatively high, a pair of stationary counter-rotating vortices forms downstream of the hump. These vortices locally deform the boundary layer and generate regions of elevated spanwise shear. The growth of secondary instabilities in these high-shear regions leads to a rapid advancement of transition towards the hump, in agreement with experimental observations.

We investigate the occurrence of flow circulation in an open triangular cavity filled with a gas at highly rarefied conditions. The cavity is subject to an external shear flow that is in either the circular or linear direction at its inlet. The problem is studied analytically in the free-molecular limit and numerically based on the direct simulation Monte Carlo (DSMC) method. The corner walls are modelled based on the Maxwell boundary condition, as either specular or diffuse. The results are obtained for arbitrary values of the outer flow speed and corner angle. Remarkably, it is found that multiple recirculation zones occupy the corner domain in the absence of molecular interactions. In the specular-corner set-up, such topologies occur at non-large outer-flow speeds and distinct corner-angle intervals of $[\pi /(n+1),\pi /n]$ with $n=3,5,\ldots$. In the diffuse-wall case, the cavity flow field contains two recirculation zones at sufficiently low corner angles for both circular and straight outer flows. With increasing angles, the straight-flow configuration differs, reducing the number of vortices to one and then none. The results are rationalised based on ballistic particle kinematics, suggesting insight into the relation between the microscopic description and the hydrodynamic (observed) generation of circulation. The effects of molecular collisions on the corner flow pattern, as well as more elaborate gas-surface interaction models, are inspected based on DSMC calculations, indicating visible impacts on the macroscopic flow structure at large Knudsen numbers.

The hydrodynamic performance of oscillating elastic plates with tapered and uniform thickness in an incompressible Newtonian fluid at varying Reynolds numbers is investigated numerically using a fully coupled fluid–structure interaction computational model. By leveraging the acoustic black hole effect, tapered plates can generate bending patterns that vary from standing wave to travelling wave oscillations, whereas plates with uniform thickness are limited to standing wave oscillations. Simulations reveal that although both standing and traveling wave oscillation modes can produce high thrust, travelling waves achieve significantly higher hydrodynamic efficiency, and this advantage is more pronounced at higher Reynolds numbers. Furthermore, regardless of the oscillation mode, tapering leads to greater hydrodynamic performance. The enhanced hydrodynamic efficiency of travelling wave propulsion is associated with the reduced amount of vorticity generated by tapered plates, while maintaining high tip displacements. The results have implications for the development of highly efficient biomimetic robotic swimmers, and more generally, the better understanding of the undulatory aquatic locomotion.

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.