The surface-gravity wave evolution, imitating tsunamis triggered by the ocean floor’s arbitrary temporal motion over a generic seafloor topography, is investigated using the linearised water-wave theory of a compressible ocean. The pressure wave bounce between the water surface and ocean floor, followed by the generation of acoustic-gravity wave (AGW) propagation away from the initial disturbance, is shown with unprecedented details. The computational novelty covers accurate pressure-wave-field computation using high-frequency AGW modes, unlike the dominant first AGW in surface waves. The mathematical problem is solved using the Fourier transformation and eigenfunction expansion techniques, following a multistep approximation of the arbitrarily deep sea. Test cases of two idealistic subsurface geometries (continental shelf and mountain range) using the ocean floor’s linear and parabolic temporal growth show elongation and shortening of the surface wavelength and changes in the propagation speed due to the variable seafloor topography through simulations. The mutual interaction of the pressure waves within the water column unravels depth-change-induced scattering. While high-frequency pressure at a shallower depth is dominant for the continental shelf, a significantly reduced amplitude across a mountain ridge is visualised with a corresponding lower impact of the acoustic-gravity wave on the surface wave. Substantial contrast in the pressure wave field triggered by a slight change in the rupture’s properties suggests its careful consideration when building tsunami prediction models. Since these AGWs are precursors to tsunamis, we believe their detection through an accurate pressure measurement will give very important information about the associated tsunami wave.

Nonlinear interactions between free-surface gravity waves and acoustic–gravity motions provide a mechanism for energy exchange in weakly compressible fluids and have long been discussed in connection with microseisms and low-frequency underwater sound. While elastic solid-Earth response has been incorporated in microseism modelling, existing formulations of acoustic–gravity wave resonant triads are almost exclusively developed for a rigid seabed, which introduces a shallow-water cutoff where the acoustic–gravity member becomes evanescent and resonance cannot occur. Here, we extend the resonant-triad framework to a compressible fluid over an elastic half-space. Seabed elasticity modifies the acoustic–gravity eigenstructure and dispersion relation, admitting propagating or interface-guided acoustic–gravity modes in regimes inaccessible under rigid-bottom assumptions and thereby removing the rigid cutoff in frequency (or depth). Using a multiple-scale expansion in the small compressibility parameter, we derive modulation equations for two counter-propagating gravity waves coupled to a single elastic acoustic–gravity mode. A key feature is an interfacial term in the solvability condition arising from the parameter dependence of the elastic boundary operator, which alters the modal normalisation and the resulting coupling and detuning coefficients. The enlarged admissible parameter space also makes laboratory-scale realisations of acoustic–gravity triad resonance substantially more feasible, enabling controlled investigation of the triad mechanism.

The droplet–microfluidic system under acoustic-field actuation represents a classical multiphase flow problem with broad relevance to engineering and biomedical applications. When an acoustic wave interacts with a viscous droplet suspended in another liquid, it induces acoustic streaming both inside and outside the droplet and exerts acoustic radiation stresses that deform its shape. In this work, we present a comprehensive analytical and numerical framework to investigate the coupled dynamics of droplet shape evolution, acoustic fields and acoustic streaming. The study considers droplets stably positioned within a standing wave at either a pressure node or a velocity node, undergoing deformations analogous to the classical Taylor regime. Our analytical model, supported by numerical simulations, reveals that the acoustic field is predominantly governed by low-order modes, up to the quadrupole. Furthermore, the acoustic-streaming pattern is dictated by the density contrast between the droplet and the surrounding fluid, whereas both density and compressibility contrasts control the droplet deformation. We also demonstrate that impedance mismatch is not the fundamental criterion for acoustic scattering. Instead, mismatches in density, or compressibility, or both, serve as the primary mechanisms. In addition, we develop a phase diagram illustrating droplet shape-deformation and streaming-pattern regimes as functions of the material properties (density ratio and compressibility ratio). These results provide deep mechanistic insights for the design and control of efficient droplet–acoustofluidic platforms and lay the groundwork for next-generation ultrasound-driven strategies for precise droplet manipulation in soft-matter and microfluidic applications.

An asymptotic approach is presented for studying the diffraction problem of in-duct acoustic modes by the termination of a rigid, circular duct with negligible thickness, based on Keller’s (1957, 1958, 1962) geometrical theory of diffraction (GTD). The diffracted field is solved first for the unflanged duct case, followed by an extension to the flanged duct case for which no closed-form exact solutions are available. The GTD solution for the primary diffraction of unflanged ducts, which invokes the half-plane diffraction coefficient obtained from Sommerfeld’s exact solution to the half-plane diffraction problem, is shown to yield agreement with the leading term of the Wiener–Hopf solution, in which the split functions of the Wiener–Hopf kernel are replaced with their steepest-descent approximations. Despite being developed for high-frequency analysis, experimental data from an unflanged duct and the numerical solutions for a flanged duct, both including the radiation directivity and the reflection coefficient, indicate that GTD solutions perform reasonably well even for wavelengths smaller than the duct’s radius, provided the frequency does not approach the cutoff condition. A reciprocity relation, which couples the absorption and emission of the (un)flanged duct, is derived from the reciprocity principle and verified by the Wiener–Hopf (if available) and GTD solutions. Physical insights are supplied by the GTD to explain why, for example, only a plane wave would be excited within the duct by a plane wave incident normally from the exterior of the duct. In cases where the uniform flow is present, an extended GTD formulation is proposed by utilising the canonical solution to the half-plane diffraction problem. The resulting correction factor for the diffracted field of unflanged ducts that accounts for an arbitrary amount of shedding vortices is consistent with Rienstra’s (1984 J. Sound Vib. vol. 94 (2), pp. 267–288) Wiener–Hopf solution. Potential strategies for addressing variants and extensions of the current work are outlined.

Retroflex consonants represent a major class of language sounds, but our understanding of their phonetic and phonological properties remains limited. From the standpoint of acoustics, recent contributions are largely lacking. Few fully fledged empirical descriptive studies have been made available to establish their presence and characteristics in the world’s languages. Within retroflex consonants, liquids and nasals are particularly rare, and very little descriptive, theoretical, or historical research has been conducted on them. Bantu languages from Africa are not included in most large-scale surveys. Recent fieldwork in the Mai-Ndombe Province of the Democratic Republic of Congo (DRC) in Central Africa confirms the existence of nasal retroflexes in North Boma (Bantu B82). This paper offers the first acoustic description of these rare nasal segments in any Bantu language. North Boma nasal retroflexes are shown to constitute a discrete class within the language’s nasal inventory. Compared to their non-retroflex counterparts, they are significantly shorter; they also display spectral energy concentrated in the lower frequencies around their centre of gravity, more peaked energy concentrations, higher values of F1 and F1 bandwidth, and lower values of F2 bandwidth. Furthermore, we reconstruct the historical development of nasal retroflexes in North Boma and show that they are the regular outcome of the merger of Proto-Bantu *n and *nd to /n/ in stem-medial position. We hypothesise that retroflexion might be a phonological substrate feature originating in extinct non-Bantu languages once spoken by Batwa communities living and foraging in the region or by Ubangi speech communities now only attested further north. This contribution showcases how detailed phonetic documentation and description are an asset for historical research.

We develop a weakly nonlinear model of duct acoustics in two and three dimensions (without flow). The work extends the previous work of McTavish & Brambley (2019 J. Fluid Mech., vol. 875, pp. 411–447) to three dimensions and significantly improves the numerical efficiency. The model allows for general curvature and width variation in two-dimensional ducts, and general curvature and torsion with radial width variation in three-dimensional ducts. The equations of gas dynamics are perturbed and expanded to second order, allowing for wave steepening and the formation of weak shocks. The resulting equations are then expanded temporally in a Fourier series and spatially in terms of straight-duct modes, and a multi-modal method is applied, resulting in an infinite set of coupled ordinary differential equations for the modal coefficients. A linear matrix admittance and its weakly nonlinear generalisation to a tensor convolution are first solved throughout the duct, and then used to solve for the acoustic pressures and velocities. The admittance is useful in its own right, as it encodes the acoustic and weakly nonlinear properties of the duct independently from the specific wave source used. After validation, a number of numerical examples are presented that compare two- and three-dimensional results, the effects of torsion, curvature and width variation, acoustic leakage due to curvature and nonlinearity and the variation in effective duct length of a curved duct due to varying the acoustic amplitude. The model has potential future applications to sound in brass instruments. Matlab source code is provided in the supplementary material.

When a fluid is exposed to acoustic actuations or harmonic boundary vibrations, a steady flow known as acoustic streaming is superimposed on the oscillatory motion. In resonating acoustofluidic devices, the manipulation of nanoparticles by acoustic radiation forces is often hindered by the presence of acoustic streaming. In this study, we demonstrate, both theoretically and numerically, that microscale acoustic streaming can be significantly reduced or even completely eliminated by creating specific acoustic resonances within well-designed fluid cavities. By suppressing acoustic streaming and the corresponding drag force it induces, we demonstrate the potential to use acoustic radiation forces for manipulating nanoparticles, regardless of their size. Additionally, building upon the theoretical findings, we present the experimental realisation of acoustophoretic patterning of polystyrene nanoparticles with diameters ranging from 100 nm to 1 $\unicode {x03BC}$m in a resonating wavelength-scale acoustofluidic device that operates at sub- or low-MHz frequencies.

The acoustically excited vibrations of a micrometric object in a viscous liquid induce a net fluid flow known as microstreaming. This phenomenon can be harnessed for a variety of microscale applications, including particle transport, fluid mixing and the propulsion of micro-swimmers. Acoustic propulsion holds significant promise for in vivo manipulation due to its inherent biocompatibility and remote actuation capability, eliminating the need for an onboard energy source. However, designing steerable swimmers powered by vibrating tails requires a detailed understanding of the relationship between the input acoustic signal and the resulting streaming flow. In this paper, we characterise experimentally and model the microstreaming generated by a vertically standing micro-cantilever attached to a vibrating plate, as a function of the excitation frequency. Significant streaming is observed only at specific frequencies corresponding to the vibration modes of the support, which both translate and bend the cantilever. Computations based on a two-dimensional semi-analytical model enable quantitative predictions of the in-plane streaming flow structure and velocity magnitude, using as input the cantilever’s vibration profile, fully characterised by laser Doppler vibrometry. In particular, comparison between experiments and simulations allows us to rationalise the frequency-dependent emergence of dipolar, circular and elliptical streaming patterns, which are respectively induced by rectilinear, circular and elliptical translations of the cantilever. This analysis also explains the prevalence of elliptical streaming structures observed in our system. Beyond advancing our fundamental understanding of streaming generated by vibrating slender bodies, these results highlight the potential for frequency-based control of micro-swimmers through predictable, mode-specific flow responses.

A theoretical model is developed to study the deformation dynamics of a biconcave red blood cell (RBC) in a viscous fluid driven by an ultrasonic standing wave. The model considers the true physiological shape of RBCs with biconcave geometry, overcoming the challenges of modelling the nonlinear acoustomechanical coupling of complex biconcave curved shells. The hyperelastic shell theory is used to describe the cell membrane deformation. The acoustic perturbation method is employed to divide the Navier–Stokes equations for viscous flows into the acoustic wave propagation equation and the mean time-averaged dynamic equation. The time-average flow–membrane interaction is considered to capture the cell deformation in acoustic waves. Numerical simulations are performed using the finite element method by formulating the final governing equation in weak form. And a curvature-adaptive mesh refinement algorithm is specifically developed to solve the error problem caused by the nonlinear response of biconcave boundaries (such as curvature transitions) in fluid–structure coupling calculations. The results show that when the acoustic input is large enough, the shape of the cell at the acoustic pressure node changes from a biconcave shape to an oblate disk shape, thereby predicting and discovering for the first time the snap-through instability phenomenon in bioncave RBCs driven by ultrasound. The effects of fluid viscosity, surface shear modulus and membrane bending stiffness on the deformation of the cell are analysed. This numerical model has the ability to accurately predict the acoustic streaming fields and associated time-averaged fluid stress, thus providing insights into the acoustic deformation of complex-shaped particles. Given the important role of the mechanical properties of RBCs in disease diagnosis and biological research, this work will contribute to the development of acoustofluidic technology for the detection of RBC-related diseases.

We present a theoretical study, supported by simulations and experiments, on the spreading of a silicone oil drop under MHz-frequency surface acoustic wave (SAW) excitation in the underlying solid substrate. Our time-dependent theoretical model uses the long-wave approach and considers interactions between fluid dynamics and acoustic driving. While similar methods have analysed the micron-scale oil and water film dynamics under SAW excitation, acoustic forcing was linked to boundary layer flow, specifically Schlichting and Rayleigh streaming, and acoustic radiation pressure. For the macroscopic drops in this study, acoustic forcing arises from Reynolds stress variations in the liquid due to changes in the intensity of the acoustic field leaking from the SAW beneath the drop and the viscous dissipation of the leaked wave. Contributions from Schlichting and Rayleigh streaming are negligible in this case. Both experiments and simulations show that, after an initial phase where the oil drop deforms to accommodate acoustic stress, it accelerates, achieving nearly constant speed over time, leaving a thin wetting layer. Our model indicates that the steady speed of the drop results from the quasi-steady shape of its body. The drop speed depends on drop size and SAW intensity. Its steady shape and speed are further clarified by a simplified travelling-wave-type model that highlights various physical effects. Although the agreement between experiment and theory on drop speed is qualitative, the results’ trend regarding SAW amplitude variations suggests that the model realistically incorporates the primary physical effects driving drop dynamics.

Supersonic jets impinging on a ground plane produce a highly unsteady jet shear layer, often resulting in extremely high noise level. The widely accepted mechanism for this jet resonance involves a feedback loop consisting of downstream-travelling coherent structures and upstream-propagating acoustic waves. Despite the importance of coherent structures, often referred to as disturbances, that travel downstream, a comprehensive discussion on the disturbance convection velocity has been limited due to the challenges posed by non-intrusive measurement requirements. To determine the convection velocity of disturbances in the jet shear layer, a high-speed schlieren flow visualisation is carried out, and phase-averaged wave diagrams are constructed from the image sets. The experiments are conducted using a Mach 1.5 jet under various nozzle pressure ratios and across a range of impingement distances. A parametric analysis is performed to examine the influence of nozzle pressure ratio on the convection velocity and phase lead/lag at specific impingement distances. The results reveal that impingement tonal frequency is nearly independent of the disturbance convection velocity, except in cases of staging behaviour. They also demonstrated that slower downstream convection velocity of the disturbance corresponds to larger coherent structures, resulting in increased noise levels. Based on the observation of acoustic standing waves, an acoustic speed-based frequency model has been proposed. With the help of the allowable frequency range calculated from the vortex-sheet model, this model can provide a good approximation for the majority of axisymmetric impingement tonal frequencies.

We present a mathematical solution for the two-dimensional linear problem involving acoustic-gravity waves interacting with rectangular barriers at the bottom of a channel containing a slightly compressible fluid. Our analysis reveals that, below a certain cutoff frequency, the presence of a barrier inhibits the propagation of acoustic-gravity modes. However, through the coupling with evanescent modes existing in the barrier region, we demonstrate the phenomenon of ‘tunnelling’ where the incident acoustic-gravity wave energy can leak to the other side of the barrier, creating a propagating acoustic-gravity mode of the same frequency. Notably, the amplitude of the tunnelling waves exponentially decays with the width of the barrier, analogous to the behaviour observed in quantum tunnelling phenomena. Moreover, a more general solution for multi-barrier and multi-modes is discussed. It is found that tunnelling energy tends to transform from an incident mode to the lowest neighbouring modes. Resonance due to barrier length results in more efficient energy transfer between modes.