We study weakly nonlinear resonant interactions between two counter-propagating capillary–gravity waves and a horizontally uniform acoustic mode in a slightly compressible fluid of finite depth. Surface tension changes the resonance condition by allowing the large capillary–gravity wavenumbers needed to match the acoustic frequency at laboratory-scale depths. For the Longuet-Higgins configuration, in which the two surface modes have equal and opposite horizontal wavenumbers, the linear eigenfunctions and resonant wavenumber are obtained in closed form in the weakly compressible regime relevant to water-wave experiments. A multiple-scale calculation gives a three-wave interaction system with explicit coupling coefficients. We then use a leading-order spatially modulated approximation to estimate the acoustic pressure signal generated when two localised surface wavepackets collide. The bottom pressure scales quadratically with the characteristic surface-wave amplitude and linearly with the initial surface-wave width; for a representative laboratory configuration, the inviscid estimate is of order tens of Pascals.

Over the past two decades, acoustic retarding structures, analogised to sonic ‘black holes’ (SBH), have garnered significant attention for their potential to achieve perfect sound absorption. Typical designs feature annular rings with progressively smaller radii designed to bring sound waves to rest at zero radius. Yet these structures still reflect significant sound, a flaw widely attributed to the engineering impossibility of achieving a true zero radius with infinite acoustic admittance. In this study, we examine the analytical solution for a typical SBH configuration and conclude that sound waves cannot be trapped or otherwise ‘stopped’ by slowing down to zero phase speed. We attribute this impossibility instead to the breakdown of the approximate side-wall boundary condition used in the original theory. When an accurate boundary condition for the configuration is used, the phase speed is found to increase to infinity leading to incompressible-flow behaviour; this result contrasts with what the term of ‘black hole’ may reasonably imply. Recent SBH literature frequently employs distributed damping, which effectively absorbs waves over a considerable bandwidth. Given these findings, it is necessary to benchmark the original SBH structure and its damped variants against traditional acoustic wedges with identical geometrical profiles. Using two-dimensional axisymmetric finite element analysis and a pink incident noise, we conclude that an ordinary wedge filled with optimised bulk porous material matches the performance of the SBH configuration and some of its variants.

We formulate a weakly nonlinear exit condition for open ends of acoustic waveguides; to our knowledge, this is the first time a general acoustic open end has been analysed outside the linear regime. The formulation neglects mean flow, vortex separation and viscous effects. The resulting admittance boundary condition, and its weakly nonlinear counterpart, extend recent weakly nonlinear modelling of curved ducts Jensen & Brambley (2026 J. Fluid Mech., vol. 1030, A19) to include open ends. We approximate free space by considering the open-ended duct to be enclosed within a much larger hard-walled concentric duct; within the larger duct, the smaller duct exit is modelled as an acoustic discontinuity. Importantly, the superposition principle is unneeded, allowing the model to be applied in the nonlinear regime. The exit condition can be calculated without needing to solve the full problem in either the outer or inner ducts, making it numerically efficient. The exit condition is validated in the linear regime by comparison with Wiener–Hopf solutions of the duct end correction, and a novel nonlinear end correction is proposed; we find that both non-plane waves and nonlinearity cause the end correction to vary significantly from Rayleigh’s classical $0.6$ radii result. A number of numerical illustrations are then discussed, demonstrating nonlinear effects, sound radiating from curved ducts, sound radiating from an exponential horn (representative of brass instrument bells) and the harmonic effects of the open end on in-duct resonances. The model has potential applications to sound in woodwind and brass instruments. Matlab source code is provided in the supplementary material.

In Laurentian French (LF), the high vowels /i y u/ are realized as lax [ɪ ʏ ʊ] in syllables closed by certain consonants. Previous work on vowel laxing has focused primarily on describing the environments in which it occurs and on providing an acoustic characterization of the process, with far less work considering laxing from an articulatory perspective. This study uses acoustic and articulatory data (via ultrasound tongue imaging) to answer two main research questions: (1) Do high vowels in laxing environments centralize and lower or just lower? and (2) Does laxing occur before the rhotic /ʁ/? For the first question, our results show that LF high vowels become both lower and more centralized when they are realized as lax. For the second, our results showed that all three vowels are produced farther back when they precede a rhotic, which could be an instance of C-to-V coarticulation, rather than laxing.

This study develops a general theory for analysing a three-dimensional (3-D) acoustofluidic system, which consists of a cavity sandwiched by parallel piezoelectric substrates. The cavity is filled with a fluid and microparticle mixture, whose movements are actuated by surface acoustic waves (SAW) generated by the piezoelectric substrates. In contrast to the formulations based on the velocity potential and streamfunction, we developed a frequency-domain perturbation method to solve the compressible Navier–Stokes equations to obtain the acoustofluidic fields for both inviscid and viscous fluids. These solutions allow for the accurate prediction of the pressure nodal positions within the sandwiched cavity, and the effects of the microfluidic cavity geometry on the pressure nodal position are examined. Our analysis shows that the in-plane pressure-node distribution is controlled by phase modulation, whereas the out-of-plane distribution is governed by the amplitude ratio of the standing SAWs produced by the two parallel substrates. For viscous fluids, a coordinated amplitude–phase modulation strategy is proposed to achieve the desirable wave node distribution. The present theoretical derivations are validated against numerical simulations and laboratory experiments, in terms of both the velocity and pressure fields. This work provides guidelines for the fabrication and operation of acoustofluidic devices, extending current 2-D acoustic control to fully 3-D manipulation of microparticles suspended in the fluid.

A frequency-resolved modal Rayleigh method, in which the classical Rayleigh criterion is reformulated using dynamic mode decomposition (DMD), is presented. This approach yields mode-specific, closed-form measures of thermoacoustic excitation and absorption. The framework reconstructs pressure and heat-release fields with an acoustic scaling, separates self- and cross-modal contributions through a finite-time kernel and augments the in-phase Rayleigh term with a phase-invariant quadrature efficiency to quantify the coupling magnitude. The method is applied to two-dimensional, acoustically forced, anechoic hydrogen–air slit flames at four equivalence ratios ($\phi = 0.4, 0.5, 0.6, 0.7$) excited at 220, 437 and 800 Hz, in addition to multi-tone forcing. The analysis shows that the flame–acoustic coupling is primarily concentrated near the flame tip, that the coupling strength and frequency response vary systematically with equivalence ratio and that low-frequency forcing promotes nonlinear energy transfer into higher harmonics. Lean flames remain near linear and decouple at high frequency, whereas richer flames that lock in at higher-frequency excitation exhibit stronger nonlinear distortion at lower frequencies. Where the modal Rayleigh index is positive, the far-field sound pressure level increases at the corresponding frequency, confirming that the proposed metrics isolate feedback-effective modes. Overall, the DMD-based modal Rayleigh method provides a compact, mode-resolved description of flame–acoustic interactions.

We quantify the conversion of incident acoustic energy into vortical motion and viscous dissipation for a plane wave passing through large-aspect-ratio slit geometries. We perform direct numerical simulations over a broad imposed parameter space in incident sound pressure level (ISPL), Strouhal number ($\textit{St}$) and Reynolds number ($\textit{Re}$). Spectral proper orthogonal decomposition yields energy-ranked coherent structures at each frequency, from which we construct mode-by-mode fields for spectral kinetic energy (KE) and viscous loss (VL) to examine the acoustic absorption mechanisms. At $\textit{ISPL} = {150}\,\textrm{dB}$, the acoustic–hydrodynamic energy conversion is highest when $\textit{St} \le 4\textit{St}_0$, corresponding to an effective Keulegan–Carpenter number (${K_c}$) larger than 40. In this regime, three-dimensional simulations show that the dominant flow response is two-dimensional, with the oscillatory shear layer near the slit corners rolling up into shedding vortices. The VL accounts for 20 %–60 % of the KE contribution. For larger $\textit{St}$, the Stokes-layer confinement produces X-shaped near-slit modes, reducing the energy input by approximately 50 %. The influence of $\textit{Re}$ depends on amplitude. Larger $\textit{Re}$ corresponds to suppressed broadband fluctuations and sharpened harmonic peaks at ${150}\,\textrm{dB}$. At $\textit{ISPL} = {120}\,\textrm{dB}$, the boundary layers remain attached, vortex shedding is weak, absorption monotonically scales with viscosity and the $\textit{Re}$- and $\textit{St}$-dependencies become comparable. Across all conditions, more than 99 % of the VL is confined to a compact region surrounding the slit mouth. The KE–VL spectra identify regimes that enhance or suppress acoustic damping in slit geometries, providing a physically interpretable basis for acoustic-based design.

This study presents a quantitative analysis of the onset of self-induced thermoacoustic instabilities in a flame propagating through a channel open only at the ignition end. Direct numerical simulations are performed for a stoichiometric mixture to examine flame–acoustic interactions in two computational set-ups: (i) a conventional truncated domain that models only the channel, imposing a constant-pressure boundary condition at the open end; and (ii) an extended domain that more closely replicates experimental conditions by resolving both the internal flow and the surrounding atmosphere, where the jet emerging from the channel exit after ignition generates additional acoustic sources. In the extended domain, both pressure and velocity at the channel exit arise naturally from the calculation rather than being prescribed. The extended-domain simulations predict a markedly different flame response, with an earlier onset of thermoacoustic instability and an accelerated transition to a non-symmetric flame front. These features arise from vortices formed in the mixing layer between the pulsating jet and the surrounding atmosphere, which act as additional sources of acoustic perturbations and trigger the premature growth of flame instabilities. Although thermoacoustic generation has traditionally been regarded as the primary mechanism of acoustic energy production, the results demonstrate that aeroacoustic contributions play an equally significant role in amplifying acoustic perturbations. Our findings underscore the critical interplay between acoustics, combustion and fluid mechanics in determining the flame dynamics and emphasise the importance of accurately representing boundary conditions that reproduce the physical interaction with the surrounding environment to achieve reliable predictive simulations.

This work investigates long-wavelength acoustic wave propagation in active permeable media consisting of a visco-thermal fluid with periodically distributed rotating solid inclusions. The macroscopic description of wave propagation in the studied media is established using two-scale asymptotic homogenisation. The steady background fluid flow generated by the rotating inclusions is first upscaled. The resulting velocity field is shown to influence the dynamic convective forces appearing in the oscillatory transport problems, which are subsequently upscaled in the harmonic regime. For small Mach numbers, the solutions of the linearised local oscillatory fluid flow and heat transfer problems, arising from the homogenisation process, yield the dynamic conductivity and effective compressibility of the equivalent homogenised fluid. Theoretical analyses and numerical results show that the dynamic conductivity is strongly affected by the rotational motion of the inclusions. Furthermore, when oscillatory convective forces balance viscous or dynamic inertial forces in the fluid flow, phenomena such as an extremely low or negative real part of the dynamic conductivity, pseudo-resonant behaviour and an acoustic analogue of the Hall effect are identified. In terms of wave propagation characteristics, the results reveal atypical phenomena, including sound wave amplification, regressive sound waves, supersonic wave propagation and weak non-reciprocal wave propagation. These depend strongly on the microstructure of the medium and constitute a macroscopic manifestation of local oscillatory convective effects. This work offers new perspectives for the control of long acoustic waves using active permeable media with internal momentum sources.

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.