Simple analytical criteria are derived to determine whether axisymmetric base flows in annuli and pipes are stable or unstable. Both axisymmetric and non-axisymmetric inviscid disturbances are considered. Our sufficient condition for stability improves upon the classical result of Batchelor & Gill (1962) J. Fluid Mech. 14(4), 529–551 following the idea of the second Kelvin–Arnol’d stability theorem. A novel sufficient condition for instability is also derived by extending the recently proposed hurdle theorem for parallel flows (Deguchi et al. 2024 J. Fluid Mech. 997, A25). These analytical criteria are applied to annular and pipe model flows and are shown to effectively predict the neutral parameters obtained from eigenvalue computations of the stability problem.

We investigate the three-dimensional melting dynamics of an initially spherical particle translating in a warmer liquid using sharp-interface simulations that fully resolve both solid and fluid phases with the Stefan condition. A wide parameter space is explored, spanning initial Reynolds number ($\textit{Re}_0$), Stefan number ($\textit{St}$) and Richardson number ($\textit{Ri}$). In the absence of buoyancy ($\textit{Ri}= 0$), the interface evolution is governed by canonical wake bifurcations. Four regimes are identified: an axisymmetric regime ($\textit{Re}_0\lt 212$) with a rounded front and planar rear; a steady planar-symmetric regime ($212\lt \textit{Re}_0\lt 273$) with an inclined rear plane; a periodic planar-symmetric regime ($273\lt \textit{Re}_0\lt 355$) where vortex shedding emerges in the wake; and a chaotic regime ($\textit{Re}_0\gt 355$) with fluctuating stagnation points and a more rounded rear. Despite these differences, all regimes exhibit a tendency towards melt-rate homogenisation over time. Besides, we introduce an aspect-ratio-based surface-area formulation that yields a predictive model, accurately capturing volume evolution across regimes. Hydrodynamic loads also reflect the coupling between shape and flow: drag follows rigid-sphere correlations only at moderate $\textit{Re}_0$; planar rears enhance drag at higher $\textit{Re}_0$; lift appears only in symmetry-broken regimes and reverses late in time; torque reorients the rear plane towards vertical, consistent with free-body experiments. When buoyancy is included, assisting configurations ($\textit{Ri}\gt 0$) suppress recirculation and maintain quasi-spherical shapes, whereas opposing or transverse buoyancy ($\textit{Ri}\lt 0$) destabilises wakes and promotes tilted planar rears. These results provide a unified framework for convection-driven melting across laminar, periodic and chaotic wakes, with implications for geophysical and industrial processes.

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 nonlinear interactions of compressional Alfvén wave and a steadily moving charged obstacle are examined in Hall magnetohydrodynamics (MHD). The interaction dynamics is shown to be described by a forced derivative nonlinear Schrödinger equation (fDNLSE). The steadily moving charged obstacle induced weak perturbation is responsible for the forcing term. The variational structure is used to investigate the exact solitary wave solutions of the fDNLSE for a special analytic form of the forcing term by constructing a proper Hamiltonian of the system. The conditions for the stability of these solitary waves are delineated through variational method. The numerical solutions using the split-step Fourier method confirm the analytical results representing the pinned solitons. The relevance and potential applications of the results in astrophysics are also discussed.

With the development of active sonar technology, the poor performance of anechoic tiles in avoiding low-frequency detection has emerged. Then tunable mechanical metamaterials with active control systems have extended applications. This work proposes active metamaterial plates composed of two plates and periodic four-link mechanisms with local resonators. By coils and magnets as well as external voltage, active feedback control is used to regulate the dynamic effective density. Based on the Fourier transform and Wiener–Hopf method, a theoretical model is derived to study the scattering of sound waves from active metamaterial plates. The fluid–structure interaction between the acoustic medium and metamaterial plates is considered. Then the vibroacoustic coupling is investigated to achieve the invisible design of submarines. Results show that the scattered sound pressure within a negative density region is effectively reduced with proper acceleration and displacement feedback coefficients. Furthermore, the finite element simulation and acoustic scattering experiment are performed to support the theoretical derivation. This research is expected to provide further insights for improving invisible effects of underwater vehicles.

We investigate the impact of streamwise-grooved and spanwise-periodic surface roughness arrays on the lower-branch viscous Tollmien–Schlichting (TS) instability in the boundary layer over an otherwise flat plate. The streamwise length scale and spanwise spacing of the arrays are of $O(L)$ and $O(\textit{Re}^{-3/8}L)$, respectively, with the latter being comparable to the characteristic wavelength of the TS modes, where $L$ is the distance from the leading edge of the plate to the peak location of the roughness arrays and $\textit{Re}$ denotes the Reynolds number based on $L$, assumed to be large. The characteristic height of the roughness arrays is of $O(\textit{Re}^{-3/8}L)$, which is greater than the boundary-layer thickness and is the required asymptotic threshold for generating $O(1)$ streaks. We show that this nonlinear streaky flow is governed by three-dimensional (3-D) boundary-layer equations supplemented by a Laplace equation in an inviscid upper deck. Prandtl’s transformation is applied to convert the curved boundary to a flat one, which not only reduces computational complexity by avoiding meshing the geometry, but also shows that the spanwise undulation of the roughness arrays enhances transverse diffusion. The Laplace equation is solved to provide the spanwise pressure gradient and velocity, which drive the streaks. The boundary-layer equations are solved efficiently using a streamwise marching scheme. The linear viscous instability of the resulting streaky flow is analysed; by exploiting the asymptotic structure, the bi-global eigenvalue problem is reduced to a one-dimensional one, where the stability is found to be controlled by the spanwise-dependent wall shear and the shape function of the roughness arrays. The results suggest that two-dimensional and weakly 3-D low-frequency modes are stabilised, while most other modes are destabilised. The present formulation provides a convenient tool for predicting streaky flows induced by riblet-like roughness of fairly large height and furthermore assessing their viscous instability properties.

At scales larger than the forcing scale, some out-of-equilibrium turbulent systems (such as hydrodynamic turbulence, wave turbulence and nonlinear optics) exhibit a state of statistical equilibrium where energy is equipartitioned among large-scale modes, in line with the Rayleigh–Jeans spectrum. Key open questions now pertain to either the emergence, decay, collapse or other non-stationary evolutions from this state. Here, we experimentally investigate the free decay of large-scale hydroelastic turbulent waves, initially in a regime of statistical equilibrium. Using space- and time-resolved measurements, we show that the total energy of these large-scale tensional waves decays as a power law in time. We derive an energy decay law from the theoretical initial equilibrium spectrum and the linear viscous damping, as no net energy flux is carried. Our prediction then shows a good agreement with experimental data over nearly two decades in time, for various initial effective temperatures of the statistical equilibrium state. We further identify the dissipation mechanism and confirm it experimentally. Our approach could be applied to other decaying turbulence systems, with the large scales initially in statistical equilibrium.

The linear instability of liquid film with insoluble surfactants on a quasiperiodic oscillating plane for disturbances with arbitrary wavenumbers is investigated. The combined effects of insoluble surfactants and quasiperiodic oscillation on the instability are described using Floquet theory. For long-wavelength instability, the solution in the limit of long wave perturbations is obtained by the asymptotic expansion method. The results show that a new stable region emerges in the low-frequency domain of the neutral stability curve in the absence of gravity. As the imposed frequency increases, this newly formed stable region is progressively absorbed into a broader stable zone. The U-shaped neutral curves with separation bandwidth appear in the presence of gravity, and the presence of the surfactants will decrease the unstable frequency bandwidth and increase the critical Reynolds number. The finite-wavelength instability is solved numerically based on the Chebyshev spectral collocation method. Both travelling-wave and standing-wave modes are found due to the existence of surface surfactants. As the surfactant concentration increases, the finite-wavelength instability region expands significantly, and the intersection point marking the transition from travelling waves to standing waves shifts progressively towards lower frequencies. The physical mechanisms underlying perturbation growth are further elucidated through an energy budget analysis. Energy budget analysis demonstrates that long-wavelength instability is dominated mainly by surface shear stress, whereas finite-wavelength instability is primarily governed by the combined effects of Reynolds stress and surface shear stress.

This paper reports analytical solutions for steadily travelling two-dimensional water waves on deep water, without gravity or surface tension, carrying a cotravelling periodic row of hollow vortices. The solutions are hollow-vortex regularisations of the exact solutions of Crowdy & Roenby (Fluid Dyn. Res., vol. 46, 2014, 031424) for the analogous waves carrying a submerged point-vortex row, the free-surface shapes of which coincide with those for pure capillary waves and, like those, exhibit steady pinchoff at a critical wave amplitude. The same pinchoff phenomenon is shown to occur for the hollow-vortex regularisations. The new wave solutions are likely to provide a useful basis for perturbative, asymptotic or numerical studies when additional effects such as gravity, capillarity or compressibility are incorporated.

A combined experimental and numerical investigation of equilibrium states arising from quasi-two-dimensional turbulent flows in a rotating quadrangular basin with a central flat region and steep slopes adjacent to the sidewalls is presented. The study examines freely decaying and continuously forced regimes. Laboratory experiments show that decaying turbulence consistently evolves into a robust equilibrium state characterised by: (i) a boundary current around the basin along the topographic contours, and (ii) a central anticyclone – features accurately reproduced by shallow-water numerical simulations at laboratory scale. Additional simulations using a mesoscale basin suggest the relevance of these findings to oceanic regimes for different initial conditions and topographic parameters. In the case of continuously forced flows, time-averaged fields reveal qualitatively similar structures, despite the randomness of the applied forcing and the consequent absence of a strict equilibrium. These results demonstrate the emergence of robust flow patterns with implications for the modelling and understanding of semi-permanent flows that are often found in statistical theories of geophysical turbulence.

The wake dynamics of a circular cylinder oscillating in the streamwise direction within a stably (density) stratified fluid is investigated using two-dimensional numerical simulations: Floquet stability analysis and dynamic mode decomposition. At a fixed Reynolds number ($ \textit{Re}=175$) and forcing frequency ratio ($f_d/f_{St}=1.6$), we examine the effects of the oscillation amplitude ($0.1 \leqslant A_D \leqslant 0.6$) and the stratification strength ($1 \leqslant \textit{Fr} \leqslant \infty$) on the wake structure and its symmetry breaking. In unstratified (homogeneous) flow ($ \textit{Fr} = \infty$), the wake transitions from an asymmetric vortex street at low amplitudes to a symmetric state at higher amplitudes. This transition occurs via a Neimark–Sacker bifurcation, with Floquet analysis identifying a critical amplitude of $A_D = 0.455$. In stratified flow, buoyancy forces improve symmetry and suppress vortex shedding for $A_D=0$. At $ \textit{Fr} = 1$, symmetry breaking first occurs at a threshold of $A_D = 0.246$, associated with a period-doubling bifurcation and subharmonic antisymmetric vortex shedding, and persists only within a finite amplitude window ($0.246 \lt A_D \lt 0.560$), beyond which the wake restabilises into a symmetric pattern. At a fixed small amplitude ($A_D = 0.1$), a secondary critical transition is observed at $ \textit{Fr} = 1.52$, marked by quasiperiodic antisymmetric shedding through a near-resonant Neimark–Sacker bifurcation. Stratification also influences force production: moderate stratification ($ \textit{Fr} \approx 2$) minimises drag through enhanced pressure recovery and suppressed wake asymmetry. These results highlight the dual role of stratification in promoting or delaying symmetry-breaking instabilities and modifying wake dynamics. Critical transition thresholds are established, providing insight into buoyancy-modulated flow control strategies relevant to geophysical and engineering applications involving oscillating bodies in stratified environments.

The interaction between marine floating structures and projectiles during water entry plays a crucial role in understanding fluid–structure interactions in polar and offshore environments. This study investigates the impact dynamics of a projectile on a floating structure, emphasising the fluid–structure coupling effects, including the impact-induced cavity evolution, stress wave propagation and fragmentation processes. The computational approach integrates fluid dynamics and discrete element methods (CFD-DEM), allowing for detailed simulation of multi-phase interactions during projectile impact. To address the disparity between fluid grid resolution and particle scale, a dual-grid strategy is incorporated, enabling accurate resolution of multi-scale interactions. The results highlight the fundamental mechanisms of impact water entry, where stress waves radiate through the structure, causing local damage and initiating the formation of fragments. These fragments, in turn, influence the stability of the cavity interface and modify the impact dynamics. The interplay between the floating structure’s buoyant support and the surrounding water contributes to complex load variations on the projectile. Ultimately, the study provides insights into the multi-scale fracture mechanisms induced by projectile impact, with potential applications in improving the design and resilience of structures in dynamic marine environments.