We present a theoretical analysis of a gyroscopic wave energy converter (GWEC), which generates electricity via the precession induced by the flywheel’s rotation and the pitch motion of a floating body. The coupled wave–body–gyroscope interaction problem is formulated under the assumptions of linear waves and resulting linear motions of both the floating body and the gyroscope. Within this framework, we identify the optimal control parameters that maximise the energy absorption efficiency. The analysis reveals that the GWEC can theoretically achieve the maximum energy absorption efficiency of 1/2 at any wave frequency through appropriate tuning of the flywheel’s rotational speed and the generator parameters. The derived theory is verified through numerical simulations in both the frequency and time domains. Furthermore, time-domain simulations incorporating the nonlinear gyroscopic response are conducted to assess the limitations of the linear gyroscopic model. These findings provide valuable insights for the future design of wave energy harvesting technologies.

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.