We investigate the influence of side-wall wetting on the linear stability of falling liquid films confined in the spanwise direction. A biglobal stability framework is developed, capturing inertia, viscosity, gravity, capillarity and geometric confinement. The base flow exhibits a curved meniscus and a streamwise velocity overshoot near the side walls. Linear stability analysis based on the Navier–Stokes equations is performed in two limiting regimes. In confined channels, where spanwise confinement stabilises moderate-wavenumber perturbations via side-wall boundary layers, wetting weakens this stabilisation; as the contact angle decreases, the neutral curves shift towards the unconfined one-dimensional limit, thus wetting acts as a relative destabilising mechanism. In contrast, in weakly confined channels where side-wall boundary layers do not provide confinement-induced stabilisation, wetting produces a net long-wave stabilisation ($k \rightarrow 0$), significantly increasing the critical Reynolds number. This effect strengthens as the contact angle decreases, indicating a competition between destabilising inertia and stabilising wetting-induced capillary forces. The predicted long-wave stabilisation effect is compared quantitatively with available experimental measurements, showing consistent trends and comparable magnitudes within the accessible parameter range. Perturbation eigenmode structures show that, in confined channels, the relative destabilisation is associated with near-wall vortical structures induced by the meniscus elevation and velocity overshoot, which reduce effective viscous damping. In contrast, in weakly confined channels, stabilisation is consistent with interface tensioning through strong anchoring of the perturbations at the side walls.

We investigate the incompressible flow inside a two-dimensional square cavity, driven by the sliding motion of its four lids, all at the same speed and with facing lids moving in opposite directions. The problem has three symmetries: two mirror symmetries with respect to the diagonals and a $\pi$ rotation invariance about the centre of the cavity. The base flow, a steady state that has all three symmetries, is the unique solution at sufficiently low values of the Reynolds number ($ \textit{Re}$) and acts as a global attractor. At higher $ \textit{Re}$, it has become unstable and shares the phase space with a globally attracting space–time symmetric periodic orbit that, in addition to the rotational invariance, is also invariant under evolution over half a period followed by reflection about either of the diagonals. In between, a wealth of solution branches and intervening bifurcations mediate the transition process. In particular, a pair of steady states that break the mirror symmetries but are mirror-symmetry images of each other regulate the appearance and disappearance of a second space–time symmetric periodic orbit and a pair of asymmetric periodic orbits that are also mirror images of each other. The catalogue of instabilities includes both local (two pitchfork, two Hopf, a saddle-node and a cyclic fold) and global (two heteroclinic and one homoclinic) bifurcations. The sequence of transitions is explained in terms of a one-dimensional path through the parameter space of a codimension-four bifurcation: the double zero bifurcation with Z$_2$ symmetry and degeneracy of the third order terms.

We give evidence of non-modal amplification mechanisms driven by swirl intensity from a bi-global linear analysis of a cold swirling flow representative of a premixed swirl burner: non-uniform, compressible, turbulent, enclosed and subject to vortex breakdown passed the expansion. The monolithic computational approach embeds a realistic axisymmetric swirler model in the computational domain. The amplification mechanisms are identified by stability and resolvent analysis under variations of the length of the annular duct section and combustion chamber, the swirl intensity and the swirler position. While the spectrum is affected by changes in the length only, the gain of the resolvent strongly depends on the swirl intensity. The results suggest an acoustically dominated amplification in the combustion chamber and a non-modal hydrodynamic-dominated process driven by the swirl intensity. Inertial waves carrying swirl fluctuations play a key role in the latter. The results are complemented by a resolvent sensitivity analysis that identifies the tip of the inner recirculation region and the surrounding shear layer as a wavemaker region that drives at high swirl numbers the non-modal amplification. The sensitivity of that region also enables the transfer of azimuthal momentum perturbations to axial momentum, hence activating a longitudinal acoustic resonance from azimuthal fluctuations.

Spatial linear instability analysis is employed to investigate the instability of a viscoelastic liquid jet in a co-flowing gas stream. The theoretical model incorporates a non-uniform axial base profile represented by a hyperbolic tangent, capturing the shear layer. The Oldroyd-B model discretised with Chebyshev polynomials is employed, and energy budget analysis is used to interpret underlying mechanisms. At low Weber numbers, the jet evolves axisymmetrically and the instability is governed by interfacial gas-pressure fluctuations; as the Weber number increases, the growing inertia drives a transition of the predominant mode from axisymmetric to helical. At weak elasticity, the instability is also primarily governed by gas-pressure fluctuations. As elasticity increases, the predominant mode transitions from axisymmetric to helical. This transition is accompanied by a migration of disturbance structures from the interface toward the jet interior and an enhanced coupling between velocity perturbation and the basic flow. These trends reveal a new predominant instability mechanism – the elasticity-enhanced shear-driven instability – which is distinct from capillary or Kelvin–Helmholtz instabilities in Newtonian jets. A $\textit{We}$–$El$ phase diagram delineates the boundary between predominant modes and experimental results obtained in a flow-focusing configuration validate the theoretical predictions. Compared with temporal stability results, the spatial framework – by directly resolving the convective downstream amplification of disturbances – achieves quantitative agreement with experiments and highlights the superiority of spatial instability analysis in capturing the dynamics of strongly convective, non-parallel jet flows. These findings provide mechanistic insight into viscoelastic jet instabilities and offer guidance for applications involving droplet and fibre formation in co-flow systems.

The vortex-induced vibration of multiple spring-mounted bodies free to move in the orthogonal direction of the flow is investigated. In a first step, we derive a linear arbitrary Lagrangian–Eulerian method to solve the fluid–structure linear problem as well as a forced problem where a harmonic motion of the bodies is imposed. We then propose a low computational-cost impedance-based criterion to predict the instability thresholds. A global stability analysis of the fluid–structure system is then performed for a tandem of cylinders and the instability thresholds obtained are found to be in perfect agreement with the predictions of the impedance-based criterion. An extensive parametric study is then performed for a tandem of cylinders and the effects of mass, damping and spacing between the bodies are investigated. Finally we also apply the impedance-based method to a three-body system to show its validity to a higher number of bodies.

The stability of the interface in a core–annular flow (CAF) of two immiscible Newtonian fluids with contrasting densities has been investigated, emphasising the role of strong circumferential rotation for the first time. The aim of the investigation is to give insight into the physical mechanisms underlying interfacial disruption. We examine the combined effects of gravity, interfacial tension, axial and azimuthal shear stresses, and centrifugal force on interface stability. The Rayleigh–Taylor instability, induced by gravity, appears as a spiral mode with a azimuthal wavenumber of one. As gravitational effects decrease, the most unstable mode number increases sharply before decreasing with increasing rotation. This non-monotonic behaviour is attributed to the interplay between azimuthal shear and centrifugal acceleration. We demonstrate that this velocity ratio fundamentally governs the onset of spiral modes by varying the ratio of the axial velocities of the core and annular fluids. Higher Reynolds numbers in the annular phase promote the emergence of higher-order spiral modes concomitant with amplified azimuthal shear at the interface. In a parametric study of the gap between the core and pipe wall, we identified a suppressive effect of reduced annular thickness on the growth of higher azimuthal wavenumbers. An energy budget analysis further delineated distinct mechanisms underpinning each instability regime and clarified transitions between them. These findings extend our understanding of interfacial stability in swirling CAFs and provide a predictive framework to control spiral-mode selection.

A joint experimental–computational investigation was conducted to examine the aerodynamic behaviour of a partially closed cavity model in Mach-6 flow. The model, consisting of a flat plate with a rectangular cavity and a forward-facing hinged door, resulted in a strong 500 Hz fluctuation with a 7.5$^\circ$ door and 25 mm cavity depth. The experiments revealed a recirculation bubble present upstream of the cavity region. The fluctuations, detected by surface pressure sensors on the upper surface, upstream cavity wall and cavity floor, were caused by oscillations of the separation bubble along the streamwise axis. Notably, this phenomenon is not explained by established empirical models for cavity flows, such as the Rossiter mechanism or closed-box acoustic resonance. To further elucidate the flow physics, detached eddy simulations (DESs) of the flow were conducted, providing a detailed understanding of the complex flow phenomena. The DES results complemented the experimental data, offering insights into the unsteady flow behaviour and the mechanisms driving the pressure fluctuations. Additional experiments and simulations were conducted for other door angles to simulate different stages of opening. The strong pressure fluctuations at approximately 500 Hz were only experimentally observed for door angles between 5.0$^\circ$ and 7.5$^\circ$ but were absent at much smaller and larger angles. Additionally, several cavity depths were tested, which demonstrated that a shallower cavity delayed the onset of fluctuations until a higher free-stream Reynolds number was reached. The combination of experimental and numerical results provides valuable initial data on the aerodynamic performance of a hypersonic forward-facing door over a cavity.

This paper examines two-dimensional liquid curtains ejected from a narrow horizontal outlet at an angle to the vertical. Curtains are characterised by the Froude number ${\textit{Fr}}=U/ ( gH ) ^{1/2}$, Reynolds number ${\textit{Re}}=UH/\nu$ and Weber number ${\textit{We}}=\rho U^{2}H/\sigma$, where $U$ is the ejection velocity, $g$ the gravity, $H$ the outlet’s half-width, $\nu$ the kinematic viscosity and $\sigma$ the surface tension. It is assumed that ${\textit{Fr}}\gg 1$ (so that the radius of the curtain’s curvature due to gravity exceeds $H$), ${\textit{Re}}\ll 1$ (viscosity is strong) and ${\textit{We}}\sim 1$ (surface tension is on par with inertia). It is shown that steady oblique curtains exist only subject to a constraint of the form ${\textit{We}}\gt f({\textit{Fr}}^{2}{\textit{Re}})$, which is more restrictive than the previously known constraint ${\textit{We}}\gt 1$. Thus, sufficiently strong viscosity and/or surface tension eliminate the steady regime and make the curtain evolve – typically, rotate around the outlet, eventually producing the teapot effect.