The present work brings to light the vibrations emerging when a circular cylinder, elastically mounted along a rectilinear path in quiescent fluid, is subjected to a forced rotation about its axis. These rotation-induced vibrations (RIV) are explored numerically for ranges of the four governing parameters. The Reynolds number and the reduced velocity (inverse of the non-dimensional natural frequency of the oscillator), based on the surface velocity of the rotating body and its diameter, are varied up to $100$ and $250$, respectively, and the structural damping ratio up to $50\,\%$. The structure to displaced fluid mass ratio ranges from $0.1$ to $1000$. Vibrations are found to occur over a vast region of the parameter space, including the four orders of magnitude of the mass ratio under study, and high levels of structural damping. The amplitude of RIV may exceed $30$ body diameters, while their frequency varies and deviates from the oscillator natural frequency, even though it is always lower. Despite its simplicity and the steady nature of the actuation, the system exhibits a considerable diversity of behaviours. Three distinct RIV regimes are encountered: two periodic regimes whose responses differ by their spectral contents, i.e. sinusoidal versus multi-harmonic, and an aperiodic regime. These regimes are all closely connected to flow unsteadiness, in particular via the interplay of the cylinder with previously formed vortices, which persist in the vicinity of the body.

We study the rebound of drops impacting non-wetting substrates at low Weber number ($\textit{We}$) through experiment, direct numerical simulation and reduced-order modelling. Submillimetre-sized drops are normally impacted onto glass slides coated with a thin viscous film that allows them to rebound without contact line formation. Experiments are performed with various drop viscosities, sizes and impact velocities, and we directly measure metrics pertinent to spreading, retraction and rebound using high-speed imaging. We complement experiments with direct numerical simulation and a fully predictive reduced-order model that applies natural geometric and kinematic constraints to simulate the drop shape and dynamics using a spectral method. At low $\textit{We}$, drop rebound is characterised by a weaker dependence of the coefficient of restitution on $\textit{We}$ than in the more commonly studied high-$\textit{We}$ regime, with nearly $\textit{We}$-independent rebound in the inertio-capillary limit, and an increasing contact time as $\textit{We}$ decreases. Drops with higher viscosity or size interact with the substrate longer, have a lower coefficient of restitution and stop bouncing sooner, in good quantitative agreement with our reduced-order model. In the inertio-capillary limit, low-$\textit{We}$ rebound has nearly symmetric spreading and retraction phases and a coefficient of restitution near unity. Increasing $\textit{We}$ or viscosity breaks this symmetry, coinciding with a drop in the coefficient of restitution and an increased dependence on $\textit{We}$. Lastly, the maximum drop deformation and spreading are related through energy arguments, providing a comprehensive framework for drop impact and rebound at low $\textit{We}$.

We must address active matter in the context of soft boundaries to bridge the gap between our understanding of active matter and the dynamics of biological systems (represented as active matter) under natural conditions. However, the physics of such active drops (matter) in contact with a soft and deformable surface has remained elusive. In this paper, we attempt to fill this gap and develop a theory for soft, active wetting. Our theory, which accounts for the various free energies for passive substrate and active drops as well as the active stresses, provides an equilibrium description of (active) particle orientation inside the drop and an equilibrium shape of the drop–soft-solid system. We obtain an analytical equation relating the activity to the internal pressure of an active drop. The equilibrium calculation further yields an ordered state of the polarisation field inside the drop. As compared to the non-active drops, the active drops with extensile activity press more into the soft surface, while the active drops with contractile activity either rise out of the soft surface (for smaller magnitude of negative activity) or make the soft surface bulge (for larger magnitude of negative activity). Finally, the three-phase contact line undergoes a rotation that depends on the strength of activity. These findings shed light on the manner in which the active stresses interact with surface tension and elasticity at the fundamental level.

In this paper we propose a novel control strategy for modulating nonlinear flapping and symmetry-breaking (S-B) bifurcations of a piezoelectric metamaterial beam behind a circular cylinder subjected to viscous flow. The beam incorporates distributed piezoelectric meta-cells connected via unidirectional circuits to enable self-sensing and adaptive control. A strongly coupled nonlinear fluid-structure-electro-control model within an arbitrary Lagrangian–Eulerian framework is developed for predicting the flapping dynamics of the large deformable piezoelectric metamaterial beam. The system exhibits multiple flow-induced modes, including limit-cycle oscillations, subharmonic responses and S-B deflections. These dynamic regimes arise from nonlinear bifurcations of the system, namely the period-doubling and spontaneous S-B bifurcations. Flapping control and wake topology transition of the system is achieved by suppressing the periodic-doubling bifurcation based on the vibration rebound effect through a self-sensing and adaptive-actuation mechanism of the beam. Floquet stability analysis confirms the effectiveness of control in delaying instability onset and suppressing chaotic transitions. Symmetry modulation of the beam is achieved via the localised perturbations induced from the piezoelectric meta-cells, which reshape the stability of the system. The transition from S-B mode to symmetry-recovery mode reflects a shift from a flow-separation-dominated to vibration-dominated vortex shedding pattern. This symmetry transition reorganises the energy exchange pathways between the flow and the beam. Quantitative analyses of the wake recovery and the energy harvesting efficiency confirm enhanced flow energy conversion under control. These results establish a framework for bifurcation control of slender structures in viscous flow, providing potential applications for underwater energy harvesting and flexible propulsion in unsteady environments.

Equilibrium, travelling-wave and periodic-orbit solutions of the Navier–Stokes equations provide a promising avenue for investigating the structure, dynamics and statistics of transitional flows. Many such invariant solutions have been computed for wall-bounded shear flows, including plane Couette, plane Poiseuille and pipe flow. However, the organisation of invariant solutions is not well understood. In this paper we focus on the role of symmetries in the organisation and computation of invariant solutions of plane Poiseuille flow. We show that enforcing symmetries while computing invariant solutions increases the efficiency of the numerical methods, and that redundancies between search spaces can be eliminated by consideration of equivalence relations between symmetry subgroups. We determine all symmetry subgroups of plane Poiseuille flow in a doubly periodic domain up to translations by half the periodic lengths and classify the subgroups into equivalence classes, each of which represents a physically distinct set of symmetries and an associated set of physically distinct invariant solutions. We calculate fifteen new travelling waves of plane Poiseuille flow in seven distinct symmetry groups and discuss their relevance to the dynamics of transitional turbulence. We present a few examples of subgroups with fractional shifts other than half the periodic lengths and one travelling-wave solution whose symmetry involves shifts by one third of the periodic lengths. We conclude with a discussion and some open questions about the role of symmetry in the behaviour of shear flows.