A finite wall-mounted cylinder (FWMC) refers to a cylinder mounted to a flat wall, characterised by flow over its free end and at the wall junction. In the present study, finite wall-mounted harbour seal vibrissal cylinders with different spanwise aspect ratios ($\textit{AR} = L/D$, where $L$ is the length of the cylinder and $D$ is its diameter) are examined at a Reynolds number of $\textit{Re} = 12\,000$ based on the cylinder diameter, with an incoming turbulent boundary layer thickness of $\delta /D = 0.16$. The far-field acoustic spectra of the harbour seal vibrissal FWMCs are broadband for all aspect ratios and effectively suppress the tonal peaks observed in the spectra of circular FWMCs. However, the effectiveness of the suppression mechanism diminishes with decreasing aspect ratio. For the shortest harbour seal vibrissal FWMC ($\textit{AR}= 3.2$), the overall sound pressure level exceeds that of its circular counterpart, and the tonal peak is replaced by broadband noise of comparable magnitude. Spanwise-intermittent recirculation zones and cellular vortex shedding are identified in the near wake of the harbour seal vibrissal FWMCs. For all harbour seal vibrissal FWMCs, as well as for circular FWMCs with $\textit{AR}$ = 6.5, hairpin vortex shedding is observed rather than classical von Kármán vortex shedding. This corresponds to the absence of tonal peaks in the far-field acoustic spectra. Wavy separation lines play a crucial role in the formation of hairpin vortices and in inducing phase differences in vortex shedding in the spanwise direction. Concentrated quadrupole streamwise vortical structures periodically appear along the span in the wake of the longest harbour seal vibrissal FWMC, which diminish with $\textit{AR}$ decreasing to $\textit{AR}$ = 6.5. This concentrated quadrupole arrangement of positive–negative streamwise vortices suppresses the vortex shedding observed along the span of circular FWMCs by disrupting the acoustic-coherent structures into smaller, spanwise-wavy organised elements. It also stabilises the flow and balances transverse ($y$) forces.

We study the collective behaviour of clusters of cylinders placed in the wake of a fixed cylinder and free to move in a direction perpendicular to that of the incoming flow, with no structural damping or stiffness. We keep the Reynolds number, defined based on the cylinder diameter, at 100 and consider five different configurations for the initial positions of the cluster cylinders: linear, rectangular, V-shaped, triangular and circular. In each configuration, we consider progressively increasing numbers of cylinders in the cluster. We show that overall, the cylinders tend to form final linear configurations, in which, after their transition, the cylinders form one or more lines. Some free-to-move cylinders might take the lead position in some of these linear formations depending on the initial configuration. These steady-state positions are achieved when the mean value of lift that acts on the cylinders becomes negligible. As a byproduct of these reconfigurations, the overall drag force that acts on the collection of cylinders reduces at their final steady-state locations in comparison with their original configurations. The complicated wakes that are observed in the fixed counterparts of these configurations are replaced by a series of vortex rows in the wake of separate lines of cylinders. Reducing the mass ratio allows the cylinders to oscillate about their mean displacement paths, but their transient paths and their final steady-state positions are not affected significantly by the decrease in the mass ratio.

Motivated by the understanding of fluid mechanics behind dry eye syndrome during the winter season, we perform the linear and nonlinear stability analysis of the tear film. To reflect the biological structure of the tear film, we model it as a viscoelastic film on a substrate with an insoluble surfactant at the air–film interface, destabilisation by van der Waals forces, variation of viscosity and elasticity along the film height, and impose a substrate-normal temperature gradient. The air–film interface tension is assumed to decrease linearly with temperature and surfactant concentration. To conduct general linear stability analysis (GLSA), we employ the pseudo-spectral method. The GLSA predicts the existence of a longwave thermocapillary-induced instability, which overcomes the stabilisation by the solutocapillary effect due to the surfactant. The elasticity of the film, van der Waals forces and slip at the film–substrate interface contribute to further destabilisation, while a decrease in viscosity along the film height stabilises the film. The longwave instability is the dominant mode of instability. Thus, we derive longwave evolution equations whose linear stability analysis confirms the predictions of GLSA. The nonlinear analysis of the derived evolution equations, carried out using COMSOL 6.2, demonstrates tear-film rupture due to pure thermocapillary instability for sufficiently high thermal Marangoni numbers. In contrast, diseased eyes suffering from lipid layer dysfunction can undergo tear-film rupture at a much lower temperature difference between the ambient air and the cornea. Consideration of a viscosity decrease with increasing film height delays tear film rupture, while van der Waals forces decrease tear film rupture time. The rupture time range predicted by our model is in good agreement with clinical observations, thereby confirming the impact of the winter season on tear film dynamics.

We investigate Taylor–Couette flow with realistic no-slip boundary conditions at all surfaces through direct numerical simulation (DNS) and theoretical analysis. Imposing physically consistent end-wall conditions at the top and bottom lids significantly alters the flow dynamics compared with that for periodic boundary conditions. We extend the classical angular-momentum-flux framework to account for axial transport, thereby extending the Eckhardt–Grossmann–Lohse model (Eckhardt et al. J. Fluid Mech. vol. 581, 2007, pp. 221–250) to no-slip boundary conditions. A systematic exploration of the parameter space $(\textit{Re}, n)$ uncovers multiple long-lived states with different roll number $n$ configurations at identical Reynolds numbers $\textit{Re}$, giving rise to pronounced hysteresis loops occurring under realistic boundary conditions. Our DNS for no-slip axial endcaps reveals a sequence of structural transitions: as the inner-cylinder Reynolds number increases, the flow evolves from Taylor vortex flow through chaotic wavy vortex flow and turbulent wavy vortex flow to an axisymmetric turbulent Taylor vortex flow. Using modal energy budgets, we identify transition mechanisms and quantify how the accessible phase-space volume and associated roll-specific angular momentum flux depend on control parameters and the specific flow state. Our findings demonstrate the impact of realistic boundary conditions on the dynamics in Taylor–Couette flow and how they change the stability landscape of multiple states. The coexistence of distinct flow patterns and their stability analysis offers promising insights into transition dynamics between laminar and turbulent regimes in closed sheared flows.