This study explores the dynamics of flexible ribbons with an added weight $G$ at the tail in uniform flow, considering key parameters like inflow Reynolds number ($Re_u$), mass ratio ($M_t$) and aspect ratio (${A{\kern-4pt}R}$). For two-dimensional ribbons, a simplified theoretical model accurately predicts equilibrium configurations and forces. Inspired by Barois & De Langre (J. Fluid Mech., vol. 735, 2013, R2), we introduce an important control parameter ($C_G$) that effectively collapses normalized forces and angle data. Vortex-induced vibration is observed, and Strouhal number ($St$) scaling laws with $C_G$ are identified. In three-dimensional scenarios, the model effectively predicts lift, but its accuracy in predicting drag is limited to situations with small $Re_u$ values. The flow along the side edges mitigates pressure differences, thereby suppressing vibration and uplift, particularly noticeable in the case of narrow ribbons. This study offers new insights into the dynamics of flexible bodies in uniform flow.

Previous studies have shown that low-frequency vortex oscillations occur around a hemisphere–cylinder body at different angles of attack, but the underlying mechanism is still unclear. In this study, we examine the origin of the vortex oscillation using numerical simulations and global linear stability analysis. The vortex oscillation is reproduced using numerical simulations, and the oscillatory modes are computed through dynamic mode decomposition (DMD). We obtain the base flow through a selective frequency damping method, which exhibits a pair of steady leeward vortices over the body. The four unstable modes are computed using a modified Arnoldi iteration. The antisymmetric mode with a Strouhal number of 0.105 is discovered to be responsible for the alternate oscillation of the vortex pair, and the mode with a Strouhal number of 0.220 corresponds to the in-phase vortex oscillation. Their frequencies have good agreement with the modes of DMD. The other two unstable modes with higher frequencies, one antisymmetric and one symmetric, are harmonic frequencies of the above two modes. The study conclusively verifies that the vortex oscillation over a hemisphere–cylinder body originates from a global flow instability.

Understanding settling motion of coral grains is important in terms of protection of coral reef systems and resotoration of the associated ecosystems. In this paper, a series of laboratory experiments was conducted to investigate the settling motion, using optical microscopy to measure shape parameters of coral grains and the particle-filtering-based object tracking to reconstruct the three-dimensional trajectory. Three characteristic descent regimes, namely, tumbling, chaotic and fluttering, are classified based on the three-dimensional trajectory, the spiral radius variation and the velocity spectrum. It is demonstrated that if one randomly picks up one coral grain, then the probabilities of occurrence of the three regimes are approximately $26\,\%$, $42\,\%$ and $32\,\%$, respectively. We have shown that first, the dimensionless settling velocity generally increases with the non-dimensional diameter and Corey shape factor and second, the drag coefficient generally decreases with the Reynolds number and Corey shape factor. Based on this, the applicability of existing models on predicting settling velocity and drag coefficient for coral grains is demonstrated further. Finally, we have proposed extended models for predicting the settling velocity. This study contributes to better understanding of settling motion and improves our predictive capacity of settling velocity for coral grains with complex geometry.

Saturated flow film boiling on a sphere has been numerically studied in this work for both vertical and horizontal flow configurations. The simulations were performed using a numerical methodology developed by the authors for boiling flows on three-dimensional unstructured meshes. For interface capturing, the coupled level set and volume of fluid method is used. The interface evolution, vapour wake dynamics and heat transfer have been thoroughly investigated by varying the saturated liquid flow velocity, sphere diameter and wall superheat. The relative importance of both the buoyancy and the inertial forces is described in terms of the Froude number $(Fr)$. The vapour bubble evolves periodically at low $Fr$ values, while a stable vapour column develops at high $Fr$ values. The interface evolution pattern obtained in the present work is in good agreement with the results of experimental studies available in the literature. For all the values of $Fr$, a stable vapour column develops for a large-diameter sphere and releases vapour bubbles of varying sizes. Furthermore, for a large-diameter sphere, surface capillary waves are observed at the interface, similar to the observations of some of the experimental studies available in the literature. The flow in the liquid and vapour wakes appears to be strongly coupled. The heat transfer in the present work is estimated using the spatially and temporally averaged Nusselt numbers. Finally, an fast Fourier transform analysis of the space-averaged Nusselt number reveals a strong interaction among the different forces.

We investigate the phenomena of crater formation and gas release caused by projectile impact on underwater beds, which occurs in many natural, geophysical and industrial applications. The bed in our experiment is constructed of hydrophobic particles, which trap a substantial amount of air in the pores of the bed. In contrast to dry beds, the air–water interface in a submerged bed generates a granular skin that provides rigidity to the medium by producing skin over the bulk. The projectile's energy is used to reorganize the grains, which causes the skin to crack, allowing the trapped air to escape. The morphology of the craters as a function of impact energy in submerged beds exhibits different scaling laws than what is known for dry beds. This phenomenon is attributed to the contact line motion on the hydrophobic fractal-like surface of submerged grains. The volume of the gas released is a function of multiple factors, chiefly the velocity of the projectile, depth of the bed and depth of the water column.

Small finite-size particles suspended in fluid flow through an enclosed curved duct can focus to points or periodic orbits in the two-dimensional duct cross-section. This particle focusing is due to a balance between inertial lift forces arising from axial flow and drag forces arising from cross-sectional vortices. The inertial particle focusing phenomenon has been exploited in various industrial and medical applications to passively separate particles by size using purely hydrodynamic effects. A fixed size particle in a circular duct with a uniform rectangular cross-section can have a variety of particle attractors, such as stable nodes/spirals or limit cycles, depending on the radius of curvature of the duct. Bifurcations occur at different radii of curvature, such as pitchfork, saddle-node and saddle-node infinite period (SNIPER), which result in variations in the location, number and nature of these particle attractors. By using a quasi-steady approximation, we extend the theoretical model of Harding et al. (J. Fluid Mech., vol. 875, 2019, pp. 1–43) developed for the particle dynamics in circular ducts to spiral duct geometries with slowly varying curvature, and numerically explore the particle dynamics within. Bifurcations of particle attractors with respect to radius of curvature can be traversed within spiral ducts and give rise to a rich nonlinear particle dynamics and various types of tipping phenomena, such as bifurcation-induced tipping (B-tipping), rate-induced tipping (R-tipping) and a combination of both, which we explore in detail. We discuss implications of these unsteady dynamical behaviours for particle separation and propose novel mechanisms to separate particles by size in a non-equilibrium manner.

Depinning of liquid droplets on substrates by flow of a surrounding immiscible fluid is central to applications such as cross-flow microemulsification, oil recovery and waste cleanup. Surface roughness, either natural or engineered, can cause droplet pinning, so it is of both fundamental and practical interest to determine the flow strength of the surrounding fluid required for droplet depinning on rough substrates. Here, we develop a lubrication-theory-based model for droplet depinning on a substrate with topographical defects by flow of a surrounding immiscible fluid. The droplet and surrounding fluid are in a rectangular channel, a pressure gradient is imposed to drive flow and the defects are modelled as Gaussian-shaped bumps. Using a precursor-film/disjoining-pressure approach to capture contact-line motion, a nonlinear evolution equation is derived describing the droplet thickness as a function of distance along the channel and time. Numerical solutions of the evolution equation are used to investigate how the critical pressure gradient for droplet depinning depends on the viscosity ratio, surface wettability and droplet volume. Simple analytical models are able to account for many of the features observed in the numerical simulations. The influence of defect height is also investigated, and it is found that, when the maximum defect slope is larger than the receding contact angle of the droplet, smaller residual droplets are left behind at the defect after the original droplet depins and slides away. The model presented here yields considerably more information than commonly used models based on simple force balances, and provides a framework that can readily be extended to study more complicated situations involving chemical heterogeneity and three-dimensional effects.

Wall temperature has a significant effect on shock wave/turbulent boundary layer interactions (STBLIs) and has become a non-negligible factor in the design process of hypersonic vehicles. In this paper, direct numerical simulations are conducted to investigate the wall temperature effects on STBLIs over a 34° compression ramp at Mach number 6. Three values of the wall-to-recovery-temperature ratio (0.50, 0.75 and 1.0) are considered in the simulations. The results show that the size of the separation bubble declines significantly as the wall temperature decreases. This is because the momentum profile of the boundary layer becomes fuller with wall cooling, which means the near-wall fluid has a greater momentum to suppress flow separation. An equation based on the free-interaction theory is proposed to predict the distributions of the wall pressure upstream of the corner at different wall temperatures. The prediction results are generally consistent with the simulation results (Reynolds number Reτ ranges from 160 to 675). In addition, the low-frequency unsteadiness is studied through the weighted power spectral density of the wall pressure and the correlation between the upstream and downstream. The results indicate that the low-frequency motion of the separation shock is mainly driven by the downstream mechanism and that wall cooling can significantly suppress the low-frequency unsteadiness, including the strength and streamwise range of the low-frequency motions.

This study proposes a novel super-resolution (or SR) framework for generating high-resolution turbulent boundary layer (TBL) flow from low-resolution inputs. The framework combines a super-resolution generative adversarial neural network (SRGAN) with down-sampling modules (DMs), integrating the residual of the continuity equation into the loss function. The DMs selectively filter out components with excessive energy dissipation in low-resolution fields prior to the super-resolution process. The framework iteratively applies the SRGAN and DM procedure to fully capture the energy cascade of multi-scale flow structures, collectively termed the SRGAN-based energy cascade reconstruction framework (EC-SRGAN). Despite being trained solely on turbulent channel flow data (via ‘zero-shot transfer’), EC-SRGAN exhibits remarkable generalization in predicting TBL small-scale velocity fields, accurately reproducing wavenumber spectra compared to direct numerical simulation (DNS) results. Furthermore, a super-resolution core is trained at a specific super-resolution ratio. By leveraging this pretrained super-resolution core, EC-SRGAN efficiently reconstructs TBL fields at multiple super-resolution ratios from various levels of low-resolution inputs, showcasing strong flexibility. By learning turbulent scale invariance, EC-SRGAN demonstrates robustness across different TBL datasets. These results underscore the potential of EC-SRGAN for generating and predicting wall turbulence with high flexibility, offering promising applications in addressing diverse TBL-related challenges.

Resonant standing waves excited on the water surface in a deep narrow rectangular cavity by a fully immersed cylinder harmonically oscillating in the vertical direction are studied theoretically and experimentally. The effect of the finite wavemaker size is considered in the framework of the potential two-dimensional flow theory. Nonlinearities and weak dissipation at solid surfaces are accounted for. The spatio-temporal structure of the waves in the presence of detuning between the forcing and the natural frequency of the system is analysed. The variation of the surface shape in space and time studied in experiments supports the assumption of two-dimensional flow. The finite size of the wavemaker causes a downshift of the effective resonant frequency of the cavity; this effect is enhanced by the nonlinearity. For small amplitude waves, the surface elevation evolution in time is decomposed into the sum of the time-periodic function, corresponding to the forcing frequency, and its second harmonic; the shape of the wavenumber spectra of these components depends on the forcing frequency. For larger wave amplitudes, additional peaks in the frequency spectrum appear. The theoretical predictions are compared with the experimental results.