This study presents a dual-channel vortex generator (VG) that leverages the snap-through behaviour of flexible sheets. The VG outperforms a similar-sized rigid VG in generating vortices within dual-channel flows while minimizing pressure loss. Numerical simulations using the immersed boundary-lattice Boltzmann method analyse the dynamics and vortex generation performance of the sheet under various system parameters. Two distinct modes are identified for the elastic sheet: a sustained snap-through mode (SSTM) and a dormant mode (DM). The sheet's mode is predominantly influenced by its length ratio (L*), bending stiffness $(K_b^\ast )$ and flow strength, with the mass ratio having a minimal impact. The sheet exhibiting regular SSTM can effectively generate vortices in both channels and the vortex generation performance can be conveniently tuned by altering the sheet's initial buckling (i.e. L*). An increase in $K_b^\ast $ results in a higher critical Reynolds number (Rec) required for mode transition. An increase in L*, however, initially raises Rec and then lowers it, suggesting an optimal length ratio (approximately 0.7 for our considered system) for minimizing the Rec necessary to trigger SSTM. Furthermore, a disparity in the flow strength between channels is found to suppress the snap-through of the sheet; a greater disparity, however, is permissible to induce the SSTM of more compliant sheets. These findings underscore the potential of snap-through behaviour for enhanced flow manipulation in dual-channel systems.

This work examines the influence of body porosity on the wake past nominally two-dimensional rectangular plates of fixed width $D$ in the moderate range of Reynolds numbers $Re = UD/\nu$ (with $U$ the incoming velocity and $\nu$ the kinematic viscosity) between 15 000 and 70 000. With porosity $\beta$ defined as the ratio of open to total area of the plate, it is well established that as porosity increases, the wake shifts from the periodic von Kármán shedding behaviour to a regime where this vortex shedding is absent. This change impacts the fluid forces acting on the plate, especially the drag, which is significantly lower for a wake without vortex shedding. We analyse experimentally the transition between these two regimes using hot-wire anemometry, particle-image velocimetry and force measurements. Coherence and phase measurements are used to determine the existence of regular, periodic vortex shedding based on the velocity fluctuations in the two main shear layers on either side of the wake. Results show that, independent of $Re$, the wake exhibits the classical Kármán vortex shedding pattern for $\beta <0.2$ but this is absent for $\beta >0.3$. In the intermediate range, $0.2<\beta <0.3$, there is a transitional regime that has not previously been identified; it is characterised by intermittent shedding. The flow alternates randomly between a vortex shedding and a non-shedding pattern and the total proportion of time during which vortex shedding is observed (the intermittency) decreases with increasing porosity.

Bioprosthetic heart valves create turbulent flow during early systole which might be detrimental to their durability and performance. Complex mechanisms in the unsteady and heterogeneous flow field complicate the isolation of specific instability mechanisms. We use linear stability analysis and numerical simulations of the flow in a simplified model to study mechanisms initiating the laminar–turbulent transition. The analysis of a modified Orr–Sommerfeld equation, which includes a model for fluid–structure interaction (FSI), indicates Kelvin–Helmholtz and FSI instabilities for a physiological Reynolds number regime. Two-dimensional parametrized FSI simulations confirm the growth rates and phase speeds of these instabilities. The eigenmodes associated with the observed leaflet kinematics allow for decoupled leaflet oscillations. A detailed analysis of the temporal evolution of the flow field shows that the starting vortex interacts with the aortic wall leading to a secondary vortex which moves towards the shear layer in the wake of the leaflets. This appears to be connected to the onset of the shear layer instabilities that are followed by the onset of leaflet motion leading to large-scale vortex shedding and eventually to a nonlinear breakdown of the flow. Numerical results further indicate that a narrower aorta leads to an earlier onset of the shear layer instabilities. They also suggest that the growing perturbations of the shear layer instability propagate upstream and may initiate the FSI instabilities on the valve leaflets.

Many turbulent flows exhibit time-periodic statistics. These include turbomachinery flows, flows with external harmonic forcing and the wakes of bluff bodies. Many existing techniques for identifying turbulent coherent structures, however, assume the statistics are statistically stationary. In this paper, we leverage cyclostationary analysis, an extension of the statistically stationary framework to processes with periodically varying statistics, to generalize the spectral proper orthogonal decomposition (SPOD) to the cyclostationary case. The resulting properties of the cyclostationary SPOD (CS-SPOD for short) are explored, a theoretical connection between CS-SPOD and the harmonic resolvent analysis is provided, simplifications for the low and high forcing frequency limits are discussed, and an efficient algorithm to compute CS-SPOD with SPOD-like cost is presented. We illustrate the utility of CS-SPOD using two example problems: a modified complex linearized Ginzburg–Landau model and a high-Reynolds-number turbulent jet.

This paper presents a new generation of fast-running physics-based models to predict the wake of a semi-infinite wind farm, extending infinitely in the lateral direction but with finite size in the streamwise direction. The assumption of a semi-infinite wind farm enables concurrent solving of the laterally averaged momentum equations in both streamwise and spanwise directions. The developed model captures important physical phenomena such as vertical top-down transport of energy into the farm, variable wake recovery rate due to the farm-generated turbulence and also wake deflection due to turbine yaw misalignment and Coriolis force. Of special note is the model's capability to predict and shed light on the counteracting effect of Coriolis force causing wake deflections in both positive and negative directions. Moreover, the impact of wind farm layout configuration on the flow distribution is modelled through a parameter called the local deficit coefficient. Model predictions were validated against large-eddy simulations extending up to 45 km downstream of wind farms. Detailed analyses were performed to study the impacts of various factors such as incoming turbulence, wind farm size, inter-turbine spacing and wind farm layout on the farm wake.

Shear-induced migration of elongated micro-swimmers exhibiting anisotropic Brownian diffusion at a population scale is investigated analytically in this work. We analyse the steady motion of confined ellipsoidal micro-swimmers subject to coupled diffusion in a general setting within a continuum homogenisation framework, as an extension of existing studies on macro-transport processes, by allowing for the direct coupling of convection and diffusion in local and global spaces. The analytical solutions are validated successfully by comparison with numerical results from Monte Carlo simulations. Subsequently, we demonstrate from the probability perspective that symmetric actuation does not yield net vertical polarisation in a horizontal flow, unless non-spherical shapes, external fields or direct coupling effects are harnessed to generate steady locomotion. Coupled diffusivities modify remarkably the drift velocity and vertical migration of motile micro-swimmers exposed to fluid shear. The interplay between stochastic swimming and preferential alignment could explain the diverse concentration and orientation distributions, including rheological formations of depletion layers, centreline focusing and surface accumulation. Results of the analytical study shed light on unravelling peculiar self-propulsion strategies and dispersion dynamics in active-matter systems, with implications for various transport problems arising from the fluctuating shape, size and other external or inter-particle interactions of swimmers in confined environments.

Accurate computation of hydroelastic waves in shallow water is critical because many hydroelastic wave applications are nearshores, such as sea-ice and floating infrastructures. In this paper, Boussinesq assumptions for shallow water are employed to derive nonlinear Boussinesq-type equations of hydroelastic waves, in which non-uniform distribution of structural stiffness and varying water depth are considered rigorously. Application of Boussinesq assumptions enables complicated three-dimensional problems to be reduced and formulated on the two-dimensional horizontal plane, therefore the proposed Boussinesq-type models are straightforward and versatile for a wide range of hydroelastic wave applications. Two configurations, a floating plate and a submerged plate, are studied. The first-order linear governing equations are solved analytically with periodic conditions assuming constant depth and uniform stiffness, and the linear dispersion relations are subsequently derived for both configurations. For flexural-gravity waves of a floating plate, unique behaviours of flexural-gravity waves different from shallow-water waves are discussed, and a generalized solitary wave solution is investigated. A nonlinear numerical solver is developed, and nonlinear flexural-gravity waves are found to have smaller wavelength and celerity than their linear counterparts. For hydroelastic waves of a submerged plate, dual-mode analytical solutions are discovered for the first time. Numerical computation has demonstrated that a plate with decreasing submerged depth is able to transfer wave energy from the deeper water to the surface layer.

A primary objective of integral methods, such as the momentum integral method, is to discern the physical processes contributing to skin friction. These methods encompass the momentum, kinetic energy and angular momentum integrals. This paper reformulates existing integrals based on the double-averaged Navier–Stokes equations, and extends their application to flows over rough walls. Our derivation yields distinct decompositions for the bottom-wall viscous friction coefficient, denoted as $C_S$, and the roughness element drag coefficient $C_R$. The decompositions comprise three terms: a viscous term, a turbulent term and a roughness (dispersive) term – regardless of the flow configuration, be it channel or boundary layer. Notably, when these integrals are evaluated for laminar flow scenarios, only the viscous term remains significant. In addition, we elucidate the spatial distributions of the terms within these decompositions. To demonstrate the practicality of our formulations, we apply them to analyse data from direct numerical simulations of turbulent half-channel flows. These flows feature aligned and staggered cubical roughness at various packing densities. Our analyses, based on kinetic-energy-oriented decompositions, reveal that when the surface coverage density $\lambda _p$ is small, the dominant terms within the decompositions are the viscous and turbulent terms. With increasing $\lambda _p$, the viscous dissipation term decreases, while the turbulent production term increases and then decreases. These variations arise from a subdued near-wall cycle and the development of a shear layer at the height of the cubes.

The importance of non-locality of mean scalar transport in two-dimensional Rayleigh–Taylor Instability (RTI) is investigated. The macroscopic forcing method is utilized to measure spatio-temporal moments of the eddy diffusivity kernel representing passive scalar transport in the ensemble averaged fields. Presented in this work are several studies assessing the importance of the higher-order moments of the eddy diffusivity, which contain information about non-locality, in models for RTI. First, it is demonstrated through a comparison of leading-order models that a purely local eddy diffusivity is insufficient to capture the mean field evolution of the mass fraction in RTI. Therefore, higher-order moments of the eddy diffusivity operator are not negligible. Models are then constructed by utilizing the measured higher-order moments. It is demonstrated that an explicit operator based on the Kramers–Moyal expansion of the eddy diffusivity kernel is insufficient. An implicit operator construction that matches the measured moments is shown to offer improvements relative to the local model in a converging fashion.

A previously developed method for large-eddy simulations (LES), based on spectral eddy-viscosity models, is generalised to the physical space representation. The method estimates the subgrid-scale (SGS) energy transfer using a similarity-type model expression for the SGS tensor obtained using Gaussian filtering of velocity fields advanced in the simulations. Following steps for the spectral space representation, the SGS transfer in the physical space is used to obtain a spatially varying eddy viscosity at each time step in LES. The computed eddy viscosity is employed to model the SGS stress tensor in the familiar Boussinesq form for use in LES. The method is tested in LES of isotropic turbulence at high Reynolds numbers where the inertial range dynamics is expected and for lower Reynolds number decaying turbulence under conditions of the classical Comte-Bellot and Corrsin experiments. In both cases the agreement with reference data is very good and the SGS transfer computed for the proposed eddy-viscosity model is highly correlated with the transfer computed for the similarity-type stress tensor.