In this paper, the reflection of shock waves with downstream expansion fan interference in two-dimensional, inviscid flow is investigated, including steady Mach reflection (MR) and the unsteady transition process from regular reflection (RR) to MR. A threshold for the configuration based on non-dimensional wedge length is proposed. The analytical model for the steady MR and RR$\rightarrow$MR transition process is established based on the classical shock and expansion wave relations, whose prediction agrees well with results obtained through inviscid numerical simulation. It is found that the expansion fan interference significantly influences the steady flow patterns, especially the height of the Mach stem and the shape of the slip line. The interaction accelerates the formation of the sonic throat, stabilizing the flow structure rapidly, and results in generally small Mach stem heights. The exposure of the triple point to the expansion fan eliminates the inflection point on the slip line, whose slope increases smoothly. The interaction further affects the time evolution of the Mach stem during the multiple-interaction stage of the RR$\rightarrow$MR transition process. It appears that the modifications come from the curvature of the incident shock brought by the wave interference. During the multiple-interaction stage, the triple point moves upstream along the curved incident shock, where the incident shock angle changes according to the curvature, resulting in the variation of the evolution velocity.

We find the optimally time-dependent (OTD) orthogonal modes about a time-varying flow generated by a strong gust vortex impacting a NACA 0012 airfoil. This OTD analysis reveals the amplification characteristics of perturbations about the unsteady base flow and their amplified spatiotemporal structures that evolve over time. We consider four time-varying laminar base flows in which a vortex with a strength corresponding to the gust ratio $G$ of $\{-1,-0.5,0.5,1\}$ impinges on the leading edge of the airfoil at an angle of attack of $12^\circ$. In these cases, the impingement of the strong gust vortex causes massive separation and the generation of large-scale vortices around the airfoil within two convective time units. As these flow structures develop around the airfoil on a short time scale, the airfoil experiences large transient vortical lift variations in the positive and negative directions that are approximately five to ten times larger than the baseline lift. The highly unsteady nature of these vortex–airfoil interactions necessitates an advanced analytical technique capable of capturing the transient perturbation dynamics. For each of the considered gust ratios, the OTD analysis identifies the most amplified region to perturbations, the location of which changes as the wake evolves differently. For interactions between a moderate positive vortex gust ($G=0.5$) and the airfoil, the area where perturbations are amplified transitions from the leading-edge vortex (LEV) sheet to the forming LEV. Later, this most amplified structure becomes supported in the airfoil wake directly behind the trailing edge. In contrast, a strong vortex gust ($G=\pm 1$) encountered by the airfoil shows the most amplified OTD mode to appear around the core of the shed vortices. This study provides an analysis technique and fundamental insights into the broader family of unsteady aerodynamic problems.

We derive leading-order governing equations and boundary conditions for a sheet of viscous fluid retracting freely under surface tension. We show that small thickness perturbations about a flat base state can lead to regions of compression, where one or both of the principal tensions in the sheet becomes negative, and thus drive transient buckling of the sheet centre-surface. The general theory is applied to the simple model problem of a retracting viscous disc with small axisymmetric thickness variations. Transient growth in the centre-surface is found to be possible generically, with the dominant mode selected depending on the imposed initial thickness and centre-surface perturbations. An asymptotic reduction of the boundary conditions at the edge of the disc, valid in the limit of large normalised thickness perturbations, reduces the centre-surface evolution equation to an ordinary differentional equation (ODE) eigenvalue problem. Analysis of this eigenvalue problem leads to insights such as how the degree of transient buckling depends on the imposed thickness perturbation and which thickness perturbation gives rise to the largest transient buckling.

Electro-osmotic flow (EOF) in nanochannels exhibits a puzzling non-monotonic dependence on salt concentration, which contrasts with observations in microchannels and remains not fully understood. In this work, we address this phenomenon through a theoretical investigation of EOF in $\mathrm{pH}$-regulated channels. New analytical approximations for electrostatic potential, EOF profile and electro-osmotic mobility beyond the Debye–Hückel limit are derived through asymptotic analysis. Our findings reveal that the surface electrostatic potential is independent of the channel size only when the half-channel size exceeds the Gouy–Chapman length. In contrast, surface ionization and net charge distribution play more crucial roles in EOF at the nanoscale, as they govern both the magnitude and the spatial distribution of the Coulomb driving force. As salt concentration increases, EOF velocity initially rises due to enhanced surface ionization, followed by a decline attributed to increased wall shear stress. This work provides key insights for EOF applications in nanofluidics and biomedical devices, and deepens the understanding of electrokinetic phenomena influenced by $\mathrm{pH}$-regulation effects.

The flow-induced oscillation of a transversely clamped buckled flexible filament in a uniform flow was explored using the penalty immersed boundary method. Both inverted and conventional configurations were analysed. The effects of bending rigidity, filament length and Reynolds number were examined. As these parameters were varied, four distinct modes were identified: conventional transverse oscillation mode, deflected oscillation mode, inverted transverse oscillation mode and structurally steady mode. The filament exhibited a 2S wake pattern under the conventional transverse oscillation mode and the small-amplitude inverted transverse oscillation mode, a P wake pattern under the deflected oscillation mode and a 2S + 2P wake pattern for the large-amplitude inverted transverse oscillation mode. Irrespective of their initial conditions, all of the filaments converged to the conventional transverse oscillation mode under low bending rigidity. Multistability was observed in the transversely clamped buckled flexible filament under moderate bending rigidity. The deflection in the oscillation mode increased with increasing filament length. The inverted buckled filament was sensitive to the Reynolds number, unlike the conventional buckled filament. The transverse oscillation mode demonstrated superior energy-harvesting performance.

We investigate convection in a thin cylindrical gas layer with an imposed flux at the bottom and a fixed temperature along the side, using a combination of direct numerical simulations and laboratory experiments. The experimental approach allows us to extend by two orders of magnitude the explored range in terms of flux Rayleigh number. We identify a scaling law governing the root-mean-square horizontal velocity and explain it through a dimensional analysis based on heat transport in the turbulent regime. Using particle image velocimetry, we experimentally confirm, for the most turbulent regimes, the presence of a drifting persistent pattern consisting of radial branches, as identified by Rein et al. (2023, J. Fluid Mech. 977, A26). We characterise the angular drift frequency and azimuthal wavenumber of this pattern as functions of the Rayleigh number. The system exhibits a wide distribution of heat flux across various time scales, with the longest fluctuations attributed to the branch pattern and the shortest to turbulent fluctuations. Consequently, the branch pattern must be considered to better forecast important wall heat flux fluctuations, a result of great relevance in the context of nuclear safety, the initial motivation for our study.

Direct numerical simulations in periodic plane channels are used to study turbulent flow over ‘patches’ of roughness distributed on otherwise smooth walls. Circular patches as well as those resembling natural bio-fouling roughness are considered. Roughnesses within the patches are statistically similar and formed by random distribution of roughness elements of truncated cone shape. The two main studied parameters are the characteristic length scale of the patches $\varLambda _P$ and roughness area coverage ratio (CR). To provide a reference, simulations of homogeneous roughness (i.e. with 100 % CR) are performed at different roughness element densities translated into different values of frontal solidity. Results show that when $\varLambda _P$ is of the order of channel half-height $\delta$, the global friction coefficient $C_f$ of patchy roughness is scattered around that of homogeneous roughness with similar ‘mean’ frontal solidity. As $\varLambda _P/\delta$ grows, asymptotic convergence towards an equilibrium value is identified. Considering the present data, a normalised $C_f$ can be satisfactorily correlated by $\varLambda _P/\delta$; the normalisation includes $C_f$ for a homogeneous roughness similar to the patch roughness at two limiting cases. This points towards the possibility to develop a universal heterogeneous roughness correlation based on a knowledge of existing homogeneous roughness correlations. Furthermore, local and global flow statistics are studied, which among others, indicate formation of secondary motions for regular patch arrangement at $\varLambda _P\approx \delta$ with implications on the outer layer similarity of global mean velocity and Reynolds stress profiles.

We consider the stability of Couette flow when travelling vibrations perturb one boundary. It is demonstrated that if the bounding surface profile takes the form of sinusoidal waves, then the otherwise stable shear flow becomes unstable for appropriately chosen values of vibration amplitude, phase speed and wavenumber. When instability arises, it is driven by centrifugal forces that are created by wave-imposed changes in the direction of fluid movement. Only subcritical waves, defined as vibrations with phase speed smaller than the maximum flow velocity, cause instability. As the fluid Reynolds number grows, the interval of vibration wavenumbers and phase speeds capable of flow destabilisation is enhanced. A range of parameters is identified for which the vibrations seem to play dual roles: they decrease the flow resistance while simultaneously generating streamwise vortices. This vibration class constitutes an energy-efficient control tool that may potentially intensify the mixing within a flow.

In this article, we investigate the behaviour of a cohesive granular material in a rotating drum. We use a model material with tuneable cohesion and vary the dimension of the drum in the radial and axial directions. The results show that the geometry of the drum may play a crucial role in the material dynamics, leading to significant changes in the surface morphology and flow regime. We attribute this behaviour to the fact that an increase in cohesion causes the grains to feel the sidewalls at a greater distance. Finally, we rationalize the results by introducing two dimensionless characteristic lengths, defined as the ratio of the drum dimensions to a cohesive length, which allow for the interpretation of the variation in the surface morphology and of the different flow regimes observed experimentally.

We present a novel technique to render objects invisible to incident waves in a water waveguide system with parallel walls at low frequencies. The invisibility of a waveguide defect, specifically a vertical surface-piercing circular cylinder, is achieved through local deformations of the waveguide walls in the immediate vicinity of the defect. Our method results in a reflection coefficient that is at least 20 times lower than in the case of a parallel waveguide. The effect is observed over a broad frequency range. Experimental results confirm the high efficiency of our approach, showing that backscattered energy is reduced by a factor of 100–5000 compared with the reference case within the considered frequency range.

Intermittent swimming behaviour is commonly observed in larval zebrafish, often attributed to energy-saving mechanisms. In this study, we utilize a hybrid approach combining deep reinforcement learning and the immersed boundary–lattice Boltzmann method to train a larval zebrafish-like swimmer to reach a target with minimized energy expenditure. We find that when the tail-beat period is fixed, continuous swimming emerges as the optimal strategy. However, when the tail-beat period is allowed to vary, intermittent swimming proves superior in energy performance, achieved through reductions in tail-beat amplitude and frequency. Our detailed analysis reveals that intermittent swimmers employ rapid backward tail flicks to attain high speeds, coupled with slower forward tail flicks and coasting phases to conserve energy. Furthermore, we derive scaling laws governing the swimming performance of trained fish. These results offer valuable insights into the intermittent swimming patterns of fish, with implications for understanding bio-inspired locomotion and informing the design of energy-efficient aquatic systems.

The impact of intrinsic compressibility effects – changes in fluid volume due to pressure variations – on high-speed wall-bounded turbulence has often been overlooked or incorrectly attributed to mean property variations. To quantify these intrinsic compressibility effects unambiguously, we perform direct numerical simulations of compressible turbulent channel flows with nearly uniform mean properties. Our simulations reveal that intrinsic compressibility effects yield a significant upward shift in the logarithmic mean velocity profile that can be attributed to the reduction in the turbulent shear stress. This reduction stems from the weakening of the near-wall quasi-streamwise vortices. In turn, we attribute this weakening to the spontaneous opposition of sweeps and ejections from the near-wall expansions and contractions of the fluid, and provide a theoretical explanation for this mechanism. Our results also demonstrate that intrinsic compressibility effects play a crucial role in the increase in inner-scaled streamwise turbulence intensity in compressible flows, as compared with incompressible flows, which was previously regarded to be an effect of mean property variations alone.

Coherent structures over two distinct, organized wall perturbations – a transverse sinusoidal bump with and without small-scale longitudinal grooves – are studied using direct numerical simulations. Large-scale spanwise rollers (SRs) form via shear layer rollup past the bump peak, enveloping a large separation bubble (SB) for both a smooth wall (SW) and a grooved wall (GW). In a GW, small-scale alternatingly spinning jets emanating from the crests’ corners merge with the shear layer, altering the SRs compared with SRs in a SW. The underlying coherence of the highly turbulent SRs is educed via phase-locked ensemble averaging. Coherent vorticity contours of SRs are ellipses tilted downward, hence causing co-gradient Reynolds stress. The limited streamwise length of SB precludes SR tumbling, unlike in a free shear layer. The coherent field reveals minibubbles attached to the bump’s downstream wall with circulation opposite to that of the SB – they are larger, stronger and more numerous in GW than in SW – reducing skin friction. Compared with SW, the swirling jets in GW increase coherent production while decreasing incoherent production. Additionally, the jets push the SRs to travel faster and farther before reattachment. The SB experiences two different modes of oscillation due to high-frequency advection of the shear layer SR and low-frequency breathing of the SB, where the former dominates in GW and the latter in SW. Negative production is caused by counter-rotating vortex dipoles inducing flow ejections (for both SW and GW) and single vortices penetrating the grooves – both occurring in the region of flow acceleration.

This study investigates how the spatial configuration of submerged three-dimensional patches of vegetation impacts turbulence. Laboratory experiments were conducted in a channel with submerged patches of model vegetation configured with different patch area densities ($\phi _{p}$), representing the bed area fraction occupied by patches, ranging from 0.13 to 0.78, and different spatial patterns transitioning from two dimensional (channel-spanning patches) to three dimensional (laterally unconfined patches). These configurations produced a range of flow regimes within the canopy, from wake interference flow to skimming flow. At low area density ($\phi _{p}\lt0.5$), turbulence within the canopy increased with increasing $\phi _{p}$ regardless of spatial configuration, while at high area density ($\phi _{p}\gt0.5$), the relationship between turbulence and $\phi _{p}$ depended on the spatial configuration of the patches. For the same patch area density, the configuration with smaller lateral gaps generated stronger turbulence within the canopy. The relative contributions of wake and shear production also varied with the spatial configuration of the patches. At low area densities, wake production dominated over shear production, while at high area densities, shear production was more dominant due to an enhanced shear layer at the top of the canopy and reduced mean velocity within the canopy. A new predictive model for the channel-averaged turbulent kinetic energy (TKE) was developed as a function of channel-averaged velocity, canopy geometry, and patch area density, which showed good agreement with the measured TKE.

Deep reinforcement learning (DRL) is employed to develop control strategies for drag reduction in direct numerical simulations of turbulent channel flows at high Reynolds numbers. The DRL agent uses near-wall streamwise velocity fluctuations as input to modulate wall blowing and suction velocities. These DRL-based strategies achieve significant drag reduction, with maximum rates $35.6\,\%$ at $Re_{\tau }\thickapprox 180$, $30.4\,\%$ at $Re_{\tau }\thickapprox 550$, and $27.7\,\%$ at $Re_{\tau }\thickapprox 1000$, outperforming traditional opposition control methods. An expanded range of wall actions further enhances drag reduction, although effectiveness decreases at higher Reynolds numbers. The DRL models elevate the virtual wall through blowing and suction, aiding in drag reduction. However, at higher Reynolds numbers, the amplitude modulation of large-scale structures significantly increases the residual Reynolds stress on the virtual wall, diminishing the drag reduction. Analysis of budget equations provides a systematic understanding of the underlying drag reduction dynamics. The DRL models reduce skin friction by inhibiting the redistribution of wall-normal turbulent kinetic energy. This further suppresses the wall-normal velocity fluctuations, reducing the production of Reynolds stress, thereby decreasing skin friction. This study showcases the successful application of DRL in turbulence control at high Reynolds numbers, and elucidates the nonlinear control mechanisms underlying the observed drag reduction.

We study the effect of turbulence on collisions between a finite-size bubble and small inertial particles based on interface-resolved simulations. Our results show that the interaction with the flow field around the bubble remains the dominant effect. Nonlinear dependencies in this process can enhance the turbulent collision rate by up to 100 % compared to quiescent flow. Fluctuations in the bubble slip velocity during the interaction with the particle additionally increase the collision rate. We present a frozen-turbulence model that captures the relevant effects providing a physically consistent framework to model collisions of small inertial particles with finite-sized objects in turbulence.

A numerical study supplemented with theoretical analysis is made, to analyse the electrophoresis of highly charged soft particles in electrolytes with trivalent counterions. The electrokinetic model is devised under the continuum hypothesis, which incorporates the ion–ion electrostatic correlations, hydrodynamic steric interactions of finite sized ions and ion–solvent interactions. The governing equations for ion transport and electric field are derived from the volumetric free energy of the system, which includes the first-order correction for the non-local electrostatic correlations of interacting ions, excess electrochemical potential due to finite ion size as well as the Born energy difference of ions due to dielectric permittivity variation. The electrolyte viscosity is considered to be a function of the local volume fraction of finite-sized ions, which causes the diffusivity of ions to vary locally. The occurrence of mobility reversal of a soft particle having the same polarity of its core and soft shell charge and formation of a coion-dominated zone in the soft layer is elaborated through this study. This can explain the mechanisms for the attraction between like-charged soft particles, as seen in the condensation of DNAs. The impact of ion–ion correlations and ion–solvent interactions of finite-sized ions are analysed by comparing them with the results based on the standard model. At a higher range of the core charge density, the ion–ion correlations induce a condensed layer of counterions on the outer surface of the core, which draws coions in the electric double layer, leading to an inversion in polarity of the charge density and mobility reversal. The dielectric decrement and ion steric interactions create a saturation in ion distribution and hence, modify the condensed layer of counterions. The enhanced fixed charge density of the polyelectrolyte layer diminishes the ion correlations due to the stronger screening effects and prevents the formation of a coion dominated zone in the Debye layer. The impact of the counterion size and the mixture of monovalent and trivalent counterions on mobility is analysed.