The impact of two-dimensional (2-D) periodic forcing on transition dynamics in laminar separation bubbles (LSBs) generated on a flat plate is investigated experimentally. Laminar separation is caused by the favourable-to-adverse pressure gradient under an inverted modified NACA $64_3\text{-}618$ and periodic disturbances are generated by an alternating current dielectric barrier discharge plasma actuator located near the onset of the adverse pressure gradient. Surface pressure and time-resolved particle image velocimetry measurements along the centreline and several wall-parallel planes show significant reductions in bubble size with active flow control. Periodic excitation leads to amplification of the Kelvin–Helmholtz (K–H) instability resulting in strong 2-D coherent roller structures. Spanwise modulation of these structures is observed and varies with the forcing amplitude. Intermediate forcing amplitudes result in periodic spanwise deformation of the mean flow at large wavelength ($\lambda _z/L_{b,5kVpp} \approx 0.76$). For high-amplitude forcing, the spanwise modulation of the mean flow agrees with the much smaller wavelength of the difference interaction of two oblique subharmonic modes ($\lambda _z/L_{b,5kVpp} \approx 0.24$). Modal decomposition shows nonlinear interaction of the forced 2-D mode leading to growth of subharmonic and harmonic content, and the observation of several half-harmonics ($[n+1/2]f_{\textit{AFC}}$) at intermediate forcing amplitudes. Strongest amplitudes of the 2-D mode and delay of transition downstream of the time-averaged reattachment are observed for the intermediate forcing amplitudes, previously only observed in numerical simulations. Consistent with numerical results, further increase of the forcing amplitude leads to rapid breakdown to turbulence in the LSB. This suggests that the most effective exploitation of the K–H instability for transition delay is connected to an optimal (moderate) forcing amplitude.

The experimental investigation focuses on the effects of a short splitter plate on the flow physics of a circular cylinder in proximity to a wall by particle image velocimetry. The Reynolds number is Re = 3900, and the near-wall cylinder is immersed in turbulent boundary layer flow. Three gap ratios (i.e. $G/D$ = 0.25, 0.5 and 1) are considered, and the splitter plate length is $L/D=0$, 0.25, 0.5, 0.75 and 1. For $G/D$ = 0.5 and 1, as $L/D$ increases from 0 to 1, the splitter plate facilitates the cylinder shear layers to elongate downstream, and the vortex formation length is increased, which leads to the increase of the range of the recirculation region. For $G/D$ = 0.25, the wall suppression on the wake vortex formation is enhanced, and the variations of the vortex formation length and the range of the recirculation region with $L/D$ are small. The Strouhal number St presents a decrease with increasing $L/D$ for the three gap ratios. The effects of $L/D$ on the vortex evolution are revealed. For $G/D$ = 0.5 and 1, as $L/D$ increases, the induction of the lower wake vortex on the wall secondary vortex becomes weaker due to the reduction in strength of the wake vortex and the increase of the vortex formation length. Additionally, the wake fluctuation intensity is decreased with the increase of $L/D$ due to the splitter plate suppression. For $G/D$ = 0.25, theL/D influences on evolution of the wake vortices and wall secondary vortex are small, which result in weaker variation of the wake fluctuation intensity with $L/D$.

We report on the experimental and theoretical characterisation of shallow water wave guiding along a curved wave guide. A curved beam of fixed height and width positioned at the bottom of a wave tank generates an effective step-like perturbation which can guide surface water waves. We construct a linear wave theory for this wave propagation and characterise the parameter region where wave guiding can develop, as well as the possible guided modes, their profile and propagation constant. The theoretical analysis is supported by experimental surface wave data. A good agreement is found between experimental data and theoretical predictions, which gives insight into the possible harnessing of wave-guiding phenomena for energy harvesting.

In this work, we conduct particle-resolved direct numerical simulations to investigate the influence of particle inertia on the settling velocity of finite-size particles at low volume fraction in homogeneous isotropic turbulence across various settling numbers. Our results for finite-size particles show only reductions of settling velocity in turbulence compared to the corresponding laminar case. Although increased particle inertia significantly reduces the lateral motion of particles and fluctuations in settling velocity, its effect on the mean settling velocity is not pronounced, except when the settling effect is strong, where increased particle inertia leads to a noticeable reduction. Mechanistically, the nonlinear drag effect, which emphasises contributions from large turbulent scales, cannot fully account for the reduction in settling velocity. The influence of small-scale turbulence, particularly through interactions with the particle boundary layer, should not be overlooked. We also analyse the dependency of turbulence’s modification on particle settling velocity within a broader parameter space, encompassing both sub-Kolmogorov point particles and finite-size particles. Additionally, we develop a qualitative model to predict whether turbulence enhances or retards the settling velocity of particles.

In gas evolving electrolysis, bubbles grow at electrodes due to a diffusive influx from oversaturation generated locally in the electrolyte by the electrode reaction. When considering electrodes of micrometre size resembling catalytic islands, direct numerical simulations show that bubbles may approach dynamic equilibrium states at which they neither grow nor shrink. These are found in undersaturated and saturated bulk electrolytes during both pinning and expanding wetting regimes of the bubbles. The equilibrium is based on the balance of local influx near the bubble foot and global outflux. To identify the parameter regions of bubble growth, dissolution and dynamic equilibrium by analytical means, we extend the solution of Zhang & Lohse (2023 J. Fluid Mech. vol. 975, R3) by taking into account modified gas fluxes across the bubble interface, which result from a non-uniform distribution of dissolved gas. The Damköhler numbers at equilibrium are found to range from small to intermediate values. Unlike pinned nanobubbles studied earlier, for micrometre-sized bubbles the Laplace pressure plays only a minor role. With respect to the stability of the dynamic equilibrium states, we extend the methodology of Lohse & Zhang (2015a Phys. Rev. E vol. 91, 031003(R)) by additionally taking into account the electrode reaction. Under contact line pinning, the equilibrium states are found to be stable for flat nanobubbles and for microbubbles in general. For unpinned bubbles, the equilibrium states are always stable. Finally, we draw conclusions on how to possibly enhance the efficiency of electrolysis.

This study investigates the formation and evolution of fishbone patterns in oblique impinging liquid microjets through high-speed imaging experiments and numerical simulations. The results identify periodic oscillations in the upper region of the liquid sheet as the primary mechanism driving fishbone instabilities, which induce rim disturbances and lead to bifurcations into diverse fishbone morphologies. Transitions between stable and unstable flow patterns are systematically mapped across varying Weber numbers and impingement angles, providing a comprehensive framework for understanding this interfacial dynamics. Two critical transitions – marking the onset and disappearance of fishbone patterns – are characterised, offering insights into the underlying physics governing the stability and instability of these flow structures.

The primary bifurcation of the flow past three-dimensional axisymmetric bodies is investigated. We show that the azimuthal vorticity generated at the body surface is at the root of the instability, and that the mechanism proposed by Magnaudet & Mougin (2007, J. Fluid Mech., vol. 572, 311–337) in the context of spheroidal bubbles extends to axisymmetric bodies with a no-slip surface. The instability arises in a thin region of the flow in the near wake, and is associated with the occurrence of strong vorticity gradients. We propose a simple yet effective scaling law for the prediction of the instability, based on a measure of the near-wake vorticity and of the radial extent of the separation bubble. At criticality, the resulting Reynolds number collapses approximately to a constant value for bodies with different geometries and aspect ratios, with a relative variation that is one order of magnitude smaller than that of the standard Reynolds number based on the free-stream velocity and body diameter. The new scaling can be useful to assess whether the steady flow past axisymmetric bodies is globally unstable, without the need for an additional stability analysis.

We study decaying turbulence in the one-dimensional (1-D) Burgers equation (Burgulence) and 3-D Navier–Stokes (NS) turbulence. We first investigate the decay in time $t$ of the energy $E(t)$ in Burgulence, for a fractional Brownian initial potential, with Hurst exponent $H$, and demonstrate rigorously a self-similar time decay of $E(t)$, previously determined heuristically. This is a consequence of the non-trivial boundedness of the energy for any positive time. We define a spatially forgetful oblivious fractional Brownian motion (OFBM), with Hurst exponent $H$, and prove that Burgulence, with an OFBM as initial potential $\varphi _0(x)$, is not only intermittent, but it also displays a, hitherto unanticipated, large-scale bifractality or multifractality; the latter occurs if we combine OFBMs, with a distribution of $H\hbox{-}$values. This is the first rigorous proof of genuine multifractality for turbulence in a nonlinear hydrodynamical partial differential equation. We then present direct numerical simulations (DNSs) of freely decaying turbulence, capturing some aspects of this multifractality. For Burgulence, we investigate such decay for two cases: (a) $\varphi _0(x)$ a multifractal random walk that crosses over to a fractional Brownian motion beyond a cross-over scale $\mathcal{L}$, tuned to go from small- to large-scale multifractality; (b) initial energy spectra $E_0(k)$, with wavenumber $k$, having one or more power-law regions, which lead, respectively, to self-similar and non-self-similar energy decay. Our analogous DNSs of the 3-D NS equations also uncover self-similar and non-self-similar energy decay. Challenges confronting the detection of genuine large-scale multifractality, in numerical and experimental studies of NS and Magnetohydrodynamics turbulence, are highlighted.

Direct numerical simulation (DNS) of a Mach 4.9 zero-pressure-gradient turbulent boundary layer spatially developing over a cooled flat plate at wall-to-recovery temperature $T_w/T_r = 0.60$ is performed. Very long, streamwise contiguous domains are used in the DNS to achieve a wide continuous range of ‘useful’ friction Reynolds numbers of $1000 \lesssim {Re}_\tau \lesssim 2500$. The DNS datasets have been analysed to assess state-of-the-art compressibility scaling relations and turbulence modelling assumptions. The DNS data show a notable distinction in Reynolds number dependence between thermal and velocity fields. Although Reynolds stress and the budgets of turbulent kinetic energy have reached Reynolds number independence in the inner layer under semi-local scaling by ${Re}_\tau \simeq 1000$, the budget terms for temperature variance and turbulent heat flux retain a clear Reynolds number dependence near the wall over a broader range up to ${Re}_\tau \simeq 1900$. Such a stronger dependence of the thermal field on the Reynolds number may lead to inaccuracy in turbulence models that are calibrated on the basis of low-Reynolds-number data. Spectral and structural analysis suggests a more significant reduction in the prevalence of alternating positive and negative structures and an increase in the streamwise uniformity of streaks in the wall heat flux $q_w$ than in the wall shear stress $\tau _w$ when the Reynolds number increases.

This paper presents numerical results for Rayleigh–Bénard convection with suspended particles at Rayleigh numbers $Ra=10^7$ and $10^8$, and unit Prandtl number. Accounting for their finite size makes it possible to investigate in detail the mechanism by which the particles, which are 10 % heavier than the fluid, get resuspended after settling, thus maintaining a two-phase circulating flow. It is shown that an essential component of this mechanism is the formation of particle accumulations, or ‘dunes’, on the bottom of the Rayleigh–Bénard cell. Ascending plumes become localised on these dunes. Particles are dragged up the dune slopes, and when they reach the top, are entrained into the rising plumes. Direct resuspension of particles from the cell bottom, if it happens at all, is very rare. For $Ra=10^7$, aspect ratios (width/height) $\Gamma =1,2,4$ are considered. It is found that in these and in the other cases simulated, at steady state, a single dune evolves, the largest linear dimension of which is comparable to the cell size. A remarkable consequence is that even at the low volume fraction considered here, 3.27 %, the particles are able to structure the flow and to determine the size and position of the largest ascending plumes. Their effect on the Nusselt number, however, remains small. This and other results are explained on the basis of the ratio of the cell-bottom viscous boundary-layer thickness to the particle diameter.

Turbidity currents (TCs) are a common kind of particle-laden flow in underwater natural environments. This work employs a Eulerian–Lagrangian model to investigate the dynamic regimes of lock-exchange TC in a moderate flow Reynolds number range (${Re} = 1716-3836$) as well as the formation and evolution mechanisms of interfacial Kelvin–Helmholtz (KH) billows composed of a fluid–particle mixture. The results demonstrate that a fluid streak with high stretching at the interface, which twists and takes on a braided structure, is the key to the onset of KH instability. An increase in ${\textit{Re}}$ results in a higher interfacial fluid velocity gradient that intensifies the shear instability, and an increase in the convergent fluid force acting on the particles. This provides an explanation for the significant increases both in quantity and strength of KH vortices as ${\textit{Re}}$ rises. The enhanced KH vortices contribute to particle suspension and streamwise transport at larger ${\textit{Re}}$, leading to an extension in the duration of the slumping stage, which exhibits a constant forward velocity regime. The spatially continuous braided structure in the vorticity sheet region is responsible for the intriguing merging phenomenon of interfacial vortices. Furthermore, TC kinetic energy increases with the increasing ${\textit{Re}}$, and the system dissipation rate decreases in the early and middle stages of the TC. This behaviour may be correlated to the reducing shear between the TC and ambient fluid by interfacial KH billows. Regarding the turbulent kinetic energy dissipation of interfacial vortices, normal strain predominates in the middle stage, while shear deformation is most prevalent in the early and later stages.

Flow through a square-duct at a moderate Reynolds number is investigated. We first employ an edge-tracking procedure in the $\pi$-rotationally symmetric sub-space of state space and identify a streamwise-localised invariant solution for square-duct flow, which is a steady travelling wave with mirror symmetries across bisectors of the duct walls. The identified invariant solution features four vortices placed in pairs at opposite duct walls and exhibits significant streamwise localisation making it the first reported localised solution in the square-duct flow. Additionally, this solution remains very close to the laminar attractor in the sense of the velocity perturbation energy and the corresponding hydraulic losses. Stability analysis of this solution demonstrates that the identified state is an edge state in the $\pi$-rotationally symmetric sub-space but not in the full space. Next, a long-time turbulence behaviour and its relevance to the symmetric streamwise-localised invariant solution are discussed. We focus on the characteristics of the averaged flow and the recurring patterns of eight- or four-vortex states, typical for the square-duct flow and related to Prandtl’s secondary flows of the second type. Through heuristic arguments, we illustrate that turbulent flow exhibits relatively quiescent interludes of increased symmetry of the velocity field across wall bisectors. We show that those periods correlate to episodes where, statistically, a four-vortex flow configuration emerges from the otherwise eight-vortex state, which is also associated with decreased symmetry of the flow field. Our results suggest that the four-vortex state appearing in the relatively quiescent periods in the flow time history, accompanied by flow field symmetrisation and the onset of streamwise localisation of turbulent flow, bears a striking similarity to the found symmetric streamwise-localised invariant solution.

This study investigates the fluid mechanisms underlying the interaction between ventilated shoulder and tail cavities under vertical launching conditions. It is found that expansion and contraction coexist within the tail cavity. When the expansion rate exceeds the contraction rate, the volume of the tail cavity increases; conversely, it decreases. Through this process, the cavity undergoes cyclic pulsation during its vertical evolution, including expansion, over-expansion, contraction and over-contraction. Before the shoulder cavity extends to the position of the tail cavity, wall confinement restricts the tail cavity from expanding towards the vehicle’s lateral wall. After the encounter between the shoulder and tail cavities, the re-entrant flow at the end of the shoulder cavity induces the tail cavity to overcome wall confinement and expand towards the lateral wall, initiating their fusion. As a result, a supercavity forms and attaches to the surface of the vehicle. Moreover, after the fusion, the pressure driving mode at the vehicle’s bottom wall shifts from the tail cavity pulsation to the re-entrant flow. In addition, an increase in the ventilation rate induces progressive expansion of the shoulder cavity’s radial dimension, and accelerates its downstream propagation. The fusion mode between the shoulder and tail cavities transitions from progressive fusion to coverage fusion.

This work experimentally explores the alignment of the vorticity vector and the strain-rate tensor eigenvectors at locations of extreme upscale and downscale energy transfer. We show that the turbulent von Kármán flow displays vorticity–strain alignment behaviour across a large range of Reynolds numbers, which is very similar to previous studies on homogeneous, isotropic turbulence. We observe that this behaviour is amplified for the largest downscale energy transfer events, which tend to be associated with sheet-like geometries. These events are also shown to have characteristics previously associated with high flow field nonlinearity and singularities. In contrast, the largest upscale energy transfer events display very different structures which showcase a strong preference for vortex compression. Notably, in both cases we find that these trends are strengthened as the probed scales approach the Kolmogorov scale. We then show further evidence for the argument that strain self-amplification is the most salient feature in characterising the cascade direction. Finally, we identify possible invariant behaviour for the largest energy transfer events, even at scales near the Kolmogorov scale.

The presence of trapped air on a solid surface can alter the direction of the liquid jets induced by cavitation bubbles, which prevents or reduces erosion. In this study, we numerically investigate mutual interaction between air trapped in a pocket on a wall and a nearby bubble in water, as well as the resultant hydrodynamic loading. Both the depth and radius of the cylindrical pocket are similar to the maximum bubble radius. The pressure imposed on the inner wall of the air pocket is assessed for various values of the air pocket size and the stand-off parameter. The deformation of the air pocket and the bubble is analysed in each of three sequential stages. During the bubble expansion stage, a shock wave reflects at the water–air interface of the pocket, and the wall inside the compressed pocket is protected from the shock wave. As the bubble jet induced during bubble contraction tends to move away from the air pocket, other liquid jets formed at the water–air interface, namely central and lateral pocket jets, can directly collide with the inner wall of the pocket after the bubble collapses. These collisions exert significant pressure on the wall under certain conditions. The formation of the central pocket jet originates from the strong fluctuation of the water–air interface by the expanding and contracting bubble. The development of the lateral pocket is related to changes in the potential energy of the air under its second contraction.