We describe and model experimental results on the dynamics of a ‘ludion’ – a neutrally buoyant body – immersed in a layer of stably stratified salt water. By oscillating a piston inside a cylinder communicating with a narrow (in one of its horizontal dimensions) vessel containing the stably stratified layer of salt water, it is easy to periodically vary the hydrostatic pressure of the fluid. The ludion or Cartesian diver, initially positioned at its equilibrium height and free to move horizontally, can then oscillate vertically when forced by the pressure oscillations. Depending on the ratio of the forcing frequency to the Brunt–Väisälä frequency of the stratified fluid, the ludion can emit its own internal gravity waves that we measure by a classical particle image velocimetry technique. Our experimental results describe first the resonance of the vertical motions of the ludion when excited at different frequencies. A theoretical oscillator model is then derived taking into account added mass and added friction coefficients and its predictions are compared with the experimental data. Then, for the larger oscillation amplitudes, we observe and describe a bifurcation towards free horizontal motions. Although the internal gravity wave frequencies are affected by the Doppler shift induced by the horizontal displacement velocities, it seems that, contrary to surface waves associated with Couder walkers (Couder et al. Nature, vol. 437, 2005, p. 238) they are not the cause of the horizontal swimming. This does not, however, exclude possible interactions between the ludion and internal gravity waves and possible hydrodynamic quantum analogies to be explored in the future.

In the linear approximation, we study the one-dimensional problem of reflectionless wave propagation on the surface of a shallow duct with spatially varying water depth, duct width and current. We show that both global and bounded exact solutions describing the reflectionless propagation in opposite directions of long waves of arbitrary shape exist for the particular variations of these parameters. A general analysis of the problem is illustrated by a few solutions constructed for the specific cases of spatial profiles of the flow and wave propagation velocities. The results obtained can be of interest to mitigate the possible impact of waves on ships, marine engineering constructions and human activity in coastal zones.

In this paper, a pulsed spark discharge plasma actuator array is deployed to control laminar–turbulent transition in a Mach 3.0 flat-plate boundary layer, and the subtle flow structures are visualized by nanoparticle planar laser scattering (NPLS) technique. Results show that the onset location of turbulence can be brought upstream by plasma actuation, corresponding to forced boundary-layer transition. Hairpin vortex packets evolved from the thermal bulbs play a vital role in the breakdown of laminar flow. With the help of a machine learning tool, all the relevant structures induced by plasma actuation are extracted from NPLS images, and a conceptual model of the hairpin vortex generation is proposed, including three stages: production and lift-up of the high-vorticity region, formation of the $\varLambda$ vortex and evolution of the hairpin vortex.

To investigate the intrinsic mechanism for mixing enhancement by variable-density (VD) behaviour, a canonical VD mixing extracted from a supersonic streamwise vortex protocol, a shock–bubble interaction (SBI), is numerically studied and compared with a counterpart of passive-scalar (PS) mixing. It is meaningful to observe that the maximum concentration decays much faster in a VD SBI than in a PS SBI regardless of the shock Mach number ($Ma=1.22 - 4$). The quasi-Lamb–Oseen-type velocity distribution in the PS SBI is found by analysing the azimuthal velocity that stretches the bubble. Meanwhile, for the VD SBI, an additional stretching enhanced by the secondary baroclinic vorticity (SBV) production contributes to the faster-mixing decay. The underlying mechanism of the SBV-enhanced stretching is further revealed through the density and velocity difference between the light shocked bubble and the heavy ambient air. By combining the SBV-accelerated stretching model and the initial shock compression, a novel mixing time estimation for VD SBI is theoretically proposed by solving the advection–diffusion equation under a deformation field of an axisymmetric vortex with the additional SBV-induced azimuthal velocity. Based on the mixing time model, a mixing enhancement number, defined by the ratio of VD and PS mixing time further, reveals the contribution from the VD effect, which implies a better control of the density distribution for mixing enhancement in a supersonic streamwise vortex.

The scaling of different features of streamwise normal stress profiles $\langle uu\rangle ^+(y^+)$ in turbulent wall-bounded flows is the subject of a long-running debate. Particular points of contention are the scaling of the ‘inner’ and ‘outer’ peaks of $\langle uu\rangle ^+$ at $y^+\approxeq ~15$ and $y^+ ={O}(10^3)$, respectively, their infinite Reynolds number limit, and the rate of logarithmic decay in the outer part of the flow. Inspired by the thought-provoking paper of Chen & Sreenivasan (J. Fluid Mech., vol. 908, 2021, p. R3), two terms of an inner asymptotic expansion of $\langle uu\rangle ^+$ in the small parameter $Re_{\tau }^{-1/4}$ are constructed from a set of direct numerical simulations (DNS) of channel flow. This inner expansion is for the first time matched through an overlap layer to an outer expansion, which not only fits the same set of channel DNS within 1.5 % of the peak stress, but also provides a good match of laboratory data in pipes and the near-wall part of boundary layers, up to the highest $Re_{\tau }$ values of $10^5$. The salient features of the new composite expansion are first, an inner $\langle uu\rangle ^+$ peak, which saturates at 11.3 and decreases as $Re_{\tau }^{-1/4}$. This inner peak is followed by a short ‘wall log law’ with a slope that becomes positive for $Re_{\tau }$ beyond ${O}(10^4)$, leading up to an outer peak, followed by the logarithmic overlap layer with a negative slope going continuously to zero for $Re_{\tau }\to \infty$.

An analytical theory is developed that describes acoustic microstreaming produced by two interacting bubbles. The bubbles are assumed to undergo axisymmetric oscillation modes, which can include radial oscillations, translation and shape modes. Analytical solutions are derived in terms of complex amplitudes of oscillation modes, which means that the modal amplitudes are assumed to be known and serve as input data when the velocity field of acoustic microstreaming is calculated. No restrictions are imposed on the ratio of the bubble radii to the viscous penetration depth and the distance between the bubbles. The interaction between the bubbles is considered both when the linear velocity field is calculated and when the second-order velocity field of acoustic microstreaming is calculated. Capabilities of the analytical theory are illustrated by computational examples.

Viscous flow around spherical macroscopic cavities in a granular material is investigated. The Stokes equation inside and the Darcy–Brinkman equation outside the cavities are considered. In particular, the interaction of two equally sized cavities positioned in tandem is examined in detail, where the asymptotic effect of the other cavity is taken into account. The present analysis gives a reasonable estimate on the volume flow into the cavity and the local enhancement of stresses. This is applicable to predict the microscale waterway formation in that material, onset of landslides, collapse of cliffs and river banks, etc.

Fully developed turbulent flow in channels with mild to strong longitudinal curvature is studied by direct numerical simulations. The Reynolds based on the bulk mean velocity and channel half-width $\delta$ is fixed at $20\,000$, resulting in a friction Reynolds number of approximately 1000. Four cases are considered with curvature varying from $\gamma = 2\delta /r_c = 0.033$ to 0.333, where $r_c$ is the curvature radius at the channel centre. Substantial differences between the mean wall shear stress on the convex and concave walls are already observed for $\gamma = 0.033$. A log-law region is absent and a region with nearly constant mean angular momentum develops in the channel centre for strong curvatures. Spanwise and wall-normal velocity fluctuations are strongly amplified by curvature in the outer region of the concave channel side. Only near the walls, where curvature effects are relatively weak, do the mean velocity and velocity fluctuation profiles approximately collapse when scaled by wall units based on the local friction velocity. Budgets of the streamwise and wall-normal Reynolds-stress equations are presented and turbulence structures are investigated through visualizations and spectra. In the case with strongest curvature, the flow relaminarizes locally near the convex wall. On the concave channel side, large elongated streamwise vortices reminiscent of Taylor–Görtler vortices develop for all curvatures considered. The maximum in the premultiplied two-dimensional wall-normal energy spectrum and co-spectrum shifts towards larger scales with increasing curvature. The large scales substantially contribute to the wall-normal velocity fluctuations and momentum transport on the concave channel side.

This text presents one of the first successful applications of a rare events sampling method for the study of multistability in a turbulent flow without stochastic energy injection. The trajectories of collapse of turbulence in plane Couette flow, and their probability and rate of occurrence are systematically computed using adaptive multilevel splitting (AMS). The AMS computations are performed in a system of size $L_x\times L_z=24\times 18$ at Reynolds number $R=370$ with an acceleration by a factor ${O}(10)$ with respect to direct numerical simulations (DNS) and in a system of size $L_x\times L_z=36\times 27$ at Reynolds number $R=377$ with an acceleration by a factor ${O}(10^3)$. The AMS results are validated by a comparison with DNS in the smaller system. Visualisations indicate that turbulence collapses because the self-sustaining process of turbulence fails locally. The streamwise vortices decay first in streamwise elongated holes, leaving streamwise invariant streamwise velocity tubes that experience viscous decay. These holes then extend in the spanwise direction. The examination of more than a thousand trajectories in the $(E_{k,x}=\int u_x^2/2\,\textrm {d}^3\boldsymbol {x},E_{k,y-z}=\int (u_y^2/2+u_z^2/2)\,\textrm {d}^3\boldsymbol {x})$ plane in the smaller system confirms the faster decay of streamwise vortices and shows concentration of trajectories. This hints at an instanton phenomenology in the large size limit. The computation of turning point states, beyond which laminarisation is certain, confirms the hole formation scenario and shows that it is more pronounced in larger systems. Finally, the examination of non-reactive trajectories indicates that both the vortices and the streaks reform concomitantly when the laminar holes close.

The phenomena of microlayer formation and its dynamic characteristics during the nucleate pool boiling regime have been widely investigated in the past. However, experimental works on real-time microlayer dynamics during nucleate flow boiling conditions are highly scarce. The present work is an attempt to address this lacuna and is concerned with developing a fundamental understanding of microlayer dynamics during the growth process of a single vapour bubble under nucleate flow boiling conditions. Boiling experiments have been conducted under subcooled conditions in a vertical rectangular channel with water as the working fluid. Thin-film interferometry combined with high-speed cinematography have been adopted to simultaneously capture the dynamic behaviour of the microlayer along with the bubble growth process. Transients associated with the microlayer have been recorded in the form of interferometric fringe patterns, which clearly reveal the evolution of the microlayer beneath the growing vapour bubble, the movement of the triple contact line and the growth of the dryspot region during the bubble growth process. While symmetric growth of the microlayer was confirmed in the early growth phase, the bulk flow-induced bubble deformation rendered asymmetry to its profile during the later stages of the bubble growth process. The recorded fringe patterns have been quantitatively analysed to obtain microlayer thickness profiles at different stages of the bubble growth process. For Re = 3600, the maximum thickness of the almost wedge-shaped microlayer was obtained as δ ~ 3.5 μm for a vapour bubble of diameter 1.6 mm. Similarly, for Re = 6000, a maximum microlayer thickness of δ ~ 2.5 μm was obtained for a bubble of diameter 1.1 mm.

The instability of an incompressible boundary-layer flow over an infinite swept wing in the presence of disc-type roughness elements and free-stream turbulence (FST) has been investigated by means of direct numerical simulations. Our study corresponds to the experiments by Örlü et al. (Tech. Rep., KTH Royal Institute of Technology, 2021, http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-291874). Here, different dimensions of the roughness elements and levels of FST have been considered. The aim of the present work is to investigate the experimentally observed sensitivity of the transition to the FST intensity. In the absence of FST, flow behind the roughness elements with a height above a certain value immediately undergoes transition to turbulence. Impulse–response analyses of the steady flow have been performed to identify the mechanism behind the observed flow instability. For subcritical roughness, the generated wave packet experiences a weak transient growth behind the roughness and then its amplitude decays as it is advected out of the computational domain. In the supercritical case, in which the flow transitions to turbulence, flow as expected exhibits an absolute instability. The presence of FST is found to have a significant impact on the transition behind the roughness, in particular in the case of a subcritical roughness height. For a height corresponding to a roughness Reynolds number $Re_{hh}=461$, in the absence of FST the flow reaches a steady laminar state, while a very low FST intensity of $Tu =0.03\,\%$ causes the appearance of turbulence spots in the wake of the roughness. These randomly generated spots are advected out of the computational domain. For a higher FST level of $Tu=0.3\,\%$, a turbulent wake is clearly visible behind the element, similar to that for the globally unstable case. The presented results confirm the experimental observations and explain the mechanisms behind the observed laminar–turbulent transition and its sensitivity to FST.

The interface between two immiscible fluids can become unstable under the effect of an imposed tangential electric field along with a stagnation point flow. This canonical situation, which arises in a wide range of electrohydrodynamic systems including at the equator of electrified droplets, can result in unstable interface deflections where the perturbed interface gets drawn along the extensional axis of the flow while experiencing strong charge build-up. Here, we present analytical and numerical analyses of the stability of a planar interface separating two immiscible fluid layers subject to a tangential electric field and a stagnation point flow. The interfacial charge dynamics is captured by a conservation equation accounting for Ohmic conduction, advection by the flow and finite charge relaxation. Using this model, we perform a local linear stability analysis in the vicinity of the stagnation point to study the behaviour of the system in terms of the relevant dimensionless groups of the problem. The local theory is complemented with a numerical normal-mode linear stability analysis based on the full system of equations and boundary conditions using the boundary element method. Our analysis demonstrates the subtle interplay of charge convection and conduction in the dynamics of the system, which oppose one another in the dominant unstable eigenmode. Finally, numerical simulations of the full nonlinear problem demonstrate how the coupling of flow and interfacial charge dynamics can give rise to nonlinear phenomena such as tip formation and the growth of charge density shocks.

Suspended particles can significantly alter the fluid properties and, in particular, can modify the transition from laminar to turbulent flow. We investigate the effect of heavy particle suspensions on the linear stability of the Kolmogorov flow by means of a multiple-scale expansion of the Eulerian model originally proposed by Saffman (J. Fluid Mech., vol. 13, issue 1, 1962, pp. 120–128). We find that, while at small Stokes numbers particles always destabilize the flow (as already predicted by Saffman in the limit of very thin particles), at sufficiently large Stokes numbers the effect is non-monotonic in the particle mass fraction and particles can both stabilize and destabilize the flow. Numerical analysis is used to validate the analytical predictions. We find that in a region of the parameter space the multiple-scale expansion overestimates the stability of the flow and that this is a consequence of the breakdown of the scale separation assumptions.

The flow-induced vibration of square cylinders under flow is known to be caused by two distinct mechanisms of interaction: vortex-induced vibrations and galloping. In the present paper we address the issue of the apparent suppression of galloping when the mass ratio between the solid and the fluid is low enough. By using a reduced-order model that we validate on pre-existing results, we show that galloping is actually not suppressed, but delayed to higher values of the flow velocity. This is explained using a linear stability analysis where the competition between unstable modes is related to the transition between vortex-induced vibration and galloping. Direct numerical simulations coupled with a moving square cylinder confirm that galloping can be found even at very low mass ratios.

In this study, we propose a scale-by-scale (SBS) energy budget equation for flows with homogeneity in at least one direction. This SBS budget represents a modified form of the equation first proposed by Danaila et al. (J. Fluid Mech., vol. 430, 2001, pp. 87–109) for the channel centreline – the primary difference is that, here, we consider the role of pressure along with the errors associated with the isotropic approximations of the interscale divergence and Laplacian of the squared velocity increment. The term encompassing the effects of mean shear is also characterised such that the present analysis can be extended straightforwardly to locations away from the centreline. We show, based on a detailed analysis of previously published channel flow direct numerical simulations and pipe flow experiments near the centreline, how several terms in the present SBS budget equation (including the third-order velocity structure function) behave with increasing Reynolds number. The behaviour of these terms is shown to imply a rate of emergence and subsequent growth of the 4/3 law scale subrange at the channel centreline and pipe axis. The analysis also suggests that the peak magnitude of the third-order velocity structure function occurs at a scale that is fixed in proportion to the Taylor microscale at sufficiently high Reynolds number.

Direct numerical simulations and linear stability analysis are carried out to study mixed convection in a horizontal duct with constant-rate heating applied at the bottom and an imposed transverse horizontal magnetic field. A two-dimensional approximation corresponding to the asymptotic limit of a very strong magnetic field effect is validated and applied, together with full three-dimensional analysis, to investigate the flow's behaviour in the previously unexplored range of control parameters corresponding to typical conditions of a liquid metal blanket of a nuclear fusion reactor (Hartmann numbers up to $10^4$ and Grashof numbers up to $10^{10}$). It is found that the instability to quasi-two-dimensional rolls parallel to the magnetic field discovered at smaller Hartmann and Grashof numbers in earlier studies also occurs in this parameter range. Transport of the rolls by the mean flow leads to magnetoconvective temperature fluctuations of exceptionally high amplitudes. It is also demonstrated that quasi-two-dimensional structure of flows at very high Hartmann numbers does not guarantee accuracy of the classical two-dimensional approximation. The accuracy deteriorates at the highest Grashof numbers considered in the study.

An experimental study is conducted on unsteady pressure fluctuations occurring near the nozzle exit and just outside the shear layer of compressible jets. These fluctuations are related to ‘trapped waves’ within the jet's potential core, as investigated and reported recently by other researchers. Round nozzles of three different diameters and rectangular nozzles of various aspect ratios are studied. The fluctuations manifest as a series of peaks in the spectra of the fluctuating pressure. Usually the first peak at the lowest frequency (fundamental) has the highest amplitude and the amplitude decreases progressively for successive peaks at higher frequencies. These ‘trapped wave spectral peaks’ are found to occur with all jets at high subsonic conditions and persist into the supersonic regime. Their characteristics and variations with axial and radial distances, jet Mach number and aspect ratio of the nozzle are documented. For round nozzles, the frequency of the fundamental is found to be independent of the jet's exit boundary layer characteristics and scales with the nozzle diameter. On a Strouhal number (based on diameter) versus jet Mach number plot it is represented by a unique curve. Relative to the fundamental the frequencies of the successive peaks are found to bear the ratios of 5/3, 7/3, 9/3 and so on, at a given Mach number. For rectangular nozzles, the number of peaks observed on the major axis is found to be greater than that observed on the minor axis by a factor approximately equal to the nozzle's aspect ratio; the fundamental is the same on either edge. For all nozzles the onset of screech tones appears as a continuation of the evolution of these peaks; it is as if one of these peaks abruptly increases in amplitude and turns into a screech tone as the jet Mach number is increased.

Fault zones have the potential to act as leakage pathways through low permeability structural seals in geological reservoirs. Faults may facilitate migration of groundwater contaminants and stored anthropogenic carbon dioxide (CO$_2$), where the waste fluids would otherwise remain securely trapped. We present an analytical model that describes the dynamics of leakage through a fault zone cutting multiple aquifers and seals. Current analytical models for a buoyant plume in a semi-infinite porous media are combined with models for a leaking gravity current and a new model motivated by experimental observation, to account for increased pressure gradients within the fault due to an increase in Darcy velocity directly above the fault. In contrast to previous analytical fault models, we verify our results using a series of analogous porous medium tank experiments, with good matching of observed leakage rates and fluid distribution. We demonstrate the utility of the model for the assessment of CO$_2$ storage security, by application to a naturally occurring CO$_2$ reservoir, showing the dependence of the leakage rates and fluid distribution on the fault/aquifer permeability contrast. The framework developed within this study can be used for quick assessment of fluid leakage through fault zones, given a set of input parameters relating to properties of the fault, aquifer and fluids, and can be incorporated into basin-scale models to improve computational efficiency. The results show the utility of using analytical methods and reduced-order modelling in complex geological systems, as well as the value of laboratory porous medium experiments to verify results.

The dependence of Reynolds shear stress on wave phase is investigated for initially isotropic turbulence distorted by a progressive surface wave through direct numerical simulations. A wave-following streamline coordinate frame is used to analyse the turbulence dynamics such that the information of the varying direction of wave orbital motions is embedded into the coordinate system, which helps capture the effect of flow curvature on the turbulence and quantify momentum exchange between the near-surface and deep regions in the wavy domain accurately. It is found that the Reynolds shear stress is enhanced under the backward slope of the wave and can be scaled by the wave steepness and the streamwise velocity fluctuations. Analyses of the budget of Reynolds shear stress indicate that such a variation with the wave phase is caused by the variation in the production of the Reynolds shear stress and the effect of pressure fluctuations. Further investigation shows that the production of the Reynolds shear stress is closely associated with the wave surface curvature. A model that includes a correction term for the curvature effect for the pressure–strain correlation term is examined and is found to agree reasonably well with the simulation result. The correction term is found to make an appreciable contribution to the model, further supporting our finding that the wave curvature plays an important role in the turbulence dynamics near the surface.

A study of small-amplitude shape oscillations of a viscous compound droplet suspended in a viscous host fluid is performed. A generalized eigenvalue problem is formulated and is solved by using the spectral method. The effects of the relevant non-dimensional parameters are examined for three cases, i.e. a liquid shell in a vacuum and a compound droplet in a vacuum or in a host fluid. The fundamental mode $l=2$ is found to be dominant. There exist two oscillatory modes: the in phase and the out of phase. In most situations, the interfaces oscillate in phase rather than out of phase. For the in-phase mode, in the absence of the host, as the viscosity of the core or the shell increases, the damping rate increases whereas the oscillation frequency decreases; when the viscosity exceeds a critical value, the mode becomes aperiodic with the damping rate bifurcating into two branches. In addition, when the tension of the inner interface becomes smaller than some value, the in-phase mode turns aperiodic. In the presence of the unbounded host fluid, there exists a continuous spectrum. The viscosity of the host may decrease or increase the damping rate of the in-phase mode. The mechanism behind it is discussed. The density contrasts between fluids affect oscillations of the droplet in a complicated way. Particularly, sufficiently large densities of the core or the host lead to the disappearance of the out-of-phase mode. The thin shell approximation predicts well the oscillation of the compound droplet when the shell is thin.