In 2017, Brosseau & Vlahovska (Phys. Rev. Lett, vol. 119, no. 3, 2017, p. 034501) found that, in a strong electric field, a weakly conductive, low-viscosity droplet immersed in a highly conductive, high-viscosity medium formed a lens shape, and liquid rings continuously detached from its equatorial plane and subsequently broke up into satellite droplets. This fascinating multiphase electrohydrodynamic (EHD) phenomenon is known as droplet equatorial streaming. In this paper, based on the unified lattice Boltzmann method framework proposed by Luo et al. (Phil. Trans. R. Soc. A Math. Phys. Engng Sci, vol. 379, no. 2208, 2021, p. 20200397), a novel lattice Boltzmann (LB) model is constructed for multiphase EHD by coupling the Allen–Cahn type of multiphase LB model and two new LB equations to solve the Poisson equation of the electric field and the conservation equation of the surface charge. Using the proposed LB model, we successfully reproduced, for the first time, the complete process of droplet equatorial streaming, including the continuous ejection and breakup of liquid rings on the equatorial plane. In addition, it is found that, under conditions of high electric field strength or significant electrical conductivity contrast, droplets exhibit fingering equatorial streaming that was unknown before. A power-law relationship is discovered for droplet total charge evolution and a theoretical model is then proposed to describe the droplet radius and height over time. The breakup of liquid rings is found to be dominated by capillary instability, while the breakup of liquid fingers is governed by the end-pinching mechanism. Finally, a phase diagram is constructed for fingering equatorial streaming and ring equatorial streaming, and a criterion equation is established for the phase boundary.

Coherent small-amplitude unsteadiness of the shock wave and the separation region over a canonical double cone flow, termed in literature as oscillation-type unsteadiness, is experimentally studied at Mach 6. The double cone model is defined by three non-dimensional geometric parameters: fore- and aft-cone angles ($\theta _1$ and $\theta _2$), and ratio of the conical slant lengths ($\varLambda$). Previous studies of oscillations have been qualitative in nature, and mostly restricted to a special case of the cone model with fixed $\theta _1 = 0^\circ$ and $\theta _2 = 90^\circ$ (referred to as the spike-cylinder model), where $\varLambda$ becomes the sole governing parameter. In the present effort we investigate the self-sustained flow oscillations in the $\theta _1$-$\varLambda$ parameter space for fixed $\theta _2 = 90^\circ$ using high-speed schlieren visualisation. The experiments reveal two distinct subtypes of oscillations, characterised by the motion (or lack thereof) of the separation point on the fore-cone surface. The global time scale associated with flow oscillation is extracted using spectral proper orthogonal decomposition. The non-dimensional frequency (Strouhal number) of oscillation is seen to exhibit distinct scaling for the two oscillation subtypes. The relationship observed between the local flow properties, instability of the shear layer, and geometric constraints on the flow suggests that an aeroacoustic feedback mechanism sustains the oscillations. Based on this understanding, a simple model with no empiricism is developed for the Strouhal number. The model predictions are found to match well with experimental measurements. The model provides helpful physical insight into the nature of the self-sustained flow oscillations over a double cone at high speeds.

In particle-laden turbulent wall flows, lift forces can influence the near-wall turbulence. This has been observed recently in particle-resolved simulations, which, however, are too expensive to be used in upscaled models. Instead, point-particle simulations have been the method of choice to simulate the dynamics of these flows during the last decades. While this approach is simpler, cheaper and physically sound for small inertial particles in turbulence, some issues remain. In the present work, we address challenges associated with lift force modelling in turbulent wall flows and the impact of lift forces in the near-wall flow. We performed direct numerical simulations of small inertial point particles in turbulent channel flow for fixed Stokes number and mass loading while varying the particle size. Our results show that the particle dynamics in the buffer region, causing the apparent particle-to-fluid slip velocity to vanish, raises major challenges for modelling lift forces accurately. While our results confirm that lift forces have little influence on particle dynamics for sufficiently small particle sizes, for inner-scaled diameters of order one and beyond, lift forces become quite important near the wall. The different particle dynamics under lift forces results in the modulation of streamwise momentum transport in the near-wall region. We analyse this lift-induced turbulence modulation for different lift force models, and the results indicate that realistic models are critical for particle-modelled simulations to correctly predict turbulence modulation by particles in the near-wall region.

The orientational dynamics of a spherical magnetic particle in linear shear flow subjected to an oscillating magnetic field in the flow plane is analysed in the viscous limit. The shear is in the $X$–$Y$ plane, the magnetic field is in the $X$ direction and the vorticity is perpendicular to the flow in the $Z$ direction. The relevant dimensionless groups are $\omega ^\ast$, the ratio of the frequency of the magnetic field and the strain rate, and $\varSigma$, the ratio of the magnetic and hydrodynamic torques. As $\varSigma$ is decreased, there is a transition from in-plane rotation, where the rotation is in the flow ($X$–$Y$) plane, to out-of-plane rotation, where the orientation vector is not necessarily in the $X$–$Y$ plane and the dynamics depends on the initial orientation. The particle rotation is phase-locked for in-plane rotation with discrete odd rotation number (number of rotations in one period of magnetic field oscillation), while the orbits are quasi-periodic with non-integer rotation number for out-of-plane rotation. For $\varSigma \gg 1$, regions of odd rotation number $n_o$ are bound by the lines $8 (n_o-1) \varSigma \omega ^\ast = 1$ and $8 (n_o+1) \varSigma \omega ^\ast = 1$, and there are discontinuous changes in the rotation number and mean and root-mean-square torque at these lines. For $\varSigma \ll 1$, the domains of in-plane rotation of finite width in the $\omega ^\ast$–$\varSigma$ plane extend into downward cusps at $\omega ^\ast = {1}/{2 n_o}$. The orbits are quasi-periodic between these domains, where the rotation is out of plane.

Microbes play a primary role in wide-ranging biogeochemical and physiological processes, where ambient fluid flows are responsible for cell dispersal as well as mixing of dissolved resources, signalling molecules and biochemical products. Determining the simultaneous (and often coupled) transport properties of actively swimming cells together with passive scalars is key to understanding and ultimately predicting these complex processes. In recent work, Ran & Arratia (J. Fluid Mech., vol. 988, 2024, A25) present the striking observation that dilute concentrations of swimming bacteria severely hinder scalar transport through Lagrangian vortex boundaries in a chaotic flow. Analysis of rotation-dominated regions suggests that local accumulation of bacteria enhances the strength of transport barriers and highlights the role of understudied elliptical Lagrangian coherent structures in bacterial and multicomponent transport.

Seafloor roughness profoundly influences the pattern and dynamics of large-scale oceanic flows. However, these kilometre-scale topographic patterns are unresolved by global numerical Earth system models and will remain subgrid for the foreseeable future. To properly represent the effects of small-scale bathymetry in analytical and coarse-resolution numerical models, we develop the stratified ‘sandpaper’ theory of flow–topography interaction. This model, which is based on the multilayer shallow-water framework, extends its barotropic antecedent to stratified flows. The proposed theory is successfully tested on the configuration representing the interaction of a zonal current with a corrugated cross-flow ridge.

Plane turbulent wall jets are traditionally considered to be composed of a turbulent boundary layer (TBL) topped by a half-free jet. However, certain peculiar features, such as counter-gradient momentum flux occurring below velocity maximum in experiments and numerical simulations, suggest a different structure of turbulence therein. Here, we hypothesize that turbulence in wall jets has two distinct structural modes, wall mode scaling on wall variables and free-jet mode scaling on jet variables. To investigate this hypothesis, experimental data from our wall jet facility are acquired using single hot-wire anemometry and two-dimensional particle image velocimetry at three nozzle Reynolds numbers 10 244, 15 742 and 21 228. Particle image velocimetry measurements with four side-by-side cameras capture the longest field of view studied so far in wall jets. Direct spatial spectra of these fields reveal modal spectral contributions to variances of velocity fluctuations, Reynolds shear stress, shear force, turbulence production, velocity fluctuation triple products and turbulent transport. The free-jet mode has wavelengths scaling on the jet length scale ${z_{T}}$, and contains two dominant submodes with wavelengths $5{z_{T}}$ and $2.5{z_{T}}$. The region of flow above the velocity maximum shows the presence of the outer jet mode whereas the region below it shows robust bimodal behaviour attributed to both wall and inner jet modes. Counter-gradient momentum flux is effected by the outer jet mode intruding into the region below velocity maximum. These findings support the hypothesis of wall and free-jet structural modes, and indicate that the region below velocity maximum could be much complex than a conventional TBL.

In this study we propose a novel data-driven reduced-order model for complex dynamics, including nonlinear, multi-attractor, multi-frequency and multiscale behaviours. The starting point is a fully automatable cluster-based network model (CNM) (Li et al., J. Fluid Mech., vol. 906, 2021, A21) that kinematically coarse grains the state with clusters and dynamically predicts the transitions in a network model. In the proposed dynamics-augmented CNM (dCNM) the prediction error is reduced with trajectory-based clustering using the same number of centroids. The dCNM is first exemplified for the Lorenz system and then demonstrated for the three-dimensional sphere wake featuring periodic, quasi-periodic and chaotic flow regimes. For both plants, the dCNM significantly outperforms the CNM in resolving the multi-frequency and multiscale dynamics. This increased prediction accuracy is obtained by stratification of the state space aligned with the direction of the trajectories. Thus, the dCNM has numerous potential applications to a large spectrum of shear flows, even for complex dynamics.

The non-Oberbeck–Boussinesq effects on the stability of a vertical natural convection boundary layer are investigated using the linearised disturbance equations for air flows up to a temperature difference of $\Delta T=100\,{\rm K}$. Based on the linear stability results, the neutral curve is shown to be sensitive to the choice of reference temperature. When evaluated using the film temperature $T_f$, a lower film Grashof number is required to trigger the linear instability for larger $\Delta T$. The relative contributions of shear and buoyant production to the perturbation kinetic energy budget reveals that the marginally unstable modes are amplified based on different mechanisms: for lower wavenumbers at relatively small Grashof number, the instability is driven by buoyancy; whereas for higher wavenumbers and larger Grashof number, the flow becomes unstable due to a shear instability. The use of reference temperature is found to scale the shear- and buoyant-driven instabilities differently so that no single reference temperature definition would collapse the neutral curves. The linear stability result further demonstrates that at a given Grashof number a higher temperature difference would give a larger amplification rate of the perturbation, which then leads to an earlier onset of the nonlinearities when evaluated at $T_f$. Finally, by comparing the amplification rates obtained from direct numerical simulation and the linear stability results, the extent of the linear regime is determined for $\Delta T = 100\,{\rm K}$.