When an oblate droplet translates through a viscous fluid under linear shear, it experiences a lateral lift force whose direction and magnitude are influenced by the Reynolds number, the droplet’s viscosity and its aspect ratio. Using a recently developed sharp interface method, we perform three-dimensional direct numerical simulations to explore the evolution of lift forces on oblate droplets across a broad range of these parameters. Our findings reveal that in the low-but-finite Reynolds number regime, the Saffman mechanism consistently governs the lift force. The lift increases with the droplet’s viscosity, aligning with the analytical solution derived by Legendre & Magnaudet (Phys. Fluids, vol. 9, 1997, p. 3572), and also rises with the droplet’s aspect ratio. We propose a semi-analytical correlation to predict this lift force. In the moderate- to high-Reynolds-number regime, distinct behaviours emerge: the $L\hbox{-}$ and $S\hbox{-}$mechanisms, arising from the vorticity contained in the upstream shear flow and the vorticity produced at the droplet surface, dominate for weakly and highly viscous droplets, respectively. Both mechanisms generate counter-rotating streamwise vortices of opposite signs, leading to observed lift reversals with increasing droplet viscosity. Detailed force decomposition based on vorticity moments indicates that in the $L\hbox{-}$mechanism-dominated regime for weakly to moderately viscous droplets, the streamwise vorticity-induced lift approximates the total lift. Conversely, in the $S\hbox{-}$mechanism-dominated regime, for moderately to highly viscous droplets, the streamwise vorticity-induced lift constitutes only a portion of the total lift, with the asymmetric advection of azimuthal vorticity at the droplet interface contributing additional positive lift to counterbalance the $S\hbox{-}$mechanism’s effects. These insights bridge the understanding between inviscid bubbles and rigid particles, enhancing our comprehension of the lift force experienced by droplets in different flow regimes.

We investigate the fluid–solid interaction of suspensions of Kolmogorov-size spherical particles moving in homogeneous isotropic turbulence at a microscale Reynolds number of $Re_\lambda \approx 140$. Two volume fractions are considered, $10^{-5}$ and $10^{-3}$, and the solid-to-fluid density ratio is set to $5$ and $100$. We present a comparison between interface-resolved (PR-DNS) and one-way-coupled point-particle (PP-DNS) direct numerical simulations. We find that the modulated energy spectrum shows the classical $-5/3$ Kolmogorov scaling in the inertial range of scales and a $-4$ scaling at smaller scales, with the latter resulting from a balance between the energy injected by the particles and the viscous dissipation, in an otherwise smooth flow. An analysis of the small-scale flow topology shows that the particles mainly favour events with axial strain and vortex compression. The dynamics of the particles and their collective motion studied for PR-DNS are used to assess the validity of the PP-DNS. We find that the PP-DNS predicts fairly well both the Lagrangian and Eulerian statistics of the particle motion for the low-density case, while some discrepancies are observed for the high-density case. Also, the PP-DNS is found to underpredict the level of clustering of the suspension compared with the PR-DNS, with a larger difference for the high-density case.

Many problems in elastocapillary fluid mechanics involve the study of elastic structures interacting with thin fluid films in various configurations. In this work, we study the canonical problem of the steady-state configuration of a finite-length pinned and flexible elastic plate lying on the free surface of a thin film of viscous fluid. The film lies on a moving horizontal substrate that drives the flow. The competing effects of elasticity, viscosity, surface tension and fluid pressure are included in a mathematical model consisting of a third-order Landau–Levich equation for the height of the fluid film and a fifth-order Landau–Levich-like beam equation for the height of the plate coupled together by appropriate matching conditions at the downstream end of the plate. The properties of the model are explored numerically and asymptotically in appropriate limits. In particular, we demonstrate the occurrence of boundary-layer effects near the ends of the plate, which are expected to be a generic phenomenon for singularly perturbed elastocapillary problems.

A combination of physics-based and data-driven post-processing techniques is proposed to extract acoustic-related shear-layer perturbation responses directly from spatio-temporally resolved schlieren video. The physics-based component uses momentum potential theory to extract the irrotational (acoustic and thermal) component from density gradients embedded in schlieren pixel intensities. For the unheated shear layer, the method filters acoustic structures and tones not evident in the raw data. The filtered data are then subjected to an efficient data-driven dynamic mode decomposition reduced-order model, which provides the forced acoustic perturbation response for broad parameter ranges. A shear layer comprising Mach 2.461 and 0.175 streams, corresponding to a convective Mach number 0.88 and containing shocks, is adopted for illustration. The overall perturbation response is first obtained using an impulse forcing in the wall-normal direction of the splitter plate, extending into subsonic and supersonic streams. Subsequently, impulse and harmonic forcings are independently applied in a pixel-by-pixel manner for a precise receptivity study. The acoustic response shows a convective wavepacket and acoustic burst from the splitter plate. The interaction with the shock and associated wave dispersion emits a second, slower, acoustic wave. Harmonic forcing indicates higher frequency-dependent sensitivity in the supersonic stream, with the most sensitive location near the outer boundary-layer region, which elicits an order of magnitude larger acoustic response compared with disturbances in the subsonic stream. Some receptive forcing regions do not generate significant acoustic waves, which may guide excitation with low noise impact.

The acoustic field radiated by a system of contra-rotating propellers in wetted conditions (with no cavitation) is reconstructed by exploiting the Ffowcs Williams–Hawkings acoustic analogy and a database of instantaneous realizations of the flow. They were generated by high-fidelity computations using a large eddy simulation approach on a cylindrical grid of 4.6 billion points. Results are also compared against the cases of the front and rear propellers working alone. The analysis shows that the importance of the quadrupole component of sound, originating from wake turbulence and instability of the tip vortices, is reinforced, relative to the linear component radiated from the surface of the propeller blades. The sound from the contra-rotating propellers decays at a slower rate for increasing radial distances, compared with the cases of the isolated front and rear propellers, again due to the quadrupole component. The quadrupole sound is often neglected in the analysis of the acoustic signature of marine propellers, by considering the only linear component. In contrast, the results of this study point out that the quadrupole component becomes the leading one in the case of contra-rotating propulsion systems, due to the increased complexity of their wake. This is especially the result of the mutual inductance phenomena between the tip vortices shed by the front and rear propellers of the contra-rotating system.

The hydrodynamic behaviours of finite-size microorganisms in turbulent channel flows are investigated using a direct-forcing fictitious domain method. The classical ‘squirmer’ model, characterized by self-propulsion through tangential surface waves at its boundaries, is employed to mimic the swimming microorganisms. We adopt various simulation parameters, including a friction Reynolds number Reτ = 180, two squirmer volume fractions 𝜑0 = 12.7 % and 2.54 % and a blocking ratio (squirmer radius/half-channel width) κ = 0.125. Results show that pushers (propelled from the rear) induce a more pronounced decrease in the velocity profile than neutral squirmers and pullers (propelled from the front). This hindrance and the induced particle inner stress τpI positively correlate with the quantity of squirmers accumulated in the near-wall region. Notably, the increase in τpI primarily occurs at the expense of diminishing the fluid Reynolds stress τfR. Compared with passive spheres, a low volume fraction (𝜑0 = 2.54 %) of pullers results in a slightly enhanced velocity profile across the channel. In the near-wall region, the swimming direction of the squirmers shows no significant tendency with respect to the flow direction. In the bulk-flow region, pushers and neutral squirmers tend to align their axes more along the flow direction, whereas pullers exhibit a slight preference for alignment with the normal direction.

Within the frameworks of the amplitude method and the linear stability theory, a statistical model of the initial stage of laminar–turbulent transition caused by atmospheric particulates (aerosols) penetrating into the boundary layer is developed. The model accounts for the process of boundary layer receptivity to particulates, asymptotic behaviour of unstable wave packets propagating downstream from particle–wall collisions and the amplitude criterion for the transition onset. The resulting analytical relationships can be used for quick predictions of the transition onset on bodies of relatively simple shape, where the undisturbed boundary layer is quasi-two-dimensional. The model allows us to explore the transition onset at realistic distributions of the particle concentration selected based on an analysis of known empirical data. As an example, a 14° half-angle sharp wedge flying in atmosphere at 20 km altitude and Mach number 4 is considered. It is shown that the transition onset corresponds to an N-factor of 15.3 for a flight under normal atmospheric conditions and 12.2 for a flight in a cloud after volcanic eruption. In accordance with physical restrictions, these values are below the upper limit $N\approx 16.8$ predicted for transition due to thermal fluctuations (perfectly ‘clean’ case). Nevertheless, they are significantly greater than $N=10$ which is commonly recommended for estimates of the transition onset in flight.

We study the dynamic deflation of a hydraulic fracture subject to fluid withdrawal through a narrow conduit located at the centre of the fracture. Recent work revealed a self-similar dipole-flow regime, when the influence of material toughness is negligibly small. The focus of the current work is on the influence of material toughness, which leads to an additional self-similar regime of fracture deflation with fixed frontal locations in the toughness-dominated regime. The two limiting regimes can be distinguished by a dimensionless material toughness $\Pi _k$, defined based on a comparison with the influence of the viscous thin film flow within the fracture: $\Pi _k \to 0$ indicates the dipole-flow regime, while $\Pi _k \to \infty$ indicates the fixed-length regime. For intermediate $\Pi _k$, the fracture’s front continues to propagate during an initial period of deflation before it remains pinned at a fixed location thereafter. A regime diagram is then derived, with key scaling behaviours for the frontal dynamics, pressure and volume evolution summarised in a table for the self-similar stage. A comparison is also attempted between theoretical predictions and available experimental observations of viscous backflows from transparent solid gelatins.

We use direct numerical simulations to investigate the energy pathways between the velocity and the magnetic fields in a rotating plane layer dynamo driven by Rayleigh–Bénard convection. The kinetic and magnetic energies are divided into mean and turbulent components to study the production, transport and dissipation in large- and small-scale dynamos. This energy balance-based characterisation reveals distinct mechanisms for large- and small-scale magnetic field generation in dynamos, depending on the nature of the velocity field and the conditions imposed at the boundaries. The efficiency of a dynamo in converting the kinetic energy to magnetic energy, apart from the energy redistribution inside the domain, is found to depend on the kinematic and magnetic boundary conditions. In a small-scale dynamo with a turbulent velocity field, the turbulent kinetic energy converts to turbulent magnetic energy via small-scale magnetic field stretching. This term also represents the amplification of the turbulent magnetic energy due to work done by stretching the small-scale magnetic field lines owing to fluctuating velocity gradients. The stretching of the large-scale magnetic field plays a significant role in this energy conversion in a large-scale turbulent dynamo, leading to a broad range of energetic scales in the magnetic field compared with a small-scale dynamo. This large-scale magnetic field stretching becomes the dominant mechanism of magnetic energy generation in a weakly nonlinear dynamo. We also find that, in the weakly nonlinear dynamo, an upscale energy transfer from the small-scale magnetic field to the large-scale magnetic field occurs owing to the presence of a gradient of the mean magnetic field.

The dependence of the Richtmyer–Meshkov instability (RMI) on post-shock Atwood number ($A_1$) is experimentally investigated for a heavy–light single-mode interface. We create initial interfaces with density ratios of heavy to light gases ranging from 1.73 to 34.07, and achieve the highest $|A_1|$ value reported to date for gaseous-interface experiments (0.95). For the first time, spike acceleration is observed in experiments with a heavy–light configuration. The models for the start-up, linear and weakly nonlinear evolution stages are evaluated over a wide range of $A_1$ conditions. Specifically, the models proposed by Li et al. (Phys. Fluids, vol. 36, 2024, 056104) and Wouchuk & Nishihara (Phys. Plasmas, vol. 4, 1997, 1028–1038) effectively describe the start-up and linear stages, respectively, across all cases. None of the considered nonlinear models is valid under all $A_1$ conditions. Based on the dependence of spike and bubble evolutions on $A_1$ provided by the present work and previous study (Chen et al., J. Fluid Mech., vol. 975, 2023, A29), the SEA model (Sadot et al., Phys. Rev. Lett., vol. 80, 1998, pp. 1654–1657), whose expression has clear physical meanings, is modified by revising the coefficient that governs its prediction for early-time evolution. The modified model applies to prediction of the weakly nonlinear evolution of RMI with $A_1$ ranging from −0.95 to −0.35 and from 0.30 to 0.86. Based on this model, an approximation of the critical $A_1$ for the occurrence of spike acceleration is obtained.

Recent experiments and simulations have sparked growing interest in the study of Rayleigh–Bénard convection in very slender cells. One pivotal inquiry arising from this interest is the elucidation of the flow structure within these very slender cells. Here we employ tomographic particle image velocimetry, for the first time, to capture experimentally the full-field three-dimensional and three-component velocity field in a very slender cylindrical cell with aspect ratio $\Gamma =1/10$. The experiments cover a Rayleigh number range $5.0 \times 10^8 \leqslant Ra \leqslant 5.0 \times 10^9$ and Prandtl number 5.7. Our experiments reveal that the flow structure in the $\Gamma =1/10$ cell is neither in the multiple-roll form nor in the simple helical form; instead, the ascending and descending flows can intersect and cross each other, resulting in the crossing events. These crossing events separate the flow into segments; within each segment, the ascending and descending flows ascend or descend side by side vertically or in the twisting manner, and the twisting is not unidirectional, while the segments near the boundary can also be in the form of a donut like structure. By applying the mode decomposition analyses to the measured three-dimensional velocity fields, we identified the crossing events as well as the twisting events for each instantaneous flow field. Statistical analysis of the modes reveals that as $Ra$ increases, the average length of the segments becomes smaller, and the average number of segments increases from 2.5 to 3.9 in the $Ra$ range of our experiments.

The interaction between a turbulent flow and a porous boundary is analysed with focus on the sensitivity of the roughness function, $\Delta U^+$, to the upscaled coefficients characterizing the wall. The study is aimed at (i) demonstrating that imposing effective velocity boundary conditions at a virtual plane boundary, next to the physical one, can efficiently simplify the direct numerical simulations (DNS); and (ii) pursuing correlations to estimate $\Delta U^+$ a priori, once the upscaled coefficients are calculated. The homogenization approach employed incorporates near-interface advection via an Oseen-like linearization, and the macroscopic coefficients thus depend on both the microstructural details of the wall and a slip-velocity-based Reynolds number, $Re_{slip}$. A set of homogenization-simplified DNS is run to study the channel flow over transversely isotropic porous beds, testing values of the grains’ pitch within $0\lt \ell ^+\lt 40$. Reduction of the skin-friction drag is attainable exclusively over streamwise-aligned inclusions for $\ell ^+$ values up to $20{-}30$. The drag increase over spanwise-aligned inclusions (or streamwise-aligned ones at large $\ell ^+$) is accompanied by enhanced turbulence levels, including intensified sweep and ejection events. The root-mean-square of the transpiration velocity fluctuations at the virtual plane, $\tilde V_{rms}$, is the key control parameter of $\Delta U^+$; our analysis shows that, provided $\tilde V_{rms} \lesssim 0.25$, then $\tilde V_{rms}$ is strongly correlated to a single macroscopic quantity, $\Psi$, which comprises the Navier-slip and interface/intrinsic permeability coefficients. Fitting relationships for $\Delta U^+$ are proposed, and their applicability is confirmed against reference results for the turbulent flow over impermeable walls roughened with three-dimensional protrusions or different geometries of riblets.

A new temporal vortex tracking algorithm allows the first long-term temporal observation of the lives of the intense vorticity structures (IVS). The algorithm is applied to direct numerical simulations of statistically stationary isotropic turbulence, with Taylor-based Reynolds numbers in the range $54 \leqslant Re_{\lambda } \leqslant 239$. In the highest Reynolds number case, the continuous time tracking of millions of ‘worms’ is achieved for more than seven integral time scales and close to 200 Kolmogorov time scales. Within an integral scale volume, more than 66 structures exist, and approximately 20 new structures are created per Kolmogorov time. More than $80\, \%$ of the structures live a solitary ‘life’ without any visible interaction with the other structures, while approximately $15\, \%$ break into new structures. Less than $2\, \%$ of the structures merge with others to form new vortices. A ‘population model’ is developed to estimate the numbers of existing vortices for very long simulated times, and it is observed that the birth rate density of these structures slowly increases with the Reynolds number. The survival functions of the IVS lives exhibit an exponential distribution, with some structures living for more than $35$ Kolmogorov time scales (more than four integral time scales). The mean lifetime of the IVS scales with the mean turnover time scale of the worms, defined by their radii and tangential velocity, attaining $\approx 6.5$ turnover time scales at high Reynolds numbers.