The orientational trajectories of rod-like particles suspended in a liquid are influenced by their surroundings, such as the type of flow and nearby walls, and deviate from the well-known Jeffery orbits in shear flows. We consider two types of shear flows between two parallel planar walls: wall-driven simple shear flow (C-flow), and parabolic flow driven by an external body force (P-flow). We simulated hydrodynamically interacting rod-like particles using a chain-of-spheres model immersed in a lattice Boltzmann fluid within a confined channel. As these particles in shear flows approach the wall, their orbits become flattened, exhibiting a ‘swinging motion’ on a plane parallel to the wall. Near the wall, the influence of the wall on the orbital motion varies depending on the flow type. In P-flow, the particles maintain their periodic swinging motions, whereas in C-flow, they stop swinging and align with the flow direction. This difference arises due to distinct hydrodynamic interactions with the wall in each flow type. Simulations also replicated the ‘pole-vaulting’ motion, where particles move away from the wall during their tumbling motion. For weakly sedimenting particles under shear flows, both flow types showed behaviour similar to that of neutrally buoyant particles. However, in P-flow, driven by gravity towards the wall, the particles cease their swinging motion and align perpendicularly to the flow direction, consistent with experimental observations.

There is a reasonable possibility that the present-day Atlantic Meridional Overturning Circulation is in a bistable regime, hence it is relevant to compute pathways of noise-induced transitions between the stable equilibrium states. Here, the most probable transition pathway of a noise-induced tipping of the northern overturning circulation in a spatially-continuous two-dimensional model with surface temperature and stochastic salinity forcings is computed directly using large deviation theory. This pathway reveals the fluid dynamical mechanisms of such a tipping. Paradoxically it starts off with a strengthening of the northern overturning circulation before a short but strong salinity pulse induces a second overturning cell. The increased atmospheric energy input of this two-cell configuration cannot be mixed away quickly enough, leading to the collapse of the northern overturning cell, and finally resulting in a southern overturning circulation. Additionally, the approach allows us to compare the probability of this transition under different parameters in the deterministic part of the salinity surface forcing, which quantifies the increase in transition probability as the bifurcation point of the system is approached.

Laminar–turbulent transition on the suction surface of the LM45.3p blade ($20\,\%$ thickness) was investigated using wall-resolved large eddy simulation (LES) at a chord Reynolds number of $Re_c=10^6$ and angle of attack $4.6^\circ$. The effects of anisotropic free stream turbulence (FST) with intensities $TI=0\,\%$–$7\,\%$ were examined, with integral length scales scaled down from atmospheric measurements. At $TI=0\,\%$, a laminar separation bubble (LSB) forms and transition is initiated by Kelvin–Helmholtz vortices. At low FST levels ($0\,\%\lt TI \leqslant 2.4\,\%$), robust streak growth via the lift-up mechanism suppresses the LSB, while transition dynamics shifts from two-dimensional Tollmien–Schlichting (TS) waves ($TI=0.6\,\%$) to predominantly varicose inner and outer instabilities ($TI=1.2\,\%$ and $2.4\,\%$) induced by the wall-normal shear and inflectional velocity profiles. The critical disturbance kinetic energy scales with $TI^{-1.80\pm 0.11}$, compared with $TI^{-2.40}$ from Mack’s correlation. For $TI\geqslant 4.5\,\%$, bypass transition dominates, driven by high-frequency boundary layer perturbations and streak breakdown via outer sinuous modes induced by the spanwise shear and inflectional velocity profiles. The scaling of streak amplitudes with $TI$ becomes sub-linear and spanwise non-uniformity characterises the turbulent breakdown. The critical disturbance kinetic energy reduces to $TI^{-0.90\pm 0.16}$, marking a transition regime distinct from modal mechanisms. The onset of bypass transition ($TI\approx 2.4\,\%{-}4.5\,\%$) aligns with prior studies of separated and flat-plate flows. A proposed turbulence spectrum cutoff links atmospheric measurements to wind tunnel data and Mack’s correlation, offering a framework for effective $TI$ estimation in practical environments.

We propose an analytical approach based on the Frenet–Serret (FL) frame field, where an FL frame and the corresponding curvature and torsion are defined at each point along magnetic field lines, to investigate the evolution of magnetic tubes and their interaction with vortex tubes in magnetohydrodynamics. Within this framework, simplified expressions for the Lorentz force, its curl, the dynamics of flux tubes and helicity are derived. We further perform direct numerical simulations on the linkage between the magnetic and vortex tubes and investigate the effect of the initial angle $\theta$, ranging from $0^{\,\circ}$ to $45^{\,\circ}$, on their evolution. Our results show that magnetic tubes with non-zero curvature generate Lorentz forces, which in turn produce dipole vortices. These dipole vortices lead to the splitting of the magnetic tubes into smaller structures, releasing magnetic energy. Both magnetic and vortex tubes exhibit quasi-Lagrangian behaviour, maintaining similar shapes during initial evolution and consistent relative positions over time. A vortex tube with strength comparable to that of the magnetic tube, where the kinetic energy induced by the vortex tube is of the same order as the magnetic energy in the magnetic tube, can inhibit magnetic tube splitting by disrupting the formation of vortex dipoles. Additionally, minor variations in the angular configuration of the vortex tubes significantly influence their interaction with the magnetic field and the evolution of large-scale flow structures.

The reduction of the hydrodynamic forces exerted on a bluff body in an incoming flow has been an issue of interest in fluid mechanics for many years. However, the Magnus effect indicates possible drag reduction but with the lift being increased significantly. This study is aimed at the simultaneous lift and drag reduction for which we consider a constant incoming flow past a circular cylinder or a sphere in the $x$-direction. Force element analysis (FEA) indicates the possibility of reducing the drag exerted on a circular cylinder or a sphere by rotating (say, clockwise about the $z$-axis) only the front half of the circular cylinder or the sphere. More precisely, we rotate the object but with the rear half covered by a closely spaced hood. Numerical simulations show that by increasing the dimensionless rotational speed $\alpha$: (i) the flow can be quickly stabilised to a steady state; (ii) the mean drag steadily decreases to zero and then becomes negative as $\alpha$ is further increased across the critical $\alpha _I = 4.11$ for the circular cylinder at $Re$ = 200, $\alpha _I = 4.81$ for the sphere at $Re$ = 200 and $\alpha _I = 4.92$ for the sphere at $Re$ = 300; (iii) the mean value of the lift decreases from zero to negative and then increases beyond zero, and in addition, the amplitude of the lift gradually decreases for the circular cylinder; the mean value of the lift decreases from zero to negative for the sphere; (iv) the side force is almost zero – the flow over the sphere is plane-symmetric about the $x{-}y$ plane. These features are compared with the flow past a rotating circular cylinder or a rotating sphere (Magnus effect). Notably, there is a range of flows that can be of practical use for: (a) the circular cylinder where the drag is greatly reduced while the lift is small in magnitude and (b) the sphere where the drag is greatly reduced while the lift is negative in magnitude and the side force is close to 0.

The shallow-water equations are widely used to model interactions between horizontal shear flows and (rotating) gravity waves in thin planetary atmospheres. Their extension to allow for interactions with magnetic fields – the equations of shallow-water magnetohydrodynamics (SWMHD) – is often used to model waves and instabilities in thin stratified layers in stellar and planetary atmospheres, in the perfectly conducting limit. Here we consider how magnetic diffusion should be added to the equations of SWMHD. This is crucial for an accurate balance between advection and diffusion in the induction equation, and hence for modelling instabilities and turbulence. For the straightforward choice of Laplacian diffusion, we explain how fundamental mathematical and physical inconsistencies arise in the equations of SWMHD, and show that unphysical dynamo action can result. We then derive a physically consistent magnetic diffusion term by performing an asymptotic analysis of the three-dimensional equations of magnetohydrodynamics in the thin-layer limit, giving the resulting diffusion term explicitly in both planar and spherical coordinates. We show how this magnetic diffusion term, which allows for a horizontally varying diffusivity, is consistent with the standard shallow-water solenoidal constraint, and leads to negative semidefinite Ohmic dissipation. We also establish a basic type of antidynamo theorem.

The Hasselmann equation for the nonlinear interactions of deep-water gravity waves differs from other four-wave kinetic equations by the interaction coefficient. The explicit formula for this coefficient (e.g. Krasitskii, J. Fluid. Mech., vol. 272, 1994, pp. 1–20; Zakharov, Eur. J. Mech. B/Fluids, vol. 18. issue 3, 1999, pp. 327–344) is of great complexity and leaves its properties obscured. We provide analytical results for the behaviour of the coefficient in different domains. The Phillips curve and discrete interaction approximation-like quadruplets are studied in detail. The coupling coefficient for the long–short wave interactions is calculated and found to be surprisingly small. This smallness greatly reduces the non-locality of the interactions.

We examine the separate effects of turbulence beneath a free surface and non–breaking surface capillary waves on the gas-transfer velocity of atmospheric oxygen into water across an air–water interface. The experiments are conducted in a recirculating open water channel with quiescent air, where atmospheric oxygen naturally dissolves into the water via the exposed surface. Through the combination of an active turbulence grid and an array of surface penetrating dowels, we are able to separate the effects of sub-surface turbulence and surface capillary waves. The findings demonstrate that the gas-transfer velocity trends with the turbulence properties, not the capillary wave properties, thus indicating that, when both are present, it is the sub-surface turbulence, not the capillary waves, that plays the dominant role in determining the rate of gas transfer across an air–water interface in the non-breaking capillary wave regime.

This study investigates the hydrodynamic interaction between a fully submerged buoyant pendulum and surface gravity waves, focusing on its primary and subharmonic resonance behaviour. The oscillatory motion of the pendulum is driven by fluid drag, with primary resonance occurring at the forcing frequency (viz. the wave frequency) and subharmonic resonance manifesting at half the forcing frequency. Both resonances exhibit nonlinear characteristics, including jump-up, jump-down phenomena and hysteresis. Furthermore, particle image velocimetry results reveal that the velocity fields of the surrounding fluid oscillate at the forcing frequency, confirming that subharmonic resonance is not induced by subharmonic excitation within the velocity field. Experimental observations are validated through both analytical and numerical methods, particularly within the primary and subharmonic resonance frequency ranges. The theoretical model describes the transverse motion of the pendulum using a nonlinear ordinary differential equation, with the method of multiple scales employed for the analytical solution. These analyses reveal the nonlinear characteristics of the system, e.g. bistable response of the primary/subharmonic resonances, and identify three distinct response regions based on the forcing frequency and amplitude. The system exhibits primary resonance regardless of the excitation strength; however, an unstable solution arises if the excitation level surpasses a specific threshold value. In contrast, subharmonic resonance is triggered only when the excitation amplitude exceeds a critical value. Furthermore, the experimental hysteresis curve confirms the theoretically predicted primary and subharmonic resonances, along with the jump-up and jump-down characteristics.

Combined surging and pitching of an airfoil at the identical frequency (i.e. synchronously), at four different phase differences, was investigated theoretically and experimentally. The most general unsteady theoretical formulation was adopted to calculate the lift coefficient, and then extended to explicitly compute the unsteady bound vortex sheet. This was used for comparison with experiments and facilitated the computation of both Joukowsky and impulsive-pressure lift contributions. Experiments were performed using a symmetric 18 % thick airfoil in an unsteady wind tunnel at an average Reynolds number of $3.0\times 10^5$, with a free-stream oscillation amplitude of 51 %, an angle-of-attack range of $2^\circ \pm 2^\circ$ and a reduced frequency of 0.097. In general, excellent correspondence was observed between theory and experiment, representing the first direct experimental validation of the general theory. It was shown, both theoretically and experimentally, that the lift coefficient was not accurately represented by independent superposition of surging and pitching effects, due to variations in the instantaneous effective reduced frequency not accounted for during pure pitching. Deviations from theory, observed at angle-of-attack phase leads of $90^\circ$ and $180^\circ$, were attributed to bursting of separation bubbles during the early stages of the acceleration phase. The largest deviations occurred when the impulsive-pressure lift contribution was small relative to the Joukowsky contribution, because the latter was most affected by bubble bursting. Bubble bursting resulted in large form-drag oscillations that occurred at identical phase angles within the oscillation cycle, irrespective of the phase difference between surging and pitching, as well as in the absence of pitching.

We address the problem of shock-induced ignition and transition to detonation in a reactive medium in the presence of mechanically induced fluctuations by a moving oscillating piston. For the inert problem prior to ignition, we provide a novel closed-form model in Lagrangian coordinates for the generation of the train of compression and expansions, their steepening into a train of N-shock waves and their reflection on the lead shock, as well as the distribution of the energy dissipation rate in the induction zone. The model is found to be in excellent agreement with numerics. Reactive calculations were performed for hydrogen and ethylene fuels using a novel high-fidelity scheme to solve the reactive Euler equations written in Lagrangian coordinates. Different regimes of ignition and transition to detonation, controlled by the time scale of the forcing and the two time scales of the chemistry: the induction and reaction times. Two novel hotspot cascade mechanisms were identified. The first relies on the coherence between the sequence of hotspot formation set by the piston forcing and forward-wave interaction with the lead shock, generalising the classic runaway in fast flames. The second hotspot cascade is triggered by the feedback between the pressure pulse generated by the first-generation hotspot cascade and the shock. For slow forcing, the sensitisation is through a modification to the classic runaway process, while the high-frequency regime leads to very localised subcritical hotspot formation controlled by the cumulative energy dissipation of the first-generation shocks at a distance comparable with the shock formation location.

We investigate the statistical properties of kinetic and thermal dissipation rates in two-dimensional/three-dimensional vertical convection of liquid metal ($Pr = 0.032$) within a square cavity. Two situations are specifically discussed: (i) classical vertical convection with no external forces and (ii) vertical magnetoconvection with a horizontal magnetic field. Through an analysis of dissipation fields and a reasonable approximation of buoyancy potential energy sourced from vertical heat flux, the issue of the ‘non-closure of the dissipation balance relation’, which has hindered the application of the GL theory in vertical convection, is partially resolved. The resulting asymptotic power laws are consistent with existing laminar scaling theories and even show certain advantages in validating simulations with large Prandtl number ($Pr$). Additionally, a full-parameter model and prefactors applicable to low-$Pr$ fluids are provided. The extension to magnetoconvection naturally introduces the approximate expression for total buoyancy potential energy and necessitates adjustments to the contributions of kinetic dissipation in both the bulk and boundary layer. The flow dimensionality and boundary layer thickness are key considerations in this analysis. The comprehension of Joule dissipation has been updated: the Lorentz force generates positive dissipation in the bulk by suppressing convection, while in the Hartmann layer, shaping the exponential boundary layer requires the fluid to perform positive work to accelerate, leading to negative dissipation. Finally, the proposed transport equations for magnetoconvection are supported by current direct numerical simulation (DNS) and literature data, and the applicability of the model is discussed.

Gravity currents are a ubiquitous density-driven flow occurring in both the natural environment and in industry. They include: seafloor turbidity currents, primary vectors of sediment, nutrient and pollutant transport; cold fronts; and hazardous gas spills. However, while the energetics are critical for their evolution and particle suspension, they are included in system-scale models only crudely, so we cannot yet predict and explain the dynamics and run-out of such real-world flows. Herein, a novel depth-averaged framework is developed to capture the evolution of volume, concentration, momentum and turbulent kinetic energy from direct integrals of the full governing equations. For the first time, we show the connection between the vertical profiles, the evolution of the depth-averaged flow and the energetics. The viscous dissipation of mean-flow energy near the bed makes a leading-order contribution, and an energetic approach to entrainment captures detrainment of fluid through particle settling. These observations allow a reconsideration of particle suspension, advancing over 50 years of research. We find that the new formulation can describe the full evolution of a shallow dilute current, with the accuracy depending primarily on closures for the profiles and source terms. Critically, this enables accurate and computationally efficient hazard risk analysis and earth surface modelling.

Attenuation of shock waves through dense granular media with varying macro-scale and micro-scale parameters has been numerically studied in this work by a coupled Eulerian–Lagrangian approach. The results elucidate the correlation between the attenuation mechanism and the nature of shock-induced unsteady flows inside the granular media. As the shock transmission becomes trivial relative to the establishment of unsteady interpore flows, giving way to the gas filtration, the shock attenuation mechanism transitions from the shock dynamics and deduction of propagation area associated with the shock transmission, to the drag-related friction dissipation alongside the gas filtration. The ratio between the maximum shock transmission length and the thickness of the particle layer is found to be a proper indicator of the nature of shock-induced flows. More importantly, it is this ratio that successfully collapses the upstream and downstream pressures of shock impacted particle layers with widely ranging thickness and volume fraction, leading to a universal scaling law for the shock attenuation effect. We further propose a correlation between the structure of particle layer and the corresponding maximum shock transmission length, guaranteeing adequate theoretical predictions of the upstream and downstream pressures. These predictions are also necessary for an accurate estimation of the spread rate of shock dispersed particle bed through a pressure-gradient-based scaling method.

We investigate the emergent three-dimensional (3-D) dynamics of a rapidly yawing spheroidal swimmer interacting with a viscous shear flow. We show that the rapid yawing generates non-axisymmetric emergent effects, with the active swimmer behaving as an effective passive particle with two orthogonal planes of symmetry. We also demonstrate that this effective asymmetry generated by the rapid yawing can cause chaotic behaviour in the emergent dynamics, in stark contrast to the emergent dynamics generated by rapidly rotating spheroids, which are equivalent to those of effective passive spheroids. In general, we find that the shape of the equivalent effective particle under rapid yawing is different to the average shape of the active particle. Moreover, despite having two planes of symmetry, the equivalent passive particle is not an ellipsoid in general, except for specific scenarios in which the effective shape is a spheroid. In these scenarios, we calculate analytically the equivalent aspect ratio of the effective spheroid. We use a multiple scales analysis for systems to derive the emergent swimmer behaviour, which requires solving a non-autonomous nonlinear 3-D dynamical system, and we validate our analysis via comparison to numerical simulations.

We investigate the momentum fluxes between a turbulent air boundary layer and a growing–breaking wave field by solving the air–water two-phase Navier–Stokes equations through direct numerical simulations. A fully developed turbulent airflow drives the growth of a narrowbanded wave field, whose amplitude increases until reaching breaking conditions. The breaking events result in a loss of wave energy, transferred to the water column, followed by renewed growth under wind forcing. We revisit the momentum flux analysis in a high-wind-speed regime, characterized by the ratio of the friction velocity to wave speed $u_\ast /c$ in the range $[0.3\,{-}\,0.9]$, through the lens of growing–breaking cycles. The total momentum flux across the interface is dominated by pressure, which increases with $u_\ast /c$ during growth and reduces sharply during breaking. Drag reduction during breaking is linked to airflow separation, a sudden acceleration of the flow, an upward shift of the mean streamwise velocity profile and a reduction in Reynolds shear stress. We characterize the reduction of pressure stress and flow acceleration through an aerodynamic drag coefficient by splitting the analysis between growing and breaking stages, treating them as separate subprocesses. While drag increases with $u_\ast /c$ during growth, it decreases during breaking. Averaging over both stages leads to a saturation of the drag coefficient at high $u_\ast /c$, comparable to what is observed at high wind speeds in laboratory and field conditions. Our analysis suggests that this saturation is controlled by breaking dynamics.

We investigate turbulent flow between two concentric cylinders, oriented either axially or azimuthally. The axial configuration corresponds to a concentric annulus, where curvature is transverse to the flow, while the azimuthal configuration represents a curved channel with longitudinal curvature. Using direct numerical simulations, we examine the effects of both types of curvature on turbulence, varying the inner radius from $r_i=0.025\delta$ to $r_i=95.5\delta$, where $\delta$ is the gap width. The bulk Reynolds number, based on bulk velocity and $\delta$, is set at $R_b\approx 5000$, ensuring fully turbulent conditions. Our results show that transverse curvature, although breaking the symmetry of axial flows, induces limited changes in the flow structure, leading to an increase in friction at the inner wall. In contrast, longitudinal curvature has a significant impact on the structure and statistics of azimuthal flows. For mild to moderate longitudinal curvatures ($r_i\gt 1.5\delta$), the convex wall stabilises the flow, reducing turbulence intensity, wall friction and turbulent kinetic energy (TKE) production. For extreme longitudinal curvatures ($r_i\leqslant 0.25\delta$), spanwise-coherent flow structures develop near the inner wall, leading to a complete redistribution of the TKE budget: production becomes negligible near the inner wall, while pressure–velocity correlations increase substantially. As a result, the mean TKE peaks near the inner wall, thereby weakening the stabilising effect of convex curvature.

Dispersion in spatio-temporal random flows is dominated by the competition between spatial and temporal velocity resets along particle paths. This competition admits a range of normal and anomalous dispersion behaviours characterised by the Kubo number, which compares the relative strength of spatial and temporal velocity resets. To shed light on these behaviours, we develop a Lagrangian stochastic approach for particle motion in spatio-temporally fluctuating flow fields. For space–time separable flows, particle motion is mapped onto a continuous time random walk (CTRW) for steady flow in warped time, which enables the upscaling and prediction of the large-scale dispersion behaviour. For non-separable flows, we measure Lagrangian velocities in terms of a new sampling variable, the average number of velocity transitions (both temporal and spatial) along pathlines, which renders the velocity series Markovian. Based on this, we derive a Lagrangian stochastic model that represents particle motion as a coupled space–time random walk, that is, a CTRW for which the space and time increments are intrinsically coupled. This approach sheds light on the fundamental mechanisms of particle motion in space–time variable flows, and allows for its systematic quantification. Furthermore, these results indicate that alternative strategies for the analysis of Lagrangian velocity data using new sampling variables may facilitate the identification of (hidden) Markov models, and enable the development of reduced-order models for otherwise complex particle dynamics.

The transport of droplets in microfluidic channels is strongly dominated by interfacial properties, which makes it a relevant tool for understanding the mechanisms associated with the presence of more or less soluble surfactants. In this paper, we show that the mobility of an oil droplet pushed by an aqueous carrier phase in a Hele-Shaw cell qualitatively depends on the nature of the surfactants: the drop velocity is an increasing function of the drop radius for highly soluble surfactants, whereas it is a decreasing function for poorly soluble surfactants. These two different behaviours are experimentally observed by using two families of surfactant with a carbon chain of variable length. We first focus on the second regime, observed here for the first time, and we develop a model which takes into account the flux of surfactants on the whole droplet interface, assuming an incompressible surfactant monolayer. This model leads to a quantitative agreement with the experimental data, without any adjustable parameter. We then propose a model for a stress-free interface, i.e. for highly soluble surfactants. In these two limits, the models become independent on the physico-chemical properties of the surfactants, and should be valid for any surfactant complying with the incompressible or stress-free limit. As such, we provide a theoretical framework with two limits for all the experimental physico-chemical configurations, which constitute the bounds for the droplet mobility for intermediate surfactant solubility.

Direct numerical simulations in a low-curvature viscoelastic turbulent Taylor vortex flow, with Reynolds numbers ranging from 1500 to 8000 and maximum chain extensibility ($L$) from 50 to 200, reveal a maximum drag reduction (MDR) asymptote. Compared with the classical MDR observed in planar wall-bounded shear flows, that is, drag reduction (DR) is $\sim -80\, \%$, this MDR state achieves only moderate levels of DR ($\sim -60\,\%$). This is due to the existence of large-scale structures (LSSs). A careful examination of the flow structures reveals that the polymer–turbulence interaction suppresses small-scale vortices and stabilizes the LSSs. These structural changes in turn lead to a reduction of Reynolds stress, and consequently to a DR flow state. Although Reynolds stress does not vanish as observed in classical MDR states, the small-scale vortices that heavily populate the near-wall region are also almost completely eliminated in this flow state. Concurrently, significant polymer stresses develop as a consequence of the interaction between polymer chains and LSSs that partially offset the magnitude of DR, leading to MDR asymptotes with moderate levels of DR. Moreover, we demonstrate that polymer deformation, i.e. deviation from the equilibrium state, is directly correlated with the LSSs dynamics, while the polymer deformation fluctuation displays a universal property in the MDR state. Hence, it is not surprising that the extent of DR exhibits a non-monotonic dependence on the maximum chain extensibility. Specifically, the variation in $L$ alters the incoherent and coherent angular momentum transport by small- and large-scale flow structures, respectively. To that end, the most DR flow state occurs at a moderate value $L=100$. Overall, this study further supports the universal property of polymer-induced asymptotic states in wall-bounded turbulence and paves the way for mechanistic understanding of drag modification that arises from the interaction of polymers with small- and large-scale flow structures.