We report an experimental study on the effects of polymer additives in the dissipative-scale flow field properties in turbulent Rayleigh–Bénard convection. The experiments were conducted in a cylindrical convection cell with a minute amount of polyacrylamide long-chain polymer. The local velocity gradient tensor was measured using an integrated home-made measurement system (J. Fluid Mech., 2024, vol. 984, p. A8). Although the single-roll large-scale circulation persists (owing to the slight tilt of the convection cell), polymers induce an anisotropic suppression of the dissipative-scale flow properties. The normal velocity gradient components are suppressed more than the shear components. The mean energy dissipation rate in both centre and side regions decreases, then levels off with increasing polymer concentration and the final reduction ratio exceeds 50 % in each region. In the side region, adding polymers has a stronger stabilising effect on the strain rate than the rotation. The anisotropic suppression of the velocity gradient tensor affects dissipation-rotation co-occurrence probability, velocity gradient triple decomposition and local streamline topology. Adding polymers also induces a deceleration effect and increases the contribution of local buoyancy in driving the flow. These results reveal that the addition of polymers can non-trivially manipulate dissipative-scale turbulence fields and energy cascades.

Predicting unsteady loads on plate-like objects during unsteady motion is important in many applications, such as ship manoeuvring, flight and biological propulsion. The drag force on a starting plate that moves normal to its surface can be severely underestimated during the acceleration phase when conventional methods are used to incorporate the effects of acceleration. These methods often introduce an inviscid added mass force that has its origin in potential flow. However, the flow field around a starting plate quickly diverges from potential flow after the start of the motion due to the continuous creation of vorticity at the plate surface. Following the concept of drag by Burgers (1921 Proc. K. Ned. Akad. Wet. 23, 774–782), we propose a model to predict the creation of vorticity on the plate surface and its advection into the vortex loop at the plate edges, based on Stokes’ first problem. This model shows that the acceleration drag force is a history force, in contrast to the inviscid added mass force that is proportional to the instantaneous acceleration of the plate. We perform experiments on starting plates over a large range of accelerations, velocities, fluid viscosities and plate geometries for which the model gives accurate predictions for the drag force during acceleration and during the relaxation phase immediately after the acceleration ceases. This model is extended to also predict the drag forces on accelerating plates during a starting motion with a non-constant acceleration.

Dynamics of spheroidal particle migration within the elasto-inertial square duct flow of Giesekus viscoelastic fluids were studied by using the direct forcing/fictitious domain method. The results show rich migration behaviours, a spheroidal particle gradually transitions from the corner (CO), channel centreline (CC), inertial rotational (IR), diagonal line and cross-section midline equilibrium positions with a decrease in the elastic number, depending on the initial particle position, initial particle orientation and fluid elasticity. From the effect of secondary flow, the IR equilibrium position is reported when the fluid inertia is relatively strong. Six (five) kinds of rotational behaviours are observed for the elasto-inertial migration of prolate (oblate) spheroids. Moreover, the critical elastic number is determined for the migration of spheroidal particles in Giesekus fluids. Near the critical elastic number, oblate and prolate spheroids can simultaneously maintain the CC, CO and IR equilibrium positions, and the initial orientation of particles affects their final rotational modes and equilibrium positions. Through comprehensive analysis, empirical formulas governing the ability of oblate and prolate spheroids to maintain the CC equilibrium position are proposed as $\textit{Wi} = 0.055\,\textit{Re}{-0.1}$ and Wi = 0.045 Re−0.35 when n = 0.5, 0.01 ≤ Wi ≤ 1. Due to the different directions of the pressure forces acting on the particles and the forces from the first normal stress difference and the second normal stress difference, the equilibrium position in Giesekus fluids is rapidly increased by increasing the secondary flow at higher elastic numbers, which is contrary to the phenomenon observed in the Oldroyd-B fluid.

Rough walls are commonly encountered in engineering applications. However, existing understanding of combustion in the turbulent boundary layer over rough walls is lacking. This study investigates turbulent boundary layer premixed flame flashback over rough walls using direct numerical simulations for the first time. The features of boundary layer flashback over walls with various roughness are explored in terms of flame morphology and flashback speed. It is found that the flame in rough-wall cases is more wrinkled compared with the smooth-wall case, particularly in the near-wall region, due to the presence of more small-scale vortical structures. Wall roughness reduces the flame flashback speed, which is attributed to the higher flow velocity at the leading edge of the flame front in rough-wall cases. The effects of wall roughness and combustion on boundary layer turbulence are revealed through two-point correlations of fluctuating velocity and wall resistance. The results show that, under non-reacting conditions, wall roughness reduces the streamwise and wall-normal extents of near-wall hairpin packets of boundary layer turbulence while increasing their inclination angles. Under reacting conditions, combustion further increases the inclination angle, with a more pronounced effect in rough-wall cases. Wall roughness influences wall resistance, primarily through its pressure component. Flame/wall interactions are also scrutinised, revealing higher wall heat loss in rough-wall cases, which is is mainly attributed to the increased wall surface area. A negative correlation between the quenching distance and the alignment of flame normal and wall normal is observed in rough-wall cases, which is weaker in smooth-wall cases.

The mixing mechanism within a single vortex has been a theoretical focus for decades, while it remains unclear especially under the variable-density (VD) scenario. This study investigates canonical single-vortex VD mixing in shock–bubble interactions (SBI) through high-resolution numerical simulations. Special attention is paid to examining the stretching dynamics and its impact on VD mixing within a single vortex, and this problem is investigated by quantitatively characterising the scalar dissipation rate (SDR), namely the mixing rate, and its time integral, referred to as mixedness. To study VD mixing, we first examine single-vortex passive-scalar (PS) mixing with the absence of a density difference. Mixing originates from diffusion and is further enhanced by the stretching dynamics. Under the axisymmetry and zero diffusion assumptions, the single-vortex stretching rate illustrates an algebraic growth of the length of scalar strips over time. By incorporating the diffusion process through the solution of the advection–diffusion equation along these stretched scalar strips, a PS mixing model for SDR is proposed based on the single-vortex algebraic stretching characteristic. Within this framework, density-gradient effects from two perspectives of the stretching dynamics and diffusion process are discovered to challenge the extension of the PS mixing model to VD mixing. First, the secondary baroclinic effect increases the VD stretching rate by the additional secondary baroclinic principal strain, while the algebraic stretching characteristic is still retained. Second, the density source effect, originating from the intrinsic nature of the density difference in the multi-component transport equation, suppresses the diffusion process. By accounting for both the secondary baroclinic effect on stretching and the density source effect on diffusion, a VD mixing model for SBI is further modified. This model establishes a quantitative relationship between the stretching dynamics and the evolution of the mixing rate and mixedness for single-vortex VD mixing over a broad range of Mach numbers. Furthermore, the essential role of the stretching dynamics on the mixing rate is demonstrated by the derived dependence of the time-averaged mixing rate $\overline {\langle \chi \rangle }$ on the Péclet number ${\textit{Pe}}$, which scales as $\overline {\langle \chi \rangle } \sim {\textit{Pe}}^{{2}/{3}}$.

In the fully developed region of a plane turbulent wall jet, the key jet parameters, including the jet velocity Um, jet half-width z1/2 and wall shear stress $ \tau_{0}$, follow the classical power-law scaling with the streamwise distance x: Um$v$/M0 ∼ (xM0/$v$2)−α, z1/2M0/$v$2 ∼ (xM0/$v$2)β and $ \tau_{0}$$v$2/(ρ$M_{0}^{2}$) ∼ (xM0/$v$2)−χ, where M0 is the source kinematic momentum flux, $v$ is the coefficient of kinematic viscosity of fluid, ρ is the mass density of fluid and α, β and χ are the positive scaling exponents. We present a theoretical framework to determine these exponents. Our framework reveals that each jet parameter exhibits a scaling transition. This transition is driven by a shift in the scaling law of the skin-friction coefficient as the Reynolds number Rem = Umzm/$v$ changes over from Rem < 8000 to Rem > 10 000, where zm is the wall-normal location corresponding to the jet velocity. Specifically, α transitions from 4(1 + γ)/(9 − γ) to 13(1 + γ)/[2(14 − γ)], β from 8/(9 − γ) to 13/(14 − γ) and χ from (9 + 7γ)/(9 − γ) to (14 + 12γ)/(14 − γ), where γ ≈ 0.05 is a parameter determined from experiments. We validate the theoretical predictions against extensive experimental datasets from the literature.

The dynamics of a fluid flow about its limit cycle can be analysed through phase reduction analysis – an approach that distils a high-dimensional dynamical system to its scalar phase dynamics. This technique provides insights into phase sensitivity, revealing the mechanisms that advance or delay phase dynamics. The phase-based reduced-order model derived from this approach serves as a foundation for identifying lock-on conditions and designing flow control techniques. Recent work by Sumanasiri et al. (J. Fluid Mech. vol. 1020, 2025, R4) applied phase reduction analysis to the fluid–structure interaction problem of aerofoil flutter in a free stream. Their analysis systematically changed the stiffness of the structural dynamics to decipher the phase dynamics mechanism of flutter. Moreover, they considered the use of optimised heaving motion to suppress the emergence of flutter. Their approach opens new avenues for modifying flow physics through innovative modifications of material properties and structural dynamics.

We developed a two-phase lattice Boltzmann model by coupling the entropic multiple-relaxation-time (EMRT or KBC) collision operator enabling low fluid viscosity, with a source term (Wang et al. 2022, Phys. Rev. E vol. 105, no 4) to independently adjust surface tension. The coupling is implemented via the exact difference method (EDM), which allows full consideration of external-force effects on the entropic stabiliser in KBC, in contrast to the recent work of Wang et al. (2022 Phys. Rev. E vol. 105) and Xu et al. (2024 Comput. Math. Appl. vol. 159, 92–101). More importantly, we address a major drawback of the EDM by explicitly demonstrating how its high-order error terms influence the pressure tensor and surface tension. Using the developed model, we investigated droplet impact and splashing on a thin liquid film at a remarkably high Weber number of ${\textit{We}} = 5000$ and Reynolds number of ${\textit{Re}} = 5000$. Droplet impact and splashing on flat surfaces and mesh structures at very high ${\textit{Re}}$ (15 200) and ${\textit{We}}$ (1020) are also studied after validating four representative cases against experiments. For droplet impact on flat surfaces, hydrophobicity promotes the growth of peripheral instabilities, leading to fingering splashing. Corona splashing transitions to fingering splashing as the liquid–gas viscosity ratio increases. For droplet impact on mesh structures, large openings promote liquid penetration, whereas small openings enhance spreading. As the solid ratio increases, the maximum spreading ratio increases monotonically but nonlinearly, whereas the maximum penetrated liquid pillar length first rises and then drops. These simulations demonstrate the proposed model offers significant advantages for accurately capturing and elucidating complex droplet impact and splashing dynamics at high ${\textit{Re}}$ and ${\textit{We}}$.

Torque-driven steering of magnetic micro/nanobots in fluids is one of the most promising platforms of controlled propulsion at the small scales, and it has been the focus of modern biomedical applications. The propulsion is a result of rotation–translation coupling and it requires non-trivial (e.g. chiral) geometry of the nanobot and the weak (millitesla) rotating magnetic field. At submicron scale, nanobots are subjected to intrinsic thermal fluctuations that may become comparable to the magnetic driving. We investigate the effect of Brownian fluctuations on the actuation and steering of magnetized nanohelices in a viscous fluid numerically, using Langevin simulations. First, we assume force-free propulsion and study the effect of thermal fluctuations on driven rotation and steering of the nanohelix. We demonstrate that the random Brownian torque dramatically impedes the nanobot’s propulsion via (i) hindering the rate of the forced rotation; (ii) altering its orientation, i.e. increasing the precession angle of the forced rotations. We further demonstrate that even for fairly low thermal noise (rotational Péclet number, $ \textit{Pe} \approx 10$), the angular velocity of the forced rotation drops by $2$–$3$ times, while the precession angle increases two fold as compared with the non-Brownian limit. Both these factors contribute to an approximately $2.5$-fold reduction of the propulsion velocity. Furthermore, when the magnitude of thermal fluctuations is comparable to magnetic driving ($ \textit{Pe} \approx 1$), we find an order-of-magnitude reduction of the propulsion speed. Although inclusion of a stochastic thermal force does not alter the propulsion velocity on average, it considerably increases its variance and further impedes the propeller’s steerability.

Dense arrays of soft hair-like structures protruding from surfaces are ubiquitous in living systems. Fluid flows can easily deform these soft hairs, which in turn impacts the flow properties. At the microscale, flows are often confined, which exacerbates this feedback loop: the hair deformation strongly affects the flow geometry. Here, I investigate experimentally and theoretically pressure-driven flows in laminar channels obstructed by a dense array of elastic fibres or ‘hairs’. I show that the system displays a nonlinear hydraulic resistance that I model by treating the hair bed as a deformable porous medium whose height results from the deflection of individual fibres. This fluid–structure interaction model encompassing flow in porous media, confinement and elasticity is then leveraged to identify the key dimensionless parameter governing the problem: $\hat {f}_0$, a dimensionless drag that combines fluid, solid and geometrical properties. Finally, I demonstrate how these results can be harnessed to design passive flow control elements for microfluidic networks.

The recirculation zone is critical for flame stabilization in combustion processes, yet a quantitative, mechanistic understanding of its inherently complex mixing state remains a challenge. To address this gap, we introduce a novel characteristic parameter, the characteristic mixture fraction ($Z_u$), defined from the observation of localized mixture uniformity within the zone. Using validated large-eddy simulation combined with the flamelet/progress-variable approach, we systematically examine the relationship between $Z_u$ and the momentum flux ratio ($J$). The results reveal that a dual-power-law scaling relationship between $Z_u$ and $J$ is a fundamental characteristic of bluff-body stabilized flows, persisting with and without chemical reactions. This scaling, however, is profoundly modified by combustion. Compared with non-reacting flows, reacting flows exhibit a shift in the transition point between power-law regimes to a higher $J$ and a shallower scaling exponent (e.g. approximately −0.15 for reacting versus −0.5 for non-reacting flows in the jet-envelopment regime). These quantitative distinctions are decisively attributed to thermophysical effects induced by heat release, interpreted through two synergistic mechanisms: at the macroscale, thermal expansion reduces density, weakening the recirculation zone’s momentum resistance; at the microscale, increased viscosity suppresses turbulent mixing efficiency. Thus, a predictive mechanistic framework centred on the parameter $Z_u$ is established, providing not only a robust metric for quantifying complex mixing states but also fundamental insights into how heat release acts on turbulent mixing. Consequently, it offers new perspectives for combustor optimization and understanding of complex mixing–combustion coupling.