In this paper, we propose a space-dependent eddy thermal diffusivity model for turbulent vertical natural convection in a fluid between two infinite vertical walls at different temperatures. Using this model, we derive analytical results for the mean temperature profile. Our results reveal that mean temperature profiles for different Rayleigh and Prandtl numbers are described by two universal scaling functions in the inner region next to the walls and the outer region near the centreline between the two walls, and the characteristic temperature scales in the inner and outer regions are expressed in terms of the two parameters of the model which determine the characteristic velocities for heat transfer in the two regions. We show that these results are in good agreement with direct numerical simulation data.

Active filaments, such as microtubules with attached cargo-carrying motor proteins, are important dynamic structures for fluid transport in and around living cells. The mathematical models of active filaments appearing in the literature typically involve combinations of follower forces, compressive tangential forces, along the filament, and an opposite force on the fluid that generates an effective surface flow. In this paper, we present a comparative dynamical systems study of active filament models examining the differences in dynamic states that occur when actuation is through follower forces alone, or the effect of surface flows is also included. We consider cases where actuation is applied only at the filament tip, or distributed uniformly along the filament length. By varying actuation strength, we show that the first bifurcations that provide the transition between the upright, whirling and beating states appear in all models. At higher values of actuation, when beating becomes unstable, however, qualitative differences between the models emerge. Those with distributed actuation produce a single, time-dependent state, which for the surface flow model is reminiscent of a rotating helix that periodically changes handedness and rotation direction. Tip actuation, however, yields complex transitions that ultimately produce a chaotic state. We link the differences in dynamics between tip and distributed actuation to differences in their respective internal stress distributions – differences that appear as early as the first bifurcation, where they affect the shapes of the unstable modes.

The effects of section shape, specifically thickness and camber, on the lift spectrum for a foil immersed in a turbulent flow are analytically and experimentally investigated. The lift response functions to incident cross-stream vortices drifting along streamlines offset from the foil within two chord lengths are computed using an analytical solution to the Blasius force equation, achieved by way of using an expanded Joukowsky mapping function that can map a circle in the complex plane to any selected foil shape. The vortex lift responses are convolved with the vorticity wavenumber–frequency spectrum for a homogenous turbulent flow to compute the overall foil lift due to incident turbulence. Calculations of the lift spectra for a series of foils with increasing maximum thickness, NACA 651A-0008, -0012 and -0016 foils, immersed in grid-generated turbulent flow agree very well with measurements up to the maximum measured frequency, $\omega C/2U \approx 40$, where $C$ is the chord and $U$ is the free-stream speed, which showed an increasing level of lift attenuation at high frequencies with increasing foil thickness. The analytical model showed that the high-frequency lift was controlled by the inertia of the incident vortices, and that the thickness of the foil near the leading-edge controls these high-frequency lift levels by decreasing the drift velocities of the approaching vortices. A simplified analytical model of the vortex inertia force, which avoided the need to implement the unsteady Kutta condition, was developed to estimate the high-frequency lift for thick foils with less computational demand. A wind tunnel experiment involving unsteady lift measurements for a foil in a turbulent flow was performed to physically confirm the model-based prediction that increasing the foil leading-edge thickness can significantly attenuate high-frequency lift, while maintaining the overall maximum thickness. Undesired components of the unsteady force measurements associated with foil vibration were removed using a novel technique of analysing measured force spectra over a series of wind tunnel speeds. The unsteady lift spectra measured for a NACA 0007-61 foil, modified to have constant thickness from 10 % to 50 % chord, showed an approximate attenuation of 8–10 decibels at reduced frequency, $\omega C/2U = 30$, relative to a NACA 0007-65 foil, which agreed well with the model-based predictions and confirmed that increasing the foil thickness in the vicinity of the leading edge yields significant high-frequency lift attenuation.

This paper presents a theoretical and computational investigation into how a propagating three-dimensional vortex modifies ambient turbulence. Using rapid distortion theory and numerical simulations, the study explores both local and non-local changes in the external vorticity field resulting from fluid displacement and stretching. Cases involving structured and unstructured turbulence reveal that the vortex introduces permanent distortions along its path, and alters the far field turbulence through reflux effects. The findings extend classical models by quantifying the impact of vortex-induced strain and displacement on turbulence, offering new insights into turbulent–turbulent interfaces and the role of coherent structures in modulating external turbulent fields.

This study experimentally investigates the aerodynamic effects of rotor–rotor interaction in a twin-rotor system operating in ground effect at a rotor-tip Reynolds number of $10^5$. The strength of the ground effect and the rotor interaction were controlled by adjusting the normalised ground standoff distance and rotor separation distance, respectively. For the single-rotor configuration, ground proximity generated a stagnation region within the wake, redirecting axial momentum radially outward to form a wall jet. As the rotor approached the ground, the stagnation region moved closer to the rotor disk, increasing the thrust coefficient. In the widely spaced twin-rotor case, the opposing wall jets from both rotors converged on the ground to form a stagnation point. From this point, the flow diverged outward, producing a fountain flow and transverse outflow. The fountain flow tilted the wakes toward each other, reducing thrust. As rotor spacing decreased, rotor-disk blockage intensified, suppressing the fountain flow. When the fountain-driven recirculating flow developed around the rotor tips, re-ingestion into the rotors caused substantial thrust reduction. Peak thrust loss could be identified using the momentum flux coefficient of the fountain flow. However, with very close rotor spacing, the weakened fountain flow contracted the recirculating region, suppressing wake deflection and largely restoring thrust. Importantly, the thrust loss induced by rotor interaction reached its maximum at smaller normalised rotor separation distances as the rotors operated closer to the ground. These findings quantitatively link the fountain-flow dynamics to thrust variation, offering new mechanistic insight into multirotor aerodynamics in ground effect.

The study of rotating Rayleigh–Taylor (RT) turbulence is of fundamental significance for geophysical processes and certain engineering applications. This work systematically investigates the effects of rotation on RT turbulence using direct numerical simulation (DNS), focusing primarily on the generation of kinetic energy and enstrophy, as well as the scale-to-scale transfer of kinetic energy. Based on the DNS results, it is demonstrated that there is a notable delay and inhibition of the mixing layer growth with enhancing rotation (quantified as a decreasing Rossby number, $Ro$). That is, energy conversion efficiency drops substantially, from approximately $50\,\%$ in the non-rotating case $Ro = \infty$ to only $10\,\%$ in the strong rotating case $Ro=0.1$. This is because rotation amplifies the viscous dissipation associated with the shear stress components in the vertical direction within the mixing layer. Regarding enstrophy generation, baroclinic effects dominate during the early stage of flow evolution, while vortex stretching and tilting become the primary contributors in the later stage. Notably, the vortex stretching and tilting term is significantly suppressed by the rotation, resulting in three-dimensional RT turbulence exhibiting an enstrophy generation mechanism more akin to two-dimensional flow. Furthermore, analysis of scale-to-scale transfer of kinetic energy reveals an increased likelihood of local inverse energy transfer events under enhanced rotation. Specifically, strong rotation (e.g. $Ro=0.1$) results in strongly helical turbulence, which contains more high-helicity regions favourable for local inverse energy transfer. Moreover, the presence of rotation leads to more coherent and elongated flow structures and an enhanced efficiency of fluid mixing within the mixing layer.

The superlinear scaling relationship between the hydrodynamic dispersion coefficient and the Péclet number in porous media has been widely acknowledged. Nevertheless, the mechanisms driving this behaviour remain inadequately understood. In this work, we investigate the mechanism responsible for this superlinear scaling using a Lagrangian framework that combines a statistical model, which links the global probability density function of tracer transition time to flow variability in porous media, with a continuous time random walk framework. Our analysis reveals that the intra-pore and inter-pore flow variabilities are the primary sources responsible for the superlinear scaling, with their relative significance characterised by a structure-specific parameter, $\chi$. Specifically, the inter-pore flow variability dominates when $\chi \gt 1$, while the intra-pore variability prevails for $0\lt \chi \lt 1$. The parameter $\chi$ is derived exclusively from the statistical distributions of pore-throat radius, length and orientation angle, which can be readily obtained from structural characterisation techniques such as X-ray computed tomography imaging. These theoretical predictions are validated through extensive numerical simulations on tube networks with substantial structural variation. This study resolves discrepancies in previous studies regarding the mechanisms of superlinear scaling in hydrodynamic dispersion and offers valuable insights into modulate dispersion and mixing in porous media.

Sinking marine snow particles, composed primarily of organic matter, control the global export of photosynthetically fixed carbon from the ocean surface to depth. The fate of sedimenting particles is partly regulated by their encounters with suspended objects, which leads to mass accretion and potentially alters their buoyancy, and with bacteria that can colonise the particles and degrade them. Their collision rates are typically calculated using two types of models focusing either on direct (ballistic) interception with a finite interaction range, or advective-diffusive capture with zero interaction range. Yet, since many relevant marine encounter scenarios span across both regimes, quantifying such encounters remains challenging because the two models yield asymptotically different predictions at high Péclet numbers. We reconcile the two approaches by quantifying encounters in the general case using theoretical analysis and simulations. By solving the advection-diffusion equation in Stokes flow around a sphere to model mass transfer to a sinking particle by finite-sized objects, we determine a new formula for the Sherwood number as a function of the Péclet number and the ratio of particle sizes. Contrary to the common assumption, we find that diffusion still plays a significant role in generating encounters even at high Péclet numbers. We predict that at Péclet numbers as high as 106 the direct interception model underestimates the encounter rate by up to two orders of magnitude. This overlooked contribution of diffusion to encounters suggests that processes affecting the fate of marine snow may proceed at a rate much higher than previously thought.

Bubble dynamics constitutes a fundamental scientific problem in fluid mechanics. Although the oscillation can be predicted through theories for bubble dynamics in previous studies, the viscous effects on the bubble migration remains difficult to predict accurately. In this study, we establish a theoretical model for bubble migration across the entire cycle. The theoretical model derives a drag coefficient expression under dynamic Reynolds numbers, and incorporates corrections to account for non-spherical bubble dynamics. A key advance is the capability to account for viscous drag without relying on constant empirical drag coefficients. Validation against experimental results demonstrates that the theoretical model effectively predicts the bubble migration. Furthermore, we discuss the correlation between drag coefficient and Reynolds number, and elucidate the effects of viscous domain range and bubble deformation on the drag coefficient of the present model.

Linear and weakly nonlinear stability analyses are carried out to understand the influence of anisotropic slip on the instability and transition characteristics of pressure-driven parallel flow in the fluid overlying a porous medium. The slip is induced on the upper plate dominating in the streamwise direction. The investigation is made by imposing Navier slip on the classical model considered by Aleria et al. (SIAM J. App. Math., vol. 84, 2024, pp. 433–463). For finite-amplitude disturbances, a weakly nonlinear stability analysis based on the cubic-Landau theory is exploited. The bifurcation phenomena are investigated as a function of slip length at the critical instability point (CIP) and as a function of Reynolds number away from the CIP. The linear stability analysis shows that Squire’s theorem does not hold for anisotropic slip, and the mode of instability along the neutral curve is sensitive to slip length. Along the instability boundary, slip stabilises (destabilises) the porous mode (odd-fluid mode), whereas in the even-fluid mode, slip can have either a stabilising or destabilising effect. When the porous mode or odd-fluid mode dominates the flow instability, only the supercritical bifurcation exists at and away from the CIP. For each value of the depth ratio, there exists a finite interval of slip parameter in which the three-dimensional disturbances are least stable and the critical mode of instability is the even-fluid mode. Both the subcritical and supercritical bifurcations are possible for the even-fluid mode of instability and the supercritical bifurcation at the CIP always shifts to a subcritical bifurcation away from the CIP. The nonlinear kinetic energy analysis reveals that modifications in energy due to gradient production and viscous dissipation are mainly responsible for inducing the subcritical instability. The role of spanwise slip, Darcy number, porosity and Beavers–Joseph coefficient is also investigated. The results demonstrates a stabilising (destabilising) impact of spanwise slip (porosity and Beavers–Joseph coefficient), and instability as well as bifurcation characteristics is a function of ${\sqrt {\textit{Da}}}/{\hat{d}}$, rather than individual Darcy number ($Da$) and depth ratio ($\hat{d}$). Overall, this study finds a significant relationship among the critical modes of instability, dimension of the least stable disturbances, bifurcation phenomena and skin-friction coefficient. The present results also witness good experimental support for the stability of flow in the fluid overlying a porous medium and slippery flow in a single-fluid layer configuration.

The settling dynamics of fractal aggregates in constant-density environments and through miscible density interfaces are investigated via particle-resolved direct numerical simulations, which provide the settling velocity as a function of the fractal dimension, Galileo number, and particle and fluid densities. In a fluid of uniform density the settling velocity increases with the fractal dimension and the Galileo number. This behaviour is captured by an empirical relationship that holds over a broad range of parameter values. In the presence of a miscible density interface, consistent with earlier observations we observe that lighter fluid is carried into the denser layer by the aggregate’s pore spaces, which we quantify based on the concept of $\alpha$-shapes. This causes the aggregate to slow down, until the lighter pore fluid is replaced by the denser fluid via a combination of diffusion and convection. The degree of the aggregate’s slowdown depends on the ratio of the density differences between the aggregate and the two fluids, and it can again be captured by an empirical relationship. The duration of the slowdown is determined by the pore fluid replacement time, which in turn depends on the relative importance of convection and diffusion, and hence on the aggregate’s geometry. A relationship is derived that captures the dependence of this replacement time on the shape of the aggregate, the ratio of the density differences, and the Galileo number.

Miniature vortex generators (MVGs) are a promising passive flow control technique for viscous drag reduction by producing large-scale vortical motions that manipulate turbulence structures in turbulent boundary layers (TBLs) without significant device drag. This study conducts hot-wire anemometry experiments to investigate the influence of the Reynolds number and the ratio of MVG height $h$ to TBL thickness $\delta _0$ (MVG height ratio $h/\delta _0$) on turbulence structures. Experiments encompass two MVG height ratios, $h/\delta _0=0.09,\;0.18$, friction Reynolds numbers ranging from ${\textit{Re}}_\tau =400$ to 2000 and measure the velocity information at various downstream stations. Spectral analysis confirms the MVG-induced vortices amplify large-scale structures in the outer region, sustaining up to 100 times the MVG height downstream. The MVGs are also found to attenuate turbulence energy across a wide range of turbulence structures below the amplification location in the logarithmic region, connected with the MVG-induced spanwise motion. Increasing the friction Reynolds number from ${\textit{Re}}_\tau =400$ to $900$ or doubling the MVG height ratio causes the amplified structures to develop into longer motions and move away from the wall, while increasing the turbulence energy attenuation proportion to the log region. Moreover, the energy attenuation amplitude of large-scale structures in the near-wall region increases with a larger MVG height ratio but decreases with increasing Reynolds numbers. The findings indicate that, at friction Reynolds numbers ${\textit{Re}}_\tau \geqslant 900$, MVGs induce spanwise motions that attenuate near-wall structures and modulate large-scale outer motions. The present configuration does not yield a global viscous drag reduction, but the turbulence modulation trends suggest the potential for viscous drag reduction when the MVG configurations are optimised to enhance favourable buffer-layer spanwise motions.

Entropically driven fluid–solid transitions in monodisperse, purely repulsive hard spheres (MPRHS) are well established in theory, simulation and experiment for atomic and colloidal systems. For MPRHS, however, coexistence is usually located via bulk free-energy calculations; the underlying microscopic balance between configurational and vibrational entropy is left implicit. Frenkel clarified this mechanism explicitly as an exchange of long-range configurational entropy for short-range vibrational entropy, but in the pristine MPRHS limit the nucleation barrier near coexistence is so high that phase separation is predicted only on astronomical time scales. Consistent with this, even unbiased simulations do not show spontaneous, equilibrium fluid–crystal coexistence; transient mixtures are mostly overtaken by a single phase; observed coexistence is still algorithmically driven. Nearly hard-sphere colloid experiments do observe fluid–crystal coexistence, but always in the presence of unavoidable triggers such as gravity and walls. We treat the hard-sphere phase diagram as settled and ask how the entropic exchange mechanism can be revealed in nearly hard-sphere colloidal simulations. We probe the mechanism on finite time scales by introducing minimal perturbations that trigger phase separation: small reductions in hardness that increase locally accessible free volume (and thus gently increase vibrational entropy), and 2 %–4 % distributed crystal seeds. These perturbations produce coexisting fluid and crystal domains with crystal fraction, phase envelope and osmotic pressure that, with systematically increasing particle hardness, approach the hard-sphere limit. These results demonstrate that slight enhancements to vibrational entropy provide a dynamically accessible route to realising the long-range/short-range entropy exchange required for phase separation.

Since the early 1990s, numerous theoretical methods have been proposed to predict Mach stem height in steady supersonic shock reflections by assembling sub-models for local flow structures, including incident/reflected shocks, the triple point, the slipline, and Mach stem curvature. We constructed an updated model and employed it as a benchmark to evaluate the performance of various sub-models corresponding to typical flow regions. The results show that the curved assumption for the free part of the slipline outperforms the straight-line approximation, considering the differences in regions after the reflected shock can improve the predictive accuracy, while using compatibility relations in the interactive part of the slipline is superior to the wave reflection model and better captures the linear slope of Mach stem height with wedge trailing edge height. Nevertheless, prediction errors in the slope and systematic biases in the overall Mach stem height prediction persist. To address these shortcomings, we developed a calibrated scaling law for the coefficient of a linear Mach stem model. Grounded in asymptotic reasoning and high-fidelity numerical simulations, this law yields a compact, easy-to-implement expression that achieves substantially higher accuracy than existing analytical composite models across the full parameter space. It retains well-established limiting cases, clarifies how inadequate sub-modelling degrades prediction accuracy, and provides uncertainty estimates for practical engineering applications.

The behaviour of near-inertial waves (NIWs) in baroclinic currents is investigated, with a focus on wave trapping and critical layer dynamics. We present theoretical analysis, supported by numerical simulations, of the Sawyer–Eliassen equation, which describes waves in the plane perpendicular to an arbitrary balanced background flow. Gradients of the background velocity and buoyancy field modulate the wave properties, in particular defining the range of frequencies for which the Sawyer–Eliassen equation is hyperbolic, i.e. wave-like. Variations in the lower limit of this range, the local minimum frequency, lead to the trapping of low-frequency, typically sub-inertial, waves through either total internal reflection or the formation of critical layers. Both mechanisms are studied. We introduce a local coordinate rotation that not only elucidates these dynamics by simplifying the governing equation, but also allows us, through direct analogy, to draw upon theory and intuition developed for barotropic problems. In the majority of physically relevant cases, the transformed coordinates are aligned with and perpendicular to isopycnals, and are thus easily utilised. Employing the coordinate transformation, we consider along-isopycnal modes, and study the behaviour of waves approaching a critical level without the need for a full ray-tracing approximation. Finally, we find qualitative differences in the critical layers that form in strongly and weakly baroclinic flows, most notably in their location. In the weakly baroclinic case, NIW energy accumulates about the minimum in the relative vorticity of the background flow, whereas in the strongly baroclinic case, we find slantwise critical layers concentrated in fronts.