This work introduces closed-form solutions to describe the compressible, cyclonic motion evolving in a hemispherical chamber configuration. The analysis begins with an expansion of the compressible Bragg–Hawthorne equation in spherical coordinates. Our basic assumptions include an adiabatic and impermeable wall, a uniformly distributed stagnation enthalpy, a chamber mass balance in the equatorial plane and a vanishing centreline cross-flow velocity. Using a Rayleigh–Janzen expansion in the squared injection Mach number, the leading-order solution is seen to recover the problem’s incompressible profile as a limiting case. Meanwhile, the first-order compressible correction is shown to produce closed-form expressions for the velocity and vorticity fields, most thermodynamic properties, the local Mach number and the helicity density. At the outset, dilatational effects on all variables are evaluated and determined to be most pronounced near the equatorial plane, and least appreciable at the chamber apex, where a stagnation region seems to form. In this process, the net integrated helicity is transformed into a single volume integral that can be directly specified at both leading and first orders as a function of the Ekman-type inflow parameter. We also manage to capture rather explicitly the dilatational distortions of two characteristic surfaces: the mantle interface that separates the updraft and downdraft regions, and the vortex core surface that tracks the peak swirl intensity. Lastly, a group parameter that combines the injection Mach number and the inflow parameter is found to effectively scale all dilatational contributions caused by variations in the mass influx, chamber geometry and characteristic speed of sound.

This study examines the transition to turbulence downstream of fluttering and non-fluttering bioprosthetic aortic valves using global linear stability theory. During systole, increasing inflow velocities result in temporally evolving flow profiles downstream of the valve which are highly influenced by the leaflet kinematics. These profiles are time averaged at the sinotubular junction over successive windows and used as boundary conditions to obtain base flows for stability analysis. Three-dimensional global modes are computed for one design of each valve type across multiple time windows, revealing several unstable modes whose frequencies and growth rates increase over time. Notably, the non-fluttering valve exhibits higher growth rates than the fluttering valve. The resulting eigenspectra show that, for each case, the most unstable eigenvalues align along two distinct parabolic branches in the complex plane. For each valve case, the modes within each branch are found to have similar group velocities, suggesting that the unstable modes along a branch constitute a coherent structure. Motivated by this, a transient growth analysis is conducted to identify the optimal initial perturbations that maximise energy gain for a given time horizon. When superimposed onto the base flow, these perturbations generate vortical structures that closely resemble those observed in fully coupled nonlinear fluid–structure interaction simulations for a similar time scale as the one used to obtain the optimal perturbations. These results suggest that the optimal perturbations may initiate the shear-layer instabilities responsible for transition to turbulence, providing valuable insight into the underlying mechanisms in the flow fields downstream of bioprosthetic valve designs.

This study uncovers a striking similarity between massively separated laminar and turbulent flows that develop over a square wing during extreme vortex gust encounters. The evolving large-scale, vortical core structures responsible for significant transient lift variations exhibit remarkable similarity across ${\textit{Re}}=600$ and 10 000. The formation of these structures is attributed to a substantial gust-induced vorticity flux produced at the wing surface, resulting in shared large-scale topological features between the low- and high-Reynolds-number flows. Although fine-scale vortical structures quickly emerge in the ${\textit{Re}}=$ 10 000 case, the large-scale structures identified by scale decomposition of the turbulent flow resemble those observed at ${\textit{Re}}=600$. These findings suggest that large-scale vortical features present in laminar extreme aerodynamic flows provide key insights into their higher Reynolds number counterparts, potentially reducing the complexity of flow modelling and control for extreme aerodynamics.

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.