Lubricant viscoelasticity arises due to a finite polymer relaxation time ($\lambda$) which can be exploited to enhance lubricant performance. In applications such as bearings, gears, biological joints, etc., where the height-to-length ratio ($H_0 / \ell _x$) is small and the shear due to the wall velocity ($U_0$) is high, a simplified two-dimensional computational analysis across the channel length and height reveals a finite increase in the load-carrying capacity of the film purely due to polymer elasticity. In channels with a finite length-to-width ratio, $a$, the spanwise effects can be significant, but the resulting mathematical model is computationally intensive. In this work, we propose simpler reduced-order models, namely via (i) a first-order perturbation in the Deborah number ($\lambda U_0 / \ell _x$) and (ii) the viscoelastic Reynolds approach extended from Ahmed & Biancofiore (J. Non-Newtonian Fluid Mech., vol. 292, 2021, 104524). We predict the variation in the net vertical force exerted on the channel walls (for a fixed film height) versus increasing viscoelasticity, modelled using the Oldroyd-B constitutive relation, and the channel aspect ratio. The models predict an increase in the net force, which is zero for the Newtonian case, versus both the Deborah number and the channel aspect ratio. Interestingly, for a fixed $\textit{De}$, this force varies strongly between the two limiting cases (i) $a \ll 1$, an infinitely wide channel, and (ii) $a \gg 1$, an infinitely short channel, implying a change in the polymer response. Furthermore, we observe a different trend (i) for a spanwise-varying channel, in which a peak is observed between the two limits, and (ii) for a spanwise-uniform channel, where the largest load value is for $a \ll 1$. When $a$ is O($1$), the viscoelastic response varies strongly and spanwise effects cannot be ignored.

Direct numerical simulations (DNS) are performed to investigate the dependence of the Prandtl number ($\textit{Pr}$) and radius ratio ($\eta =r_{i}/r_{o}$) on the asymmetry of the mean temperature radial profiles in turbulent Rayleigh–Bénard convection (RBC) within spherical shells. Unlike planar RBC, the temperature drop, and the thermal and viscous boundary layer thicknesses, at the inner and outer boundaries are not identical in spherical shells. These differences in the boundary layer properties in spherical RBC contribute to the observed asymmetry in the radial profiles of temperature and velocity. The asymmetry originates from the differences in curvature and gravity at the two boundaries, and in addition, is influenced by $\textit{Pr}$. To investigate the $\eta$ and $\textit{Pr}$ dependence of these asymmetries, we perform simulations of Oberbeck–Boussinesq convection for $\eta = 0.2,0.6$ and $0.1 \leqslant Pr \leqslant 50$, and for a range of Rayleigh numbers ($Ra$) varying between $5 \times 10^{6}$ and $5 \times 10^{7}$. The Prandtl numbers that we choose cover a broad range of geophysical relevance, from low-$\textit{Pr}$ regimes ($\textit{Pr}=0.1$) representative of gas giants such as Jupiter and Saturn, to high-$\textit{Pr}$ regimes characteristic of organic flows used in the convection experiments ($\textit{Pr}=50$). A centrally condensed mass, with the gravity profile $g \sim 1/r^{2}$, is employed in this study. Our results show that the asymmetry at smaller $\eta$ exhibits a stronger $\textit{Pr}$ dependence than at larger $\eta$. Various assumptions for quantifying this asymmetry are evaluated, revealing that different assumptions are valid in different $\textit{Pr}$ regimes. It is shown that the assumption of the equal characteristic plume separation at the inner and outer boundaries, as well as the assumption of the identical thermal fluctuation scales between the two boundary layers, is valid only for $0.2 \lesssim Pr \lesssim 1$. In contrast, assumptions based on the equivalency of the local thermal boundary layer Rayleigh numbers and laminar natural-convective boundary layers are validated at $\textit{Pr}=50$ for the explored parameter space. Furthermore, new assumptions based on the statistical analysis of the inter-plume islands are proposed for $\textit{Pr}=0.1$ and $50$, and these are validated against the DNS data. These findings provide insights into the $(Pr,\eta)$ dependence of asymmetry in spherical RBC, and offer a framework for studying similar systems in geophysical and astrophysical contexts.

Plumes generated from a point buoyant source are relevant to hydrothermal vents in lakes and oceans on and beyond Earth. They play a crucial role in determining heat and material transport and thereby local biospheres. In this study, we investigate the development of rotating point plumes in an unstratified environment using both theory and numerical simulations. We find that in a sufficiently large domain, point plumes cease to rise beyond a penetration height $h_{{f}}$, at which buoyancy flux from the heat source is leaked laterally to the ambient fluid. The height $h_{{f}}$ is found to scale with the rotational length scale $h_{ \!{ f}}\sim L_{ \!\textit{ rot}}^p\equiv ({F_0}/{f^3})^{{1}/{4}},$ where $F_0$ is the source buoyancy flux, and $f=2\varOmega$ is the Coriolis parameter ($\varOmega$ is the rotation rate). In a limited domain, the plume may reach the top boundary or merge with neighbouring plumes. Whether rotational effects dominate depends on how $L_{\textit{rot}}^{p}$ compares to the height of the domain $H$ and the distance between the plumes $L$. Four parameter regimes can therefore be identified, and are explored here through numerical simulation. Our study advances the understanding of hydrothermal plumes and heat/material transport, with applications ranging from subsurface lakes to oceans in icy worlds such as Snowball Earth, Europa and Enceladus.

We study aeolian saltation over an erodible bed at full transport capacity in a wind tunnel with a relatively thick boundary layer. Lagrangian tracking of size-selected spherical particles resolves their concentration, velocity and acceleration. The mean particle concentration follows an exponential profile, while the mean particle velocity exhibits a convex shape. In contrast to current assumptions, both quantities appear sensitive to the friction velocity. The distributions of horizontal accelerations are positively skewed, though they contain negative tails associated with particles travelling faster than the fluid. The mean wind velocity profiles, reconstructed down to millimetric distances from the bed using the particle equation of motion, have an approximately constant logarithmic slope and do not show a focal point. The aerodynamic drag force increases with distance from the wall and, for the upward moving particles, exceeds the gravity force already at a few particle diameters from the bed. The vertical drag component resists the motion of both upward and downward moving particles with a magnitude comparable to the lift force, which is much smaller than gravity but non-negligible. Coupling the assumption of ballistic vertical motion and the measured streamwise velocities, the mean trajectories are reconstructed and found to be strongly influenced by aerodynamic drag. This is also confirmed by the direct identification of trajectory apexes, and demonstrated over a wide range of friction velocities. Taken together, these results indicate that aerodynamic drag and lift may play a more significant role in the saltation process than presently recognized, being complementary rather than alternative to splash processes.

This study examines the dynamics of vortical interactions and their implications for mitigating thermoacoustic instability in a turbulent combustor. The regions of intense vortical interactions are identified as vortical communities in the network space of weighted directed vortical networks constructed from two-dimensional experimental velocity data. One can expect vortical interactions in the combustor to be strongest near the moment of vortex shedding, as the shed vortices gradually weaken due to dissipation while convecting downstream. However, we show that, during the state of thermoacoustic instability, there is a non-trivial consistent phase lag of approximately $52^\circ$ between the shedding of the coherent structures from the backward-facing step and the time instant when the vortical interactions attain their local maximum value. We explain this phase lag by investigating the correlation between acoustic pressure fluctuations, spatio-temporal dynamics of coherent structures and vortical interactions in the reaction field of the combustor. We also show the aperiodic variation of vortical interactions during the states of combustion noise and aperiodic epochs of intermittency. Furthermore, the spatio-temporal evolution of pairs of vortical communities with the maximum inter-community interactions provides insight into explaining the critical regions detected in the reaction field during the states of intermittency and thermoacoustic instability, also identified in previous studies. We further show that the most efficient suppression of thermoacoustic instability via air microjet injection is achieved when steady air jets are introduced to disrupt the maximum inter-community interactions present during the state of thermoacoustic instability.

This study experimentally investigates wake recovery mechanisms behind a floating wind turbine subjected to imposed fore-aft (surge) and side-to-side (sway) motions. Wind tunnel experiments with varying free-stream turbulence intensities ($\textit{TI}_{\infty } \in [1.1, 5.8]\,\%$) are presented. Rotor motion induces large-scale coherent structures – pulsating for surge and meandering for sway – whose development critically depends on the energy ratio between the incoming turbulence and the platform motion. The results provide direct evidence supporting the role of these structures in enhancing wake recovery, as previously speculated by Messmer, Peinke & Hölling (J. Fluid Mech., vol. 984, 2024, A66). These periodic structures significantly increase Reynolds shear stress gradients, particularly in the streamwise–lateral direction, which are key drivers of wake recovery. However, their influence diminishes with increasing $\textit{TI}_{\infty }$: higher background turbulence weakens the coherent flow patterns, reducing their contribution to recovery. Beyond a threshold turbulence level – determined by the energy, frequency and direction of motion – rotor-induced structures no longer contribute meaningfully to recovery, which becomes primarily driven by the free-stream turbulence. Finally, we show that the meandering structures generated by sway motion are more resilient in turbulent backgrounds than the pulsating modes from surge, making sway more effective for promoting enhanced wake recovery.

The crystallisation that occurs when a drop is in contact with a cold surface is a particularly challenging phenomenon to capture experimentally and describe theoretically. The situation of a liquid–liquid interface, where crystals appear on a mobile interface is scarcely studied although it provides a defect-free interface. In this paper, we quantify the dynamics of crystals appearing upon the impact of a drop on a cool liquid bath. We rationalise our observations with a model considering that crystals appear at a constant rate depending on the thermal shock on the expanding interface. This model provides dimensionless curves on the number and the surface area of crystals that we compare with our experimental measurements.

Vertically bounded, horizontally propagating internal waves may become unstable through triad resonant instability, in which two sibling waves in background noise draw energy from a parent internal tide. If the background stratification is uniform, then the condition for pure resonance between the parent and sibling wave frequencies and horizontal and vertical wavenumbers can be found semi-analytically from the roots of a polynomial expression. In non-uniform stratification, determining the frequencies and horizontal wavenumbers for which resonance occurs is less straightforward. We develop a theory for near-resonant excitation of a pair of sibling waves from a low-mode internal wave in which the proximity to pure resonance is characterised by the discrepancy between the forced sibling wave frequencies and the natural frequency of these modes. Knowing this discrepancy can be used methodically to determine pure resonance conditions. This inviscid theory is compared with numerical simulations of effectively inviscid waves. For comparison with laboratory experiments, the theory is adapted to include viscous effects both in the bulk of the fluid and at the side walls of the tank. We find that our theoretical predictions for frequencies and wavenumbers of the fastest growing sibling waves are generally consistent between theory, simulations and experiments, though theory overpredicts the growth rate observed in experiments. In all cases, the growth rate of sibling waves decreases with decreasing parent wave frequency, becoming negligibly small in experiments if the parent wave has frequency less than $\approx 0.7$ of the buoyancy frequency at the surface.

We simulate the formation of a condensate on a sphere, generated by an inverse energy cascade originating from a stochastic forcing at spherical harmonic wavenumber $ l_{\!f} \gg 1$. The condensate forms as two pairs of oppositely signed vortices lying on a great circle that is randomly rotating in three dimensions. The vortices are separated by $ 90^\circ$ and like signed vortices are located at opposite poles. We show that the configuration is the maximum energy solution to a Hamiltonian dynamical system with a single degree of freedom. An analysis in wavenumber space reveals that interactions between widely separated scales of motions dominate the formation process. For comparison, we also perform freely decaying simulations with random initial conditions and prescribed spectra. The late time solutions consist of four coherent vortices, similar to the solutions of the forced simulations. However, in the freely decaying simulations the vortex configuration is not stationary but exhibits periodic motions.

Flow-induced compaction of soft, elastically deformable porous media occurs in numerous industrial processes. A theoretical study of this problem, and its interplay with gravitational and mechanical compaction, is presented here in a one-dimensional configuration. First, it is shown that soft media can be categorised into two ‘types’, based on their compaction behaviour in the limit of large applied fluid pressure drop. This behaviour is controlled by the constitutive laws for effective pressure and permeability, which encode the rheology of the solid matrix, and can be linked to the well-known poroelastic diffusivity. Next, the interaction of gravitational and flow-induced compaction is explored, with the resultant asymmetry between upward and downward flow leading to distinct compaction behaviour. In particular, flow against gravity – upwards – must first relieve gravitational stresses before any bulk compaction of the medium can occur, so upward flow may result in compaction of some regions and decompaction of others, such that the overall depth remains fixed. Finally, the impact of a fixed mechanical load on the sample is considered: again, it is shown that flow must ‘undo’ this external load before any bulk compaction of the whole medium can occur in either flow direction. The interplay of these different compaction mechanisms is explored, and qualitative differences in these behaviours based on the ‘type’ of the medium are identified.

The non-uniform evaporation rate at the liquid–gas interface of binary droplets induces solutal Marangoni flows. In glycerol–water mixtures (positive Marangoni number, where the more volatile fluid has higher surface tension), these flows stabilise into steady patterns. Conversely, in water–ethanol mixtures (negative Marangoni number, where the less volatile fluid has higher surface tension), Marangoni instabilities emerge, producing seemingly chaotic flows. This behaviour arises from the opposing signs of the Marangoni number. Perturbations locally reducing surface tension at the interface drive Marangoni flows away from the perturbed region. Continuity of the fluid enforces a return flow, drawing fluid from the bulk towards the interface. In mixtures with a negative Marangoni number, preferential evaporation of the lower-surface-tension component leads to a higher concentration of the higher-surface-tension component at the interface as compared with the bulk. The return flow therefore creates a positive feedback loop, further reducing surface tension in the perturbed region and enhancing the instability. This study investigates bistable quasi-stationary solutions in evaporating binary droplets with negative Marangoni numbers (e.g. water–ethanol) and examines symmetry breaking across a range of Marangoni numbers and contact angles. Bistable domains exhibit hysteresis. Remarkably, flat droplets (small contact angles) show instabilities at much lower critical Marangoni numbers than droplets with larger contact angles. Our numerical simulations reveal that interactions between droplet height profiles and non-uniform evaporation rates trigger azimuthal Marangoni instabilities in flat droplets. This geometrically confined instability can even destabilise mixtures with positive Marangoni numbers, particularly for concave liquid–gas interfaces, as in wells. Finally, through a Lyapunov exponent analysis, we confirm the chaotic nature of flows in droplets with a negative Marangoni number. We emphasise that the numerical models are intentionally simplified to isolate and clarify the underlying mechanisms, rather than to quantitatively predict specific experimental outcomes; in particular, the model becomes increasingly limited in regimes of rapid evaporation.

Biologically inspired aero/hydrodynamics attracts considerable interest because of promising efficiency and manoeuvring capabilities. Yet, the influence that external perturbations, typical of realistic environments, can have over the flow physics and aerodynamic performance remains a scarcely investigated issue. In this work, we focus on the impact of free stream turbulence (FST) on the aerodynamics of a flapping wing with a prescribed (heaving and pitching) motion at a chord-based Reynolds number of 1000. The problem is tackled by means of direct numerical simulations using an immersed boundary method and a synthetic turbulence generator. The effect of two key parameters, i.e. the turbulence intensity and integral length scale of FST, is described by characterising the phase- and spanwise-averaged flows and aerodynamic coefficients. In particular, we show how FST effectively enhances the dissipation of the vortices generated by the flapping wing once they are sufficiently downstream of the leading edge. The net (i.e. time-averaged) thrust is found to be marginally sensitive to the presence of FST, whereas the characteristic aerodynamic fluctuations appear to scale linearly with the turbulence intensity and sublinearly with the integral length scale. Moreover, we reveal a simple mechanism where FST triggers the leading-edge vortex breakup, which in turns provides the main source of aerodynamic disturbances experienced by the wing. Finally, we show how the frequency spectra of the aerodynamic fluctuations are governed by the characteristic time scales involved in the problem.

Interactions between shock waves and gas bubbles in a liquid can lead to bubble collapse and high-speed liquid jet formation, relevant to biomedical applications such as shock wave lithotripsy and targeted drug delivery. This study reveals a complex interplay between acceleration-induced instabilities that drive jet formation and radial accelerations causing overall bubble collapse under shock wave pressure. Using high-speed synchrotron X-ray phase contrast imaging, the dynamics of micrometre-sized air bubbles interacting with laser-induced underwater shock waves are visualised. These images offer full optical access to phase discontinuities along the X-ray path, including jet formation, its propagation inside the bubble, and penetration through the distal side. Jet formation from laser-induced shock waves is suggested to be an acceleration-driven process. A model predicting jet speed based on the perturbation growth rate of a single-mode Richtmyer–Meshkov instability shows good agreement with experimental data, despite uncertainties in the jet-driving mechanisms. The jet initially follows a linear growth phase, transitioning into a nonlinear regime as it evolves. To capture this transition, a heuristic model bridging the linear and nonlinear growth phases is introduced, also approximating jet shape as a single-mode instability, again matching experimental observations. Upon piercing the distal bubble surface, jets can entrain gas and form a toroidal secondary bubble. Linear scaling laws are identified for the pinch-off time and volume of the ejected bubble relative to the jet’s Weber number, characterising the balance of inertia and surface tension. At low speeds, jets destabilise due to capillary effects, resulting in ligament pinch-off.