Wakes and the dynamic interactions of multiple wakes have been a focal point of numerous research endeavours. Traditionally, wake interaction studies have focused on wakes produced by similar bodies. In contrast, the present study positions a non-shedding porous disc adjacent to periodically shedding solid discs of varying diameters and dimensional shedding frequencies. Using hot-wire measurements, we explore the intriguing interaction between these wakes. Remarkably, our findings reveal that the wake of the non-shedding disc acquires oscillations from the wake of the shedding disc, irrespective of their distinct frequencies. We demonstrate high receptivity of the porous disc’s wake and connect our findings to real-life applications.

In this paper, we showcase how flow obstruction by a deformable object can lead to symmetry breaking in curved domains subject to angular acceleration. Our analysis is motivated by the deflection of the cupula, a soft tissue located in the inner ear that is used to perceive rotational motion as part of the vestibular system. The cupula is understood to block the rotation-induced flow in a toroidal region with the flow-induced deformation of the cupula used by the brain to infer motion. By asymptotically solving the governing equations for this flow, we characterise regimes for which the sensory system is sensitive to either angular velocity or angular acceleration. Moreover, we show the fluid flow is not symmetric in the latter case. Finally, we extend our analysis of symmetry breaking to understand the formation of vortical flow in cavernous regions within channels. We discuss the implications of our results for the sensing of rotation by mammals.

Vertical thermal convection exhibits weak turbulence and spatio-temporally chaotic behaviour. For this configuration, we report seven new equilibria and 26 new periodic orbits. These orbits, together with four previously studied in Zheng et al. (J. Fluid Mech., 2024b, vol. 1000, p. A29) bring the number of periodic-orbit branches computed so far to 30, all solutions to the fully nonlinear three-dimensional Navier–Stokes equations. These new and unstable invariant solutions capture intricate spatio-temporal flow patterns including straight, oblique, wavy, skewed and distorted convection rolls, as well as bursts and defects. These interesting and important fluid mechanical processes in a small flow unit are shown to also appear locally and instantaneously in a chaotic simulation in a large domain. Most of the solution branches show rich spatial and/or spatio-temporal symmetries. The bifurcation-theoretic organisation of these solutions is discussed; the bifurcation scenarios include Hopf, pitchfork, saddle-node, period-doubling, period-halving, global homoclinic and heteroclinic bifurcations, as well as isolas. Furthermore, these orbits are shown to be able to reconstruct statistically the core part of the attractor, so that these results may contribute to a quantitative description of transitional fluid turbulence using periodic orbit theory.

Deformable microchannels emulate a key characteristic of soft biological systems and flexible engineering devices: the flow-induced deformation of the conduit due to slow viscous flow within. Elucidating the two-way coupling between oscillatory flow and deformation of a three-dimensional (3-D) rectangular channel is crucial for designing lab-on-a-chip and organ-on-a-chip microsystems and eventually understanding flow–structure instabilities that can enhance mixing and transport. To this end, we determine the axial variations of the primary flow, pressure and deformation for Newtonian fluids in the canonical geometry of a slender (long) and shallow (wide) 3-D rectangular channel with a deformable top wall under the assumption of weak compliance and without restriction on the oscillation frequency (i.e. on the Womersley number). Unlike rigid conduits, the pressure distribution is not linear with the axial coordinate. To validate this prediction, we design a polydimethylsiloxane-based experimental platform with a speaker-based flow-generation apparatus and a pressure acquisition system with multiple ports along the axial length of the channel. The experimental measurements show good agreement with the predicted pressure profiles across a wide range of the key dimensionless quantities: the Womersley number, the compliance number and the elastoviscous number. Finally, we explore how the nonlinear flow–deformation coupling leads to self-induced streaming (rectification of the oscillatory flow). Following Zhang and Rallabandi (J. Fluid Mech., vol. 996, 2024, p. A16), we develop a theory for the cycle-averaged pressure based on the primary problem’s solution, and we validate the predictions for the axial distribution of the streaming pressure against the experimental measurements.

In the standard picture of fully developed turbulence, highly intermittent hydrodynamic fields are nonlinearly coupled across scales, where local energy cascades from large scales into dissipative vortices and large density gradients. Microscopically, however, constituent fluid molecules are in constant thermal (Brownian) motion, but the role of molecular fluctuations in large-scale turbulence is largely unknown, and with rare exceptions, it has historically been considered irrelevant at scales larger than the molecular mean free path. Recent theoretical and computational investigations have shown that molecular fluctuations can impact energy cascade at Kolmogorov length scales. Here, we show that molecular fluctuations not only modify energy spectrum at wavelengths larger than the Kolmogorov length in compressible turbulence, but also significantly inhibit spatio-temporal intermittency across the entire dissipation range. Using large-scale direct numerical simulations of computational fluctuating hydrodynamics, we demonstrate that the extreme intermittency characteristic of turbulence models is replaced by nearly Gaussian statistics in the dissipation range. These results demonstrate that the compressible Navier–Stokes equations should be augmented with molecular fluctuations to accurately predict turbulence statistics across the dissipation range. Our findings have significant consequences for turbulence modelling in applications such as astrophysics, reactive flows and hypersonic aerodynamics, where dissipation-range turbulence is approximated by closure models.

We present experiments of settling and dissolving sugar grains continuously sieved above a water tank with varying grain size and mass flux. Through drag and dissolution, grains force a downward flow whose dynamics are analysed in a laser sheet through particle image velocimetry and the use of home-made fluorescent sugar to track the negatively buoyant sugary water. We reveal different regimes, mostly controlled by the grain size, from a particle-constrained laminar flow at large grain size, to a turbulent plume with an effectively fluid-like behaviour when grains are small. The transitions between regimes are predicted from dimensionless numbers quantifying fluid–particle coupling, collective effects between grains and the possible onset of a Rayleigh–Taylor instability at the source. When a quasi-steady regime is reached, all grains dissolve above a finite depth, below which the flow is exclusively driven by dissolved sugar. We derive simple idealised models based on the source properties that predict the depth of this dissolution layer as well as the characteristic flow velocity.

The Boltzmann kinetic equation is considered to compute the transport coefficients associated with the mass flux of intruders in a granular gas. Intruders and granular gas are immersed in a gas of elastic hard spheres (molecular gas). We assume that the granular particles are sufficiently rarefied so that the state of the molecular gas is not affected by the presence of the granular gas. Thus, the gas of elastic hard spheres can be considered as a thermostat (or bath) at a fixed temperature $T_g$. In the absence of spatial gradients, the system achieves a steady state where the temperature of the granular gas $T$ differs from that of the intruders $T_0$ (energy non-equipartition). Approximate theoretical predictions for the temperature ratio $T_0/T_g$ and the kurtosis $c_0$ associated with the intruders compare very well with Monte Carlo simulations for conditions of practical interest. For states close to the steady homogeneous state, the Boltzmann equation for the intruders is solved by means of the Chapman–Enskog method to first order in the spatial gradients. As expected, the diffusion transport coefficients are given in terms of the solutions of a set of coupled linear integral equations which are approximately solved by considering the first Sonine approximation. In dimensionless form, the transport coefficients are nonlinear functions of the mass and diameter ratios, the coefficients of restitution and the (reduced) bath temperature. Interestingly, previous results derived from a suspension model based on an effective fluid–solid interaction force are recovered when $m/m_g\to \infty$ and $m_0/m_g\to \infty$, where $m$, $m_0$ and $m_g$ are the masses of the granular particles, intruders and molecular gas particles, respectively. Finally, as an application of our results, thermal diffusion segregation is exhaustively analysed.

A spherical cap, lined internally with a surfactant-laden liquid film, is studied numerically as a model of lung alveoli. Large-amplitude oscillations are considered (deep breathing), which may lead to collapse of the surfactant monolayer during compression, with formation of a sub-surface reservoir that replenishes the monolayer during re-expansion. Independent conservation equations are satisfied for the monolayer and the total surface concentration of surfactant and a novel kinetic expression is introduced to model the two-way internal transport with the reservoir. Marangoni stresses, which drive shearing flow, are not significantly hindered by the collapse of the monolayer, unless the latter is singularly stiff. However, volumetric flow rate and wall shear stress exhibit abrupt changes with monolayer collapse, mainly because of the strong modification of capillary stresses. These changes induce complex temporal variability in the epithelial shear, a condition known to stimulate enhanced surfactant secretion. The effect may counterbalance the predicted increase with amplitude in surfactant drift from the alveolar opening, thereby contributing to homeostasis. Nano-particles deposited on the liquid layer are slowly transported by the flow towards the alveolar rim, with exit half-time in order-of-magnitude agreement with in vivo data. Thus, Marangoni stresses are proposed as a key mechanism of alveolar clearance. Both particle displacement speed and surfactant drift from the alveoli are found to vary with solubility, with the former increasing monotonically and the latter exhibiting maximum at intermediate solubilities.

The low Reynolds number solution of the wind–wave interaction problem is found in Cimarelli et al. (2023 J. Fluid Mech. vol. 956, A13), to be characterised by a skewed pattern of small-elevation waves on the bottom of a turbulent wind where drag reduction is caused by a wave-induced Stokes sublayer. The inhomogeneous, anisotropic and multiscale phenomena at the basis of this interesting solution are analysed here by means of the generalised Kolmogorov equation. It is found that the large and coherent structures populating the wind are the result of an upward shift of the self-sustaining production mechanisms of turbulence and of intense reverse energy cascade phenomena. The upward shift of production and the intensification of the reverse cascade are recognised to be the result of a periodically distributed pumping of scale energy induced by the pressure field associated with the wave-induced Stokes sublayer. The low dissipative nature of the wind–wave interface region is also investigated and is found to be related to a layering effect generated by the simultaneous presence of wave-induced pressure fluctuations and of wind-induced velocity fluctuations that interact with each other in an incoherent manner. Finally, the theoretical framework provided by the generalised Kolmogorov equation is also used to rigorously define two relevant cross-over scales for the filtering formalism, the shear scale identifying the energy-containing motion and the split energy cascade scale identifying the cross-over between forward and backward cascades. Well-defined quantitative criteria for the definition of spatial resolution and for the selection of turbulence closures in coarse-grained approaches to the wind–wave problem are provided.

We present a new solution to the nonlinear shallow water equations (NSWEs) and show that it accurately predicts the swash flow due to obliquely approaching bores in large-scale wave basin experiments. The solution is based on an application of Snell’s law of refraction in settings where the bore approach angle $\theta$ is small. We therefore use the weakly two-dimensional NSWEs (Ryrie 1983 J. Fluid Mech. 129, 193), where the cross-shore dynamics are independent of, and act as a forcing to, the alongshore dynamics. Using a known solution to the cross-shore dynamics (Antuono 2010 J. Fluid Mech. 658, 166), we solve for the alongshore flow using the method of characteristics and show that it differs from previous solutions. Since the cross-shore solution assumes a constant forward-moving characteristic variable, $\alpha$, we call our solution the ‘small-$\theta$, constant-$\alpha$’ solution. We test our solution in large-scale experiments with data from 16 wave cases, including both normally and obliquely incident waves generated using the wall reflection method. We measure water depths and fluid velocities using in situ sensors within the surf and swash zones, and track shoreline motion using quantitative imaging. The data show that the basic assumptions of the theory (Snell’s law of refraction and constant-$\alpha$) are satisfied and that our solution accurately predicts the swash flow. In particular, the data agrees well with our expression for the time-averaged alongshore velocity, which is expected to improve predictions of alongshore transport at coastlines.

We investigate Lighthill’s proposed turbulent mechanism for near-wall concentration of spanwise vorticity by calculating mean flows conditioned on motion away from or toward the wall in an (friction Reynolds number) ${\textit{Re}}_\tau =1000$ database of plane-parallel channel flow. Our results corroborate Lighthill’s proposal throughout the entire logarithmic layer, but extended by counter-flows that help explain anti-correlation of vorticity transport by advection and by stretching/tilting. We present evidence also for Lighthill’s hypothesis that the vorticity transport in the log layer is a ‘cascade process’ through a scale hierarchy of eddies, with intense competition between transport outward from and inward to the wall. Townsend’s model of attached eddies of hairpin-vortex type accounts for half of the vorticity cascade, whereas we identify necklace type or ’shawl vortices’ that envelop turbulent sweeps as supplying the other half.

Surface roughness of fairly small (micron-sized) height is known to influence significantly three-dimensional boundary-layer transition. In this paper, we investigate this sensitive effect from the viewpoint that roughness alters the base flow thereby inducing new instabilities. We consider distributed roughness in the form of a wavy wall with its height being taken to be of $\mathit{O} (R^{-1/3 } \delta ^{\ast })$, where the Reynolds number $R$ is defined using the local boundary-layer thickness $\delta ^{\ast }$. Despite having a height much smaller than $\delta ^{\ast }$, the roughness is high enough to induce nonlinear responses. The roughness-distorted boundary-layer flow is characterised by a wall layer (WL) – a thin layer adjacent to the surface – the main layer and a critical layer (CL) – the vicinity of a special position at which a singularity of the Rayleigh equation occurs. The widths of both the WL and CL are of $\mathit{O} (R^{-1/3} \delta ^{\ast })$. Surface roughness alters the base flow significantly, leading to $\mathit{O} (1)$ vorticity distortions in these layers. We show for the first time that the nonlinearly distorted flows in these layers support small-scale local instabilities due to the roughness-induced $\mathit{O} (1)$ vorticities. Two types of modes, CL and WL modes, are identified. The CL modes have short wavelengths and high frequencies, with the spatial and temporal instabilities being governed by essentially the same equation. Thus, we focus on the former, which can be formulated as a linear generalised eigenvalue problem. The WL modes have short wavelengths but $\mathit{O} (1)$ frequencies. The temporal WL mode is governed by a linear eigenvalue problem similar to that for the CL modes, while the spatial WL mode is described by a nonlinear eigenvalue problem. The onset of these small-scale fluctuations could form a crucial step in the transition to turbulence.

We explore the fundamental flow structure of temporally evolving inclined gravity currents with direct numerical simulations. A velocity maximum naturally divides the current into inner and outer shear layers, which are weakly coupled by momentum and buoyancy exchanges on time scales that are much longer than the typical time scale characterising either layer. The outer layer evolves to a self-similar state and can be described by theory developed for a current on a free-slip slope (Van Reeuwijk et al. 2019, J. Fluid Mech., vol. 873, pp. 786–815) when expressed in terms of outer-layer properties. The inner layer evolves to a quasi-steady state and is essentially unstratified for shallow slopes, with flow statistics that are virtually indistinguishable from fully developed open channel flow. We present the classic buoyancy–drag force balance proposed by Ellison & Turner (1959, J. Fluid Mech., vol. 6, pp. 423–448) for each layer, and find that buoyancy forces in the outer layer balance entrainment drag, while buoyancy forces in the inner layer balance wall friction drag. Using scaling laws within each layer and a matching condition at the velocity maximum, the entire flow system can be solved as a function of the slope angle, in good agreement with the simulation data. We further derive an entrainment law from the solution, which exhibits relatively high accuracy across a wide range of Richardson numbers, and provides new insights into the long runout of oceanographic gravity currents on mild slopes.

Linear-stability modelling suggests that all sufficiently large riblets promote maximally growing spanwise rollers (García-Mayoral & Jiménez 2011 J. Fluid Mech. vol. 678, 317–347), yet direct numerical simulations (DNS) have shown that this is not the case (Endrikat et al. 2021 J. Fluid Mech. vol. 913, A37) some riblet shapes do not form spanwise rollers at all. Thus, the drag-reduction breakdown across all riblet shapes cannot be solely attributed to maximally growing spanwise rollers, prompting a reappraisal of the modelling. In this paper, comparing DNS data with riblet-resolving linear-stability predictions shows that the spanwise rollers are actually marginal modes, not maximally growing instabilities. This riblet-resolved linear analysis also predicts that not all riblet shapes promote spanwise rollers, in agreement with DNS, and unlike earlier linear-stability modelling, which relied on a one-dimensional (1-D) mean flow and on an over-simplified effective wall-admittance boundary condition. These riblet-resolved calculations further inform how to capture the effect of the riblet shape in a 1D model. Once captured, predictions with an effective boundary condition match riblet-resolved results, but still do not indicate what features of the riblet geometry promote the roller instability. Thus, the wall admittance is measured near the riblet crests, in both the riblet-resolved linear analysis and DNS, to show that the in-groove dynamics is dominated by a balance between the overlying pressure and unsteady inertia, and not viscous diffusion, as previously assumed. This pressure–unsteady-inertia balance sets the linear scaling of the wall admittance with riblet size, as observed in DNS, and is a key factor in setting the streamwise wavelength of the spanwise rollers. Furthermore, modelling this pressure–unsteady-inertia balance in the wall admittance reveals the role of riblet slenderness in promoting spanwise rollers, which provides the missing link in previous correlations between the riblet geometry and the presence or lack of rollers.

Hysteresis in the transition between regular reflection (RR) and Mach reflection (MR) has been predicted theoretically and numerically for decades, yet successful experimental demonstrations have remained limited to wedge-angle-variation-induced hysteresis. This work presents the first successful experimental demonstration of Mach-number-variation-induced hysteresis. Utilising a newly developed continuously variable Mach 5–8 wind-tunnel nozzle, Mach-sweep experiments were conducted on a pair of wedges at three different angles ($25^{\circ }$, $27^{\circ }$ and $28^{\circ }$). A stable RR was first established at Mach 7 within the dual-solution domain for each angle, and then the Mach number was decreased to 5. For the $27^{\circ }$ and $28^{\circ }$ cases, transition from RR to MR was observed at Mach 5.3 and 5.9, respectively, during the downward Mach sweep, and the MR state persisted throughout the upward sweep back to Mach 7. During the $25^{\circ }$ case, a stable RR was maintained throughout the entire Mach sweep, prompting further experiments into the effect of free-stream disturbances on the stability of the RR state. Preliminary results revealed a free-stream-disturbance-induced hysteresis and that the RR state is metastable with potential stochastic behaviour.

Mixing and heat transfer rates are typically enhanced in high-pressure transcritical turbulent flow regimes. This is largely due to the rapid variation of thermophysical properties near the pseudo-boiling region, which can significantly amplify velocity fluctuations and promote flow destabilisation. The stability conditions are influenced by the presence of baroclinic torque, primarily driven by steep, localised density gradients across the pseudo-boiling line; an effect intensified by differentially heated wall boundaries. As a result, enstrophy levels increase compared with equivalent low-pressure systems, and flow dynamics diverge from those of classical wall-bounded turbulence. In this study the dynamic equilibrium of these instabilities is systematically analysed using linear stability theory. It is shown that under isothermal wall transcritical conditions, the nonlinear thermodynamics near the pseudo-boiling region favour destabilisation more readily than in subcritical or supercritical states; though this typically requires high-Mach-number regimes. The destabilisation is further intensified in non-isothermal wall configurations, even at low Brinkman and significantly low Mach numbers. In particular, the sensitivity of neutral curves to Brinkman number variations, along with the modal and non-modal perturbation profiles of hydrodynamic and thermodynamic modes, offer preliminary insight into the conditions driving early destabilisation. Notably, a non-isothermal set-up (where walls are held at different temperatures) is found to be a necessary condition for triggering destabilisation in low-Mach, low-Reynolds-number regimes. For the same Brinkman number, such configurations accelerate destabilisation and enhance algebraic growth compared with isothermal wall cases. As a consequence, high-pressure transcritical flows exhibit increased kinetic energy budgets, driven by elevated production rates and reduced viscous dissipation.

Unsteady, non-equilibrium stagnation-point boundary layers are analysed using a newly developed engineering correlation that links the magnitude of atomic mass fraction fluctuations in the free stream to their corresponding values at the wall. Analytical solutions to the species conservation equation alongside empirical correlations are used to derive a generalised correlation, taking into account diffusive transport, finite-rate reactions and arbitrary surface catalycity. Fully coupled transient numerical simulations are performed to assess the accuracy of the approximate theory, resulting in an agreement of ${\lt } 12.5$ %. Four scaling parameters are identified: the Damkoehler number, and ratios of boundary-layer thickness, Stokes-layer thickness and wall catalycity. The magnitude of atomic-mass-fraction fluctuations at the wall is highest for frozen boundary layers and non-catalytic materials. Typical experimental operating conditions of high-enthalpy facilities are used to assess the relevance of oscillating mass fractions on gas–surface interaction. It is found that wall conditions can be severely affected by unsteadiness, leading to additional uncertainties in the interpretation of test results. The derived theory provides a first simple analytical framework, enabling improved analysis of transient high-enthalpy experiments and motivates future studies employing higher-fidelity models in order to remove uncertainty in the determination of gas–surface interaction rates.

Supersonic turbulent channels subjected to sudden spanwise acceleration at initial friction Reynolds numbers of approximately 500 and different Mach numbers are studied through direct numerical simulations. The response to the spanwise acceleration creates a transient period where the flow exhibits three-dimensionality in the mean statistics. This enables a detailed study of the thermal transport and development of velocity transformations and Reynolds analogies for compressible turbulent flows in swept-like conditions. Extensions of velocity transformations to three-dimensional (3-D) flows demonstrate near-wall self-similarity of the velocity, providing evidence for Morkovin’s hypothesis in non-equilibrium conditions. A similarity solution for the spanwise velocity, valid during the initial transient, is also presented. During the transient, both the thermal fluctuations and turbulent kinetic energy (TKE) decrease, consistent with previous observations in incompressible flows (Lozano-Durán et al. 2020 J. Fluid Mech. 883, A20, Moin et al. 1990 Phys. Fluids A: Fluid Dyn. 2, 1846–1853). For sufficiently strong spanwise acceleration, $Q_{3}$ $(+T',+v')$ and $Q_{1}$ $(-T',-v')$ events become more significant than sweep and ejections across the channel, creating changes in sign in the velocity–temperature covariances. The temporal evolution of the orientation and sizes of the TKE and temperature-carrying structures is quantified through structure identification and spectra. Finally, the generalized Reynolds analogy (Zhang et al. 2012 Phys. Rev. Lett. 109, 054502) is derived for a transient 3-D flow, allowing predictions of the mean temperature from the velocity.

Amphibious unmanned vehicles promise next-generation water-based missions by eliminating the need for multiple vehicles to traverse water and air separately. Existing research-grade quadrotors can navigate in water and air and cross the water–air boundary, but it remains unclear how their transition is affected by rotor kinematics and geometry. We present here experimental results from isolated small rotors (diameters $\sim 10\,\mathrm{cm}$) dynamically transitioning from water to air. We discovered that rotors experience an abrupt change in frequency, lift and torque before reaching the interface, and the change is linked to the surface depression caused by a free surface vortex. We explored how the surface dynamics are affected by advance ratio, rotor diameter, number of rotor blades and input throttle. Free surface vortices above rotating objects have been studied in the context of unbaffled stirred tanks, but not in the field of small amphibious rotorcraft. We show that existing free surface vortex models can be adapted to explain water-to-air rotor performance. A better understanding of water–air rotor transitions helps to (i) assess the amphibious capability of existing aerial rotors, and (ii) suggest efficient water–air transition strategies for next-generation amphibious vehicles.

In 1910, Cunningham developed a heuristic expression to predict the drag on a slow-moving spherical particle in a gas; a drag that deviates from Stokes’ law when the particle’s size is comparable to the gas’s mean free path. More than a decade later, Millikan proposed a physical argument for correcting Cunningham’s work: the resulting expression is known today as the ‘Cunningham correction factor’. Despite his contribution, Millikan missed a simpler way to correct Cunningham’s expression, one that would have preserved its generality. In this article, this new, simpler form of the Cunningham correction factor is expanded to provide a predictive heuristic for non-spherical particles through the definition of a ‘correction tensor’. Its accuracy is tested against experiments and kinetic theory for the sphere, and solutions to the Boltzmann equation for a range of spheroids and an infinitesimally thin circular disc.