A series of new laboratory experiments explore the transient flow in an enclosed space of depth $H$, which is subject to an upward displacement ventilation flux, $Q_V$, and which contains a localised heat source of buoyancy flux $F_s$, when the buoyancy of the ventilation air changes by $\Delta g'$. Initially, the plume, produced by the heat source, entrains the ventilation air, leading to a two-layer stratification which depends on the dimensionless strength of convection, $\mu \propto F_s^{1/3}H^{5/3}/Q_V$. When the buoyancy of the ventilation air decreases, $\Delta g' \lt 0$, a new layer of relatively dense fluid grows next to the floor. The fluid entrained by the plume from this new layer causes the plume to intrude between the original upper and lower layers. For a sufficiently large decrease in buoyancy, $|\Delta g' Q_V /F_s| \gt 1$, then as the new lower layer grows, the plume eventually becomes negatively buoyant relative to the original lower layer and intrudes between the new lowest layer and the original lower layer. When the buoyancy of the air supply increases, $\Delta g'\gt 0$, it mixes with the fluid in the original lower layer. If the increase in buoyancy is sufficient, $\Delta g' Q_V/F_s\gt 1$, then the new supply air eventually also mixes with the original upper layer. In each case, a new two-layer stratification becomes re-established. We propose new models for the evolution of the transient flow, assuming that the buoyancy profile can be approximated by a staircase of well-mixed layers. These layers are emptied or filled through the action of the plume and ventilation. We find that the model predictions are consistent with our new experiments in each of the four regimes. We conclude by discussing the implications of these transient flows for thermal comfort and the mixing of contaminants into the occupied lower region of the space.

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.

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.

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.

Addition of polymers modifies a turbulent flow in a manner that depends non-trivially on the interplay of fluid inertia, quantified by the Reynolds number $\textit{Re}$, and the elasticity of the dissolved polymers, given by the Deborah number $\textit{De}$. We use direct numerical simulations to study polymeric flows at different $\textit{Re}$ and $\textit{De}$ numbers, and uncover various features of their dynamics. Polymeric flows exhibit a non-unique scaling of the energy spectrum that is a function of $\textit{Re}$ and $\textit{De}$, owing to different dominant contributions to the total energy flux across scales, with the weakening of fluid nonlinearity with decreasing $\textit{Re}$ also leading to the reduction of the polymeric scaling range. This behaviour is also manifested in the real space scaling of structure functions. We also shed light on how the addition of polymers results in slowing down the fluid nonlinear cascade resulting in a depleted flux, as velocity fluctuations with less energy persist for longer times in polymeric flows, especially at intermediate $\textit{Re}$ numbers. These velocity fluctuations exhibit intermittent, large deviations similar to that in a Newtonian flow at large $\textit{Re}$, but differ more and more as $\textit{Re}$ becomes smaller. This observation is further supported by the statistics of fluid energy dissipation in polymeric flows, whose distributions collapse on to the Newtonian at large $\textit{Re}$, but increasingly differ from it as $\textit{Re}$ decreases. We also show that polymer dissipation is significantly less intermittent compared with fluid dissipation, and even less so when elasticity becomes large. Polymers, on an average, dissipate more energy when they are stretched more, which happens in extensional regions of the flow. However, owing to vortex stretching, regions with large rotation rates also correlate with large polymer extensions, albeit to a relatively less degree than extensional regions.

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.

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.

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.

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.

We present a theoretical approach that derives the wavenumber $k^{-1}$ spectral scaling in turbulent velocity spectra using random field theory without assuming specific eddy correlation forms or Kolmogorov’s inertial-range scaling. We argue for the mechanism by Nikora (1999 Phys. Rev. Lett. 83 (4), 734), modelling turbulence as a superposition of eddy clusters with eddy numbers inversely proportional to their characteristic length scale. Statistical mixing of integral scales within these clusters naturally yields the $k^{-1}$ scaling as an intermediate asymptotic regime. Building on the spectrum modelling introduced in Jetti et al. (2025b Z. Angew. Math. Physik. 74 (3), 123), we develop and apply an integral formulation of the general velocity spectrum that reproduces the $k^{-1}$ regime observed in field spectra, thereby bridging theoretical derivation and empirical observations. The model is validated using wind data at a coastal site, and tidal data in a riverine environment where the –1 scaling persists beyond the surface layer logarithmic region. The results confirm the robustness of the model at various flow conditions, offering new insights into the spectral energy distribution in geophysical and engineering flows.

Interactions between hyperelastic bio-membranes and fluid play a crucial role in the flight (or swimming) motion of many creatures, such as bats, flying squirrels and lemurs. Bio-membranes are characterised by high stretchability and micro-bending stiffness, leading to unique fluid–solid coupling properties (Mathai et al., 2023, Phys. Rev. Lett., vol. 131, 114003). This study presents a high-fidelity numerical exploration of the hyperelastic characteristics of a pitching foil inspired by bio-membranes in fluid within a low Reynolds number regime. The focus is on the effect of foil compliance on its self-propulsion performance, mimicking natural propulsion mechanisms, with the foil free to move in the horizontal direction. We find that with certain compliance, the foil may experience a velocity crisis, meaning that its propulsive capability is completely lost. This phenomenon is caused by the loss of beat speed when the foil’s passive deformation is out of phase with the pitching motion. By contrast, the two motions can be in phase at proper compliance, leading to an increased beat speed. This will significantly enhance propulsive velocity up to $33\,\%$ compared with the rigid case. The results demonstrate the feasibility of compliance tuning to circumvent the velocity crisis and improve the propulsive speed, which are helpful in the design of micro aerial robots using biomimetic membranes.

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.

This paper theoretically introduces a new architecture for pumping leaky-dielectric fluids. For two such fluids layered in a channel, the mechanism utilises Maxwell stresses on fluid interfaces (referred to as menisci) induced by a periodic array of electrode pairs inserted between the two fluids and separated by the menisci. The electrode pairs are asymmetrically spaced and held at different potentials, generating an electric field with variation along the menisci. To induce surface charge accumulation, an electric field (and thus current flow) is also imposed in the direction normal to the menisci, using flat upper and lower electrodes, one in each fluid. The existence of both normal and tangential electric fields gives rise to Maxwell stresses on each meniscus, driving the flow in opposite directions on adjacent menisci. If the two menisci are the same length, then a vortex array is generated that results in no net flow; however, if the spacing is asymmetric, then the longer meniscus dominates, causing a net pumping in one direction. The pumping direction can be controlled by the (four) potentials of the electrodes, and the electrical properties of the two fluids. In the analysis, an asymptotic approximation is made that the interfacial electrode period is small compared to the fluid layer thicknesses, which reduces the analytical difficulty to an inner region close to the menisci. Closed-form solutions are presented for the potentials, velocity field and resulting pumping speed, for which maximum values are estimated, with reference to the electrical power required and feasibility.

Gamero-Castaño and colleagues have reported that a large number of calculated shapes for electrified cone jets collapse into a nearly universal geometry when scaled with a characteristic length $R_G$ previously introduced by Gañán-Calvo et al. (J. Aerosol Sci., vol. 25, 1994, pp. 1121–1142). The theoretical reasons for that unexpected success were, however, unclear. Recently, Pérez-Lorenzo & Fernández de la Mora (J. Fluid Mech., vol. 931, 2022, A4) have noted that a slightly different length scale $L_j$ is suggested by the asymptotic jet structure inferred by Gañán-Calvo (Phys. Rev. Lett., vol. 79, 1997, pp. 217–220) from energy conservation and the hypothesis that the asymptotic electric field is that given by Taylor’s static model. This article aims to identify which of these two scales best collapses calculated cone-jet structures, and whether there is an alternative superior one. The characteristic lengths are tested against a large set of numerical solutions of a cone-jet model. The effectiveness of each scaling is determined through analyses based on the standard deviation of the numerical solutions. Despite the slight difference between $R_G$ and $L_j$, this analysis clearly identifies $L_j$ as the most accurate scaling for all cone-jet parameters tested. Differentiating between both scales would not have been possible with experimental measurements, but requires the use of high-fidelity numerical solutions. Surprisingly, the success of $L_j$ is not limited to the jet region, but extends to the cone and the neck. These findings provide a slightly superior scaling enjoying a considerably firmer theoretical basis.

We experimentally investigate the rotational dynamics of neutrally buoyant flat bodies of revolution (spheroids, disks and rings with different cross-sectional shapes) in shear flows. In the Stokes regime, the axis of revolution of these rigid particles moves in one of a family of closed periodic Jeffery orbits. Inertia is able to lift the orbit degeneracy and induces drift among several rotations towards limiting stable orbits. Furthermore, permanent alignment can be achieved for disks and rings with triangular cross-sectional shapes, provided the inertia is sufficiently high. The bifurcations between the different dynamics are compared with those predicted by small-inertia asymptotic theories and numerical simulations.

Large-scale spanwise motions in shock wave–turbulent boundary-layer interactions over a $ 25^{\circ }$ compression ramp at Mach 2.95 are investigated using large-eddy simulations. Spectral proper orthogonal decomposition (SPOD) identifies coherent structures characterised by low-frequency features and a large-scale spanwise wavelength of $ O(15\delta _{0})$, where $ \delta _{0}$ is the incoming boundary-layer thickness. The dominant frequency is at least one order of magnitude lower than that of the shock motions. These large-scale spanwise structures are excited near the shock foot and are sustained along the separation shock. Global stability analysis (GSA) is then employed to investigate the potential mechanisms driving these structures. The GSA identifies a stationary three-dimensional (3-D) mode at a wavelength of $ 15\delta _{0}$ with a similar perturbation field, particularly near the separation shock. Good agreement is achieved between the leading SPOD mode and the 3-D GSA mode both qualitatively and quantitatively, which indicates that global instability is primarily responsible for the large-scale spanwise structures surrounding the shock. The reconstructed turbulent separation bubble (TSB) using the 3-D global mode manifests as spanwise undulations, which directly induce the spanwise rippling of the separation shock. Furthermore, the coupled TSB motions in the streamwise and spanwise directions are examined. The TSB oscillates in the streamwise direction while simultaneously exhibiting spanwise undulations. The filtered wall-pressure signals indicate the dominant role of the streamwise motions.

Fingering instabilities readily occur if a less viscous fluid displaces a more viscous fluid in a narrow gap due to the action of destabilising viscous forces. If the fluids are miscible, the instability can be suppressed in the limit of large advection as complicated flow structures are formed across the gap. Using a fluid to displace a monolayer of non-colloidal particles suspended in the same fluid, Luo et al. (2025 J. Fluid Mech. vol. 1011, A48) suppress the formation of the cross-gap structures and identify a new fingering mechanism which instead relies on long-range dipolar disturbance flows generated by the particle confinement.

In the rapidly rotating limit, we derive a balanced set of reduced equations governing the strongly nonlinear development of the convective wall-mode instability in the interior of a general container. The model illustrates that wall-mode convection is a multiscale phenomenon where the dynamics of the bulk interior diagnostically determine the small-scale dynamics within Stewartson boundary layers at the sidewalls. The sidewall boundary layers feedback on the interior via a nonlinear lateral heat-flux boundary condition, providing a closed system. Outside the asymptotically thin boundary layer, the convective modes connect to a dynamical interior that maintains scales set by the domain geometry. In many ways, the final system of equations resembles boundary-forced planetary geostrophic baroclinic dynamics coupled with barotropic quasi-geostrophic vorticity. The reduced system contains the results from previous linear instability theory but captured in an elementary fashion, providing a new avenue for investigating wall-mode convection in the strongly nonlinear regime. We also derive the dominant Ekman-flux correction to the onset Rayleigh number for large Taylor number, ${\textit {Ra}} \approx 31.8 \,{\textit{Ta}}^{1/2} - 4.43 \,{\textit{Ta}}^{5/12} + {\mathcal{O}}({\textit{Ta}}^{1/3})$ for no-slip boundaries. However, we find that the linear onset in a finite cylinder differs noticeably compared with a Cartesian channel. We demonstrate some of the reduced model’s nonlinear dynamics with numerical simulations in a cylindrical container.