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.

The integration of electro-osmotic effect to the underlying flow enhances solute dispersion precision in microfluidic systems, which is crucial for applications such as drug delivery and on-chip fluidic functionalities. We investigate, in this study, the solute dispersion characteristics of couple-stress fluids in a two-dimensional microchannel configuration under the combined effects of electro-osmotic actuation and applied pressure gradients. We consider both homogeneous and heterogeneous reactions in the present analysis. Couple-stress fluids, which account for additional stresses due to the presence of the microstructures in the fluids, offer a more accurate model to describe the rheological behaviour of biofluids. While previous studies have addressed longitudinal Gaussianity and transverse uniformity of solute distribution, we focus uniquely in this endeavour on longitudinal uniformity. Using Mei’s multiscale homogenisation technique, we solve a two-dimensional convection–diffusion model, extending it to third-order approximation to analyse the dispersion coefficient, concentration profiles, and variation rates of concentration within microchannel flow. Results show that forcing and couple-stress parameters enhance the gradients of the longitudinal variation rate, while boundary absorption reduces this variation rate near the walls. The couple-stress parameter exhibits dual behaviour: initially, it enhances solute dispersion, but beyond a certain value of couple-stress parameter $B_{cr}$ (which depends on forcing comparison and the Debye–Hückel parameter), it reduces dispersion. In the absence of pressure, solute distribution remains longitudinally uniform. However, as the pressure gradient increases, concentration levels drop sharply, and the distribution shifts to a parabolic profile, underscoring the significant influence of pressure on flow behaviour in electro-osmotic flow.

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.

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.

The propagation of detonations in a non-uniform mixture exhibits notable distinctions from that in a uniform mixture. This study first delves into the analytical analysis of the one-dimensional shock transmission problem and the two-dimensional shock propagation in a mixture with temperature non-uniformity. Additionally, the research extends to the numerical simulation of the propagation of shocks and detonations, building upon the insights garnered from the analytical analysis. The numerical results indicate that introducing a temperature interface in a non-uniform gas creates a discrete flow field and wavefront, resulting in oblique shocks that connect hot and cold layers. A competitive mechanism between the transverse waves and non-uniformity is responsible for the detonation propagation. The temperature amplitude tends to inhibit the propagation of transverse waves. In contrast, the wavelengths primarily affect the spacing and strength of these transverse waves, especially during the early stages of propagation. In a Zel’Dovich–von Neumann–Döring detonation, the non-uniformities distort the detonation front, creating transverse wave spacings comparable to the wavelength and reducing the front velocity. However, the detonation can recover its Chapman–Jouguet velocity and approach a steady states as intrinsic instabilities come into play. In the steady state, the cell sizes are found to be determined by the temperature amplitude. When the temperature amplitude is sufficiently high, the detonation cells effectively disappear.

We study the stability of plane Poiseuille flow (PPF) and plane Couette flow (PCF) subject to streamwise system rotation using linear stability analysis and direct numerical simulations. The linear stability analysis reveals two asymptotic regimes depending on the non-dimensional rotation rate ($\textit{Ro}$): a low-$\textit{Ro}$ and a high-$\textit{Ro}$ regime. In the low-$\textit{Ro}$ regime, the critical Reynolds number $\textit{Re}_c$ and critical streamwise wavenumber $\alpha _c$ are proportional to $\textit{Ro}$, while the critical spanwise wavenumber $\beta _c$ is constant. In the high-$\textit{Ro}$ regime, as $\textit{Ro} \rightarrow \infty$, we find $\textit{Re}_c = 66.45$ and $\beta _c = 2.459$ for streamwise-rotating PPF, and $\textit{Re}_c = 20.66$ and $\beta _c = 1.558$ for streamwise-rotating PCF, with $\alpha _c\propto 1/Ro$. Our results for streamwise-rotating PPF match previous findings by Masuda et al. (J. Fluid Mech., vol. 603, 2008, pp. 189–206). Interestingly, the critical values of $\beta _c$ and $\textit{Re}_c$ at $\textit{Ro} \rightarrow \infty$ in streamwise-rotating PPF and PCF coincide with the minimum $\textit{Re}_c$ reported by Lezius & Johnston (J. Fluid Mech., vol. 77, 1976, pp. 153–176) and Wall & Nagata (J. Fluid Mech., vol. 564, 2006, pp. 25–55) for spanwise-rotating PPF at $\textit{Ro}=0.3366$ and PCF at $\textit{Ro}=0.5$. We explain this similarity through an analysis of the perturbation equations. Consequently, the linear stability of streamwise-rotating PCF at large $\textit{Ro}$ is closely related to that of spanwise-rotating PCF and Rayleigh–Bénard convection, with $\textit{Re}_c = \sqrt {Ra_c}/2$, where $Ra_c$ is the critical Rayleigh number. To explore the potential for subcritical transitions, direct numerical simulations were performed. At low $\textit{Ro}$, a subcritical transition regime emerges, characterised by large-scale turbulent–laminar patterns in streamwise-rotating PPF and PCF. However, at higher $\textit{Ro}$, subcritical transitions do not occur and the flow relaminarises for $\textit{Re} \lt Re_c$. Furthermore, we identify a narrow $\textit{Ro}$ range where turbulent–laminar patterns develop under supercritical conditions.

We study the hydrodynamic and acoustic fields of turbulent jets issuing from nozzles modified by the addition of cylindrical tabs on the inner surface, one diameter upstream of the exit. The tabs are designed to promote significant growth of steady streaks in the nozzle turbulent boundary layer. A baseline smooth nozzle is also studied for comparison. Acoustic measurements are made using an azimuthal array for Mach numbers in the range 0.4 $\leqslant M_{\kern-1pt j} \leqslant$ 0.9. The tabs are found to reduce the emitted sound levels by up to 3 dB/St. In terms of overall sound pressure levels, reductions of up to 3 dB are observed at all measured polar angles in the range 20° $\leqslant \theta \leqslant$ 90°. Time-resolved particle image velocimetry experiments are conducted to measure the three components of velocity for a series of cross-stream planes at $M_{\kern-1pt j} =$ 0.7. A Floquet-based Fourier decomposition is applied for the azimuthally periodic flow field, and spectral proper orthogonal decomposition is then employed to extract coherent structures. Comparison of the structures obtained for nozzles with and without tabs shows an enhancement of the streaky structures by the tabs and a damping of Kelvin–Helmholtz wavepackets. A linear model based on the one-way Navier–Stokes equations is employed to explore the underlying amplification mechanisms and how these are impacted by the tabs. The model reproduces the growth–attenuation mechanism observed in the data, showing that the changes in the mean flow induced by the streaks work to reduce the amplification of the noise-generating coherent structures associated with linear spatial growth mechanisms.

Wall slip sensitivity and non-sphericity and orientation effects are investigated for a moving no-slip solid body immersed in a fluid above a plane slip wall with a Navier slip. The wall–particle interactions are examined for the body motion in a quiescent fluid (resistance problem) or when freely suspended in a prescribed ‘linear’ or quadratic ambient shear flow. This is achieved, assuming Stokes flows, by using a boundary method which reduces the task to the treatment of six boundary-integral equations on the body surface. For a wall slip length $\lambda$ small compared with the wall–particle gap $d$ a ‘recipe’ connecting, at $O((\lambda /d)^2),$ the results for the slip wall and another no-slip wall with gap $d+\lambda$ is established. A numerical analysis is performed for a family of inclined non-spheroidal ellipsoids, having the volume of a sphere with radius $a,$ to quantity the particle behaviour sensitivity to the normalised wall slip length $\overline {\lambda }=\lambda /a,$ the normalised wall–particle gap ${\overline {d}}=d/a$ and the particle shape and orientation (here one angle $\beta ).$ The friction coefficients for the resistance problem exhibit quite different behaviours versus the particle shape and $({\overline {d}}, \overline {\lambda },\beta ).$ Some coefficients increase in magnitude with the wall slip. The migration of the freely suspended particle can also strongly depend on $({\overline {d}}, \overline {\lambda },\beta )$ and in a non-trivial way. For sufficiently small $\overline {d}$ a non-spherical particle can move faster than in the absence of a wall for a large enough wall slip for the ambient ‘linear’ shear flow and whatever the wall slip for the ambient quadratic shear flow.

For hypersonic inlets, buzz is a self-sustained oscillatory flow characterised by strong nonlinear and unsteady behaviour. Our recent study shows that, unlike conventional alterations in flow conditions at the inlet entrance or exit, flexible lip deformation is a newly identified trigger for buzz. However, the mechanism by which this fluid–structure interaction (FSI) behaviour induces buzz remains unclear. To clarify how FSI acts as a dominant factor in triggering flow instability leading to buzz, this study investigates a more general flexible plate model within the inlet. The results show that the plate FSI introduces a prolonged instability accumulation process for buzz evolution, resulting in a ‘gradual-onset’ characteristic differing from previous studies. During this process, plate FSI amplifies downstream flow oscillations while accumulating unstable energy. Eventually, the excessive unstable energy causes the shock train to destabilise and be disgorged from the inlet, initiating a complete instability process dominated by buzz. Notably, buzz induced by plate FSI exhibits unsteady characteristics similar to those observed in rigid inlets. Therefore, as an internal self-excited disturbance source, plate FSI produces relatively weaker disturbances than conventional flow modifications, but exhibits highly persistent accumulation effects and distinct multistage characteristics. This study reveals the buzz evolution mechanism under plate FSI, providing new insights into flow instability in hypersonic inlets.

We investigate the motion of a thin liquid drop on a pre-stretched, highly bendable elastic sheet. Under the lubrication approximation, we derive a system of fourth-order partial differential equations, along with appropriate boundary and contact line conditions, to describe the evolution of the fluid interface and the elastic sheet. Extending the classical analysis of Cox and Voinov, we perform a four-region matched asymptotic analysis of the model in the limit of small slip length. The central result is an asymptotic relation for the contact line speed in terms of the apparent contact angles. We validate the relation through numerical simulations. A key implication of this result is that a soft substrate retards drop spreading but enhances receding, compared to the dynamics on a rigid substrate. The relation remains valid across a wide range of bending modulus, despite the distinguished limit assumed in the analysis.

Quantum turbulence is characterised by the collective motion of mutually interplaying thin and discrete vortex filaments of fixed circulation which move in two mutually interacting fluid components. Despite this very peculiar nature determined by quantum-mechanical effects, turbulence in quantum fluids may exhibit very similar features to classical turbulence in terms of the vortex dynamics, energy spectrum and decay and intermittency. The recent work by Blaha et al. (2025 J. Fluid. Mech. 1015, A57) reveals an additional classical behaviour of quantum turbulence, by showing that the trajectories of starting vortices shed by accelerating airfoils in a quantum fluid are almost indistinguishable from their counterpart in classical viscous flows. These results strongly support the suggestive idea that turbulent flows, both classical and quantum, may be described by the collective dynamics of interacting, thin and discrete filaments of fixed circulation.

Microfluidic paper-based analytical devices (${\unicode{x03BC}}$PADs) have gained considerable attention due to their ability to transport fluids without external pumps. Fluid motion in ${\unicode{x03BC}}$PADs is driven by capillary forces through the network of pores within paper substrates. However, the inherently low flow speeds resulting from the small pore sizes in paper often limit the performance of ${\unicode{x03BC}}$PADs. Recent studies have introduced multilayered ${\unicode{x03BC}}$PADs composed of stacked paper sheets, which enable significantly faster fluid transport through inter-layer channels. In this study, we present a combined theoretical and experimental investigation of water imbibition dynamics through channels formed by multiple paper layers. Upon contact with water, the paper layers absorb water and undergo swelling, altering channel geometry and consequently affecting flow dynamics. We develop a mathematical model that extends the classical Washburn equation to incorporate the effects of water absorption and swelling. The model predictions show excellent agreement with experimental observations of water flow through multilayered paper channels. The results elucidate how water absorption and swelling influence capillary imbibition, and suggest potential strategies for regulating flow rates in multilayered ${\unicode{x03BC}}$PADs.

This study introduces a boundary element method to solve the three-dimensional problem of internal tide generation over arbitrary isolated seamounts in a uniformly stratified finite-depth fluid with background rotation, without assumptions on the size or slope of the topography. Focusing on linearly propagating waves with small tidal excursions, the approach employs a vertical mode decomposition to describe the wavefield and the wave energy flux. We apply the model to the generation of internal tides by a unidirectional barotropic tide interacting with an axisymmetric Gaussian seamount. We study the conversion rate and flow field for various topographic configurations. We qualitatively recover some of the two-dimensional results of Papoutsellis et al. (2023 J. Fluid Mech. 964, A20), and find topographies with weak conversion rates, as discussed by Maas (2011 J. Fluid Mech. 684, 5–24). Furthermore, our results reveal the previously underestimated influence of the Coriolis frequency on the wavefield and on the spatial distribution of radiated energy flux. Due to Coriolis effects, the energy fluxes are shifted slightly counter-clockwise in the northern hemisphere. We explain in detail how this shift increases with the magnitude of the Coriolis frequency and the topographic features and why such effects are absent in models based on the weak topography assumption.