The electrophoresis of charged colloidal particles in fluids exhibiting odd viscosity represents a fundamental challenge in understanding transport phenomena within charge-stabilised chiral active suspensions. Here, we consider a charged chiral active fluid, where electrokinetics is coupled to odd Stokes flow, to explore how classical results from electrophoresis in Newtonian fluids are modified in the presence of odd viscosity. In particular, we derive a general expression for the electrophoretic mobility for particles of any shape, under weak external electric fields, using the Lorentz reciprocal theorem for odd fluids. By applying this result to a charged sphere at low zeta potentials, we obtain an exact, closed-form analytical expression for the electrophoretic mobility, valid for arbitrary values of the Debye screening length and the odd-viscosity coefficient. Similar to Newtonian fluids, we find that the electrophoretic mobility is proportional to the translational mobility of an uncharged sphere, modulated by the Henry function. However, unlike in Newtonian fluids, odd viscosity leads to directional asymmetries in the electrophoretic mobility tensor that persist even for thin electric double layers. This case contrasts significantly with a charged anisotropic particle suspended in an isotropic Newtonian fluid, where anisotropic effects would vanish under the same electrostatic-screening conditions.

This work uncovers a counterintuitive effect of structural damping on vortex-induced vibrations (VIV). The influence of structural damping is examined numerically in the canonical problem usually considered to study these vibrations driven by flow-body synchronisation, i.e. a circular cylinder free to oscillate within a uniform cross-current, for Reynolds numbers up to $160$, based on the body diameter and inflow velocity. For rectilinear VIV without structural restoring force, the peak-amplitude responses, which develop for low structure to displaced fluid mass ratios, are always attenuated by damping, as previously reported. Yet, the lower-amplitude responses occurring for higher mass ratios exhibit a contrasting trend: they are amplified by damping. The amplification can be substantial and leads to vibrations that become significant compared with the peak-amplitude responses. It is observed over the entire Reynolds number range of VIV, and is even accompanied by an extension of this range in the subcritical region, relative to the threshold of $47$ that marks the onset of flow unsteadiness for a fixed body. The enhancement of VIV by structural damping is interpreted in light of the distribution of fluid–structure energy transfer in the amplitude–frequency domain. Such an enhancement is a counterintuitive but general phenomenon, which is shown to persist along curvilinear trajectories and when a structural restoring force is added to the system.

We report on the shape taken by the interface of a liquid bath when hit by a smooth oblique steady jet. When the angle between the jet and the bath decreases below $50^\circ$, a cavity is formed in front of the jet. In the inertial regime that we explore, the jet boundary layer detaches in the impact region, thereby delimiting a core jet region outside of which the liquid is mainly in hydrostatic equilibrium. The shape of the outer meniscus is shown to be related to that outside a tilted fibre piercing the fluid interface. In order to unravel the flow features and separation, we perform direct numerical simulations and show that the flow detachment displays an asymmetry, which results in the acceleration of the liquid below the surface, thereby creating a depression. With this observation, we propose a model balancing the suction force of this depression with the weight of the displaced water and the surface tension force to obtain a prediction for the typical width of the cavity.

Following recent work (Gonzalez & Taha 2022 J. Fluid Mech., vol. 941, A58; Peters & Ormiston 2025 AIAA J., vol. 63, pp. 6–20), this manuscript clarifies what the Gauss–Appell principle determines in incompressible, inviscid flow and how it connects to classical projection methods. At a fixed time, freezing the velocity and varying only the material acceleration leads to minimisation of a quadratic subject to acceleration-level constraints. First-order conditions yield a Poisson–Neumann problem for a reaction pressure whose gradient removes the non-solenoidal and wall-normal content of the provisional residual, precisely the well-known Leray–Hodge projection. Thus, Gauss–Appell enforces the instantaneous kinematic constraints and recovers Euler at the instant. Once the impressed physics is specified, for instance via external body forces, the reaction pressure is uniquely determined (up to an additive constant) as the Lagrange multiplier enforcing incompressibility and wall impermeability; it does no work on divergence-free, wall-tangent motions. This is the well-established interpretation of pressure in incompressible flow. The direct, fixed-time application of this principle determines the reaction pressure for an already-specified velocity field and does not, by itself, select circulation or stagnation points, because these are properties of the velocity state, not the instantaneous acceleration correction. The formal decomposition of the pressure into impressed and reaction components admits representational freedom that does not imply physical non-uniqueness of the constraint force. Orthogonality conventions such as Dirichlet orthogonality can fix the representational freedom as an additional modelling choice. This variational viewpoint also yields a simple computational diagnostic: the minimised Appellian equals a $L^2$ norm of the reaction-pressure gradient which vanishes for constraint-compatible updates and grows with the magnitude of divergence and wall-flux mismatch.

We derive asymptotic models for the ultimate regimes in horizontal convection (HC) and pure internally heated convection (IHC), in analogy with our recent (2024) extension of the ultimate-regime model for Rayleigh–Bénard convection (RBC). To derive the corresponding models for HC and IHC, we combine turbulent boundary-layer relations with the exact dissipation balances for these two systems. For HC, the resulting scaling relations are consistent with the rigorous transport bound of Siggers et al. (2004 J. Fluid Mech. vol. 517, 55–70). For pure IHC, they are consistent with the exact HC–IHC balance analogy of Wang et al. (2021 Geophys. Res. Lett. vol. 48, e2020GL091198) and with the rigorous bounds on the convective-flux asymmetry in the equal-temperature-plates configuration (Arslan et al. 2021 J. Fluid Mech. vol. 919, A15). The main difference between RBC and HC/IHC is that, in the latter two cases, the global kinetic-energy balance does not contain the additional response factor (dimensionless convective heat flux in HC or inverse bulk temperature in IHC), whereas it does in RBC. As a consequence, for fixed Prandtl number ${\textit{Pr}}$, the ultimate-regime scaling exponent is $1/3$ for both HC and IHC, rather than $1/2$ as in RBC.

Droplet ripening is conventionally modelled by macroscopic interfacial theories, which inherently neglect the intrinsic microscopic structures of the liquid–vapour system, specifically the finite diffuse interface and the adjacent Knudsen layer. Resolving these structures is critical, as they govern mass transfer rates in regimes where interfacial transport kinetics dominate over bulk diffusion, particularly in micro- and nanodroplet interactions. To elucidate the underlying fundamental physical mechanisms, we investigate droplet ripening in a single-component liquid–vapour system using the Enskog–Vlasov kinetic model. This approach naturally captures the full spatial structure of both the diffuse interface and the Knudsen layer. We first focus on two-droplet interactions, deriving a theoretical growth rate based on the intrinsic imbalance of molecular fluxes at the interface. Numerical simulations quantitatively validate this prediction, confirming that the droplet-radius change rate scales linearly with the thermodynamic driving force. However, a distinct deviation from this linear behaviour emerges in the late stage of ripening. We attribute this breakdown to the overlap of diffuse interfaces, which reduces the liquid density and induces thermodynamic destabilisation. Finally, our simulations of three-droplet systems confirm the universality of the proposed theoretical model. These findings provide a microscopic understanding of ripening and help bridge nanoscale dynamics with macroscopic coarsening theories.

We study experimentally the detachment of a large pendant drop of non-Brownian monodisperse solid spheres in a Newtonian liquid, for high solid volume fractions ($0.55\leq \phi \leq 0.605$) compared with the critical volume fraction $\phi _{{c}}$ of the suspension. This set-up allows us to monitor both the bulk-effective deformation rate and the mean stress at the neck of the drop throughout detachment. The neck effective viscosity is found to decrease close to exponentially with the current neck radius, from a large initial value, $\eta _{{i}}$, down to the suspending liquid one. Experiments with different drop-to-particle size ratios indicate that, above $\phi _{{c}}$, the initial value $\eta _{{i}}$ is set by the viscosity-limited dilation of the particle phase. Observations on a transparent, doubly index-matched system reveal increasing deviation from axial symmetry and the collapse of capillary menisci at the drop interface during the exponential decay. A simplified model, based on the observed rheological evolution and the close-to-conical neck shape, captures the steeply accelerated detachment dynamics and shows how $\eta _{{i}}$ sets the breakup duration.

The spread of a pulse of solute in a pressure-driven channel flow is well described for a wide range of Newtonian flows for which the viscosity and diffusivity are constants. Over many decades, various extensions have been suggested for the dispersion in pressure-driven non-Newtonian channel flows. While many theoretical studies have examined the effect of shear-rate-dependent viscosity on dispersion for a variety of non-Newtonian constitutive models, the solute diffusivity has invariably been treated as a constant. This assumption, however, is in contrast to the expectation that the diffusivity of a colloidal particle is inversely related to the viscosity, e.g. recall the Stokes–Einstein relation. We account for this coupling of transport coefficients – viscosity and diffusivity – by assuming a generalised form of the Stokes–Einstein equation, inspired by the recognition that the viscosity is now a field, although only transport transverse to the main flow direction is relevant because of the common assumptions of Taylor–Aris dispersion. Thus, we derive a general formula for axial dispersion in steady, pressure-driven shear-rate-dependent flows in uniform channels. In particular, we apply our general relation to calculate the Taylor–Aris dispersion coefficient for steady flows of a shear-thinning Carreau fluid and a viscoelastic Phan-Thien–Tanner fluid. Finally, we highlight new theoretical questions raised by this transport situation, where the underlying diffusivity is also a (tensorial) field related to variations in viscosity.

Flow structures directly responsible for local unsteady skin-friction generation in turbulent channel flows are identified using the newly developed canonical correlation decomposition (CCD) method. The dominant structures take the form of streamwise streaks that are spanwise-localised around the position where the skin friction is targeted and exhibit progressively shorter streamwise extents as the mode number increases. The resulting CCD spectrum shows a clear low-rank behaviour; flow reconstruction using only the first 4 CCD modes recovers more than 80 % of the examined skin-friction variation, in contrast to inefficient skin-friction reconstructions using other correlation-based methods. When the opposition control technique is used to reduce drag, the application of CCD shows that drag reduction is achieved by lifting the original streak structures and generating thinner and shorter streaks with opposite phases underneath. These findings demonstrate that CCD isolates the causally relevant flow structures governing the turbulent skin-friction generation and modification, which is expected to find use in various drag control applications in wall-bounded turbulence.

This article presents a new flow feature observed behind a rectangular wing in water: the breakdown of the wing-tip vortex induced by the temporary injection of air into the vortex core downstream of the wing. For certain combinations of Reynolds number and angle of attack, a stationary air bubble is trapped in the core at some distance from the wing and can persist for several minutes after the injection is stopped. For other parameter values, the bubble drifts downstream or upstream until it reaches the wing, or it disintegrates immediately. Measurements of the vortex properties and bubble characteristics are presented and discussed. The breakdown behaviour, which is unrelated to cavitation, is found to depend mainly on the tip vortex circulation and on the axial flow component in the vortex core. Only configurations with a velocity excess, with respect to the free stream, at high angle of attack, allow the formation of a breakdown bubble.

The receptivity of the inviscid flow on the stagnation streamline of a blunt body in supersonic flow is investigated theoretically for incoming free-stream disturbances. The wave transmission and coupling are quantified by solving the linearised shock-fitting problem with a spectral method, whereas the steady base flow is obtained using a nonlinear shock-fitting spectral solver. Revisiting previous theoretical work, we identify and correct an error in a key coefficient in the analysis by Morkovin (1960 J. Appl. Mech., 27, pp. 223–229), overturning the prior conclusion of body-induced damping and revealing amplification instead. The post-shock entropy disturbances display singular behaviour near the stagnation point, which is treated analytically. Acoustic disturbances dominate pressure and velocity responses, while density is affected by both acoustic and entropy modes. The base flow pressure gradient introduces weak coupling between the acoustic and entropic components of the response. The actual stagnation-line base flow amplifies all disturbances more than the simplified model of uniform post-shock flow; as well as a shock without a body, and the differences are quantified for a range of Mach numbers. The responses to entropy, fast acoustic and slow acoustic waves are compared as functions of the free-stream Mach number.

Turbulent channel flow controlled by spanwise wall oscillations is studied using direct numerical simulations to improve how spanwise forcing reduces skin-friction drag. Harmonic wall oscillations generate a periodic transverse Stokes layer whose thickness $\delta$ is determined by the forcing period $T$. Although an optimal $T$ that maximises drag reduction is known to exist, its physical significance remains unclear. To elucidate it, we extend the spanwise Stokes layer by augmenting wall oscillation with an additional spanwise body force. In this formulation, $\delta$ and $T$ become decoupled and can be varied independently. The oscillating wall thus appears as a special and suboptimal case of spanwise forcing. Optimal performance is obtained for substantially smaller $T$ and larger $\delta$ than those of the classical Stokes layer. For the conditions examined, with Reynolds number and forcing amplitude held fixed, the maximum drag reduction increases by approximately one third, while the maximum net energy saving improves markedly from $-35\,\%$ to $+16\,\%$. These findings suggest that drag-reduction strategies based on spanwise forcing deserve renewed scrutiny: wall oscillation represents only one possible actuation method, and not necessarily the most effective one.

The force on a spherical particle moving arbitrarily in a fairly general class of unsteady potential flows is calculated. It is found that the force, which can be expressed as the gradient of a potential, takes the form of an infinite series of progressively higher order in the ratio of the sphere’s radius to the scales of the surrounding flow. The first few terms conform with the known form usually referred to as ‘added mass force’ but, when the remaining terms are non-negligible, this concept becomes less relevant. Thus, unlike Faxèn’s extension of Stokes’s drag law, it proves impossible to generalise the idea of added mass to particles that are not much smaller than the flow scales. The kinetic energy of the fluid in excess of that which it would have in the absence of the sphere is also calculated when the flows considered are unbounded.

Attempts to disentangle shear-flow turbulence often focus on identifying relatively simple solutions, such as travelling waves or periodic orbits. We show, however, that capturing multiscale features requires considering states at least as complex as quasi-time-periodic solutions. Approximations of these states can be computed efficiently using a quasi-linear model, consistent with the large-Reynolds-number asymptotic analysis. The quasi-linear structure is key to producing multiscale critical layers that generate vortices obeying Taylor’s frozen-flow hypothesis.

Interfacial instability dominates the dynamics as a cavitation bubble oscillates in close proximity to a liquid surface, driving perturbations on both the bubble wall and the liquid surface. The penetration of the liquid layer initiates ventilation, exposing the bubble interior and thereby altering its subsequent dynamics. To quantitatively elucidate the interfacial coupling-induced instability, we develop a theoretical model that couples the perturbation equation with the bubble oscillation equation, considering the liquid viscosity. The model predicts the transition boundaries between ventilation patterns by critical stand-off parameters, which scale exponentially with the liquid viscosity to the −1/3 power. The boundary between complete and partial ventilation regimes shows negligible viscous dependence due to the vanishingly short perturbation growth time. Furthermore, we derive the scaling law of ventilation time, defining it as the instant of perturbation penetration. A series of experiments on bubble oscillation near a liquid surface was conducted, which verified the predictions of the theoretical model. This offers a practical framework for the engineering application of near-surface bubble collapse.

Turbulence-induced friction is a significant contributor to energy consumption in the fluid-transport and piping industries. Here, we describe a passive approach to suppress turbulence and reduce friction: we show that a local increase in streamwise flow curvature, combined with changing a circular cross-section to an oval, relaminarises turbulent flow in curved pipes. We exemplify this effect in a $180^{\circ }$ bend at ${\textit{Re}}_D=10\,000$ and $20\,000$ (based on bulk velocity $U_B$ and pipe diameter $D$), well above the limit for sustained turbulence in straight pipes and the linear stability limit in $180^{\circ }$ bends. Curvature inhibits streamwise Reynolds stresses, and cross-sectional modifications weaken the unstable secondary flow, together disrupting the near-wall regeneration cycle and collapsing turbulence. Simulations and experiments confirm that these geometric modifications suppress turbulence and reduce pressure loss by 53 % and 36 % compared with the baseline $180^{\circ }$ bend and a fully developed straight pipe of equal length, respectively. The results establish a passive, mechanism-based route to relaminarisation in curved pipes with implications for energy-efficient control in other wall-bounded flows with curvature.

We examine elastic travelling-wave (‘arrowhead’) solutions in a viscoelastic, unidirectionally body-forced flow, focusing on their existence and morphological changes as the Weissenberg number ${\textit{Wi}}$ and streamwise duct length $L$ are varied. We find that, First, branch topology varies from an isola at low $L$ through a two-sided reconnection at intermediate $L$ to a branch that exists at asymptotically large ${\textit{Wi}}$ for larger $L$. At intermediate $L$, more than two arrowhead solutions can coexist at a given $({\textit{Wi}},L)$ choice due to extra saddle–node bifurcations. Second, the canonical arrowhead consists of two legs joined by an arched head that blocks throughflow and traps a counter-rotating vortex pair, while a polymer strand can emerge as a by-product of a strong extensional region attached to/detached from the arrowhead arch. Third, a minimal domain length $L_{min }$ required to sustain an arrowhead is found to vary non-monotonically with ${\textit{Wi}}$; for ${{\textit{Wi}}}\geqslant 20$, detached-strand states control $L_{min }$ with a relation $L_{min }\approx 0.125\,{{\textit{Wi}}}+1.5$. And fourth, in sufficiently long domains, the upper branch becomes a localised single arrowhead whose streamwise extent depends on ${\textit{Wi}}$, whereas the lower branch can proliferate into a train of arrowheads at high ${\textit{Wi}}$, a phenomenon not previously reported.

We show that both temporal and spatial symmetry breaking in canonical K-type boundary layer transition arise as organised structures with quantifiable energetic pathways rather than unstructured noise. Before the skin-friction maximum, the flow is described by a periodic, spanwise-symmetric fundamental harmonic response (FHR) to the Tollmien–Schlichting wave. The FHR is spatially compact, produces hairpin packets and remains fully harmonic despite a turbulence-like appearance, thereby delimiting the deterministic regime. Past this point, a distinct regime change occurs: a hierarchy of quasi-periodic and aperiodic structures emerges, followed shortly by anti-symmetric structures that develop similarly despite no anti-symmetric inputs. We identify these structures as symmetry-decomposed spectral and space–time proper orthogonal modes that resolve the progression from deterministic harmonics to broadband dynamics. We introduce inter-modal and inter-symmetry energy budgets derived from symmetry-decomposed Navier–Stokes equations. They reveal a directed energy transfer from the FHR into the leading temporal and spatial symmetry breaking modes and, subsequently, into broadband residual fluctuations, showing that broadband dynamics grow only once inter-modal transfer is active, while inter-symmetry transfer also strongly amplifies broadband anti-symmetric fluctuations once asymmetry is present. These key insights support a view of laminar–turbulent transition as a sequence of symmetry breaking events, energetically driven by dominant space–time modes that route energy from harmonic flow to broadband turbulence.

We perform numerical simulations of forced homogeneous isotropic turbulence over a range of bulk viscosities, Reynolds numbers and Mach numbers to investigate the scaling of key flow statistics. Using the Helmholtz decomposition, we analyse the scalings of Favre-averaged turbulent kinetic energy (TKE), root-mean-square (r.m.s.) pressure, pressure dilatation, dilatational dissipation and higher-order velocity-gradient moments. Additionally, new models are proposed for the pressure-dilatation term and the bulk-viscosity dependence of dilatational dissipation. Although the solenoidal and dilatational components of the Favre-averaged TKE are not strictly orthogonal, our numerical results demonstrate that their ratio is well approximated by the squared ratio of the corresponding r.m.s. velocities. The r.m.s. pressure approaches the pseudo-sound scaling as bulk viscosity increases. Within the Donzis r.m.s. pressure model (Donzis & John 2020 Phys. Rev. Fluids 5(8), 084609), we find that the solenoidal contribution becomes dominant for large bulk viscosity. Pressure dilatation is found to depart systematically from pseudo-sound predictions: without bulk viscosity it favours transfer from kinetic to internal energy, while finite bulk viscosity can reverse this transfer at high Mach numbers. The scaling exponent of dilatational dissipation is shown to vary with bulk viscosity, enabling a corrected model for its exponent and prefactor. Velocity-gradient skewness and flatness reveal that the onset of shocklet-induced divergence is delayed with increasing bulk viscosity and may be suppressed entirely. The results extend recent velocity-ratio-based scaling frameworks and provide modelling insights into compressible turbulence.

Stochastic models of near-wall turbulence commonly rely on the Markovian assumption, despite evidence that coherent structures induce long-lived temporal correlations. Here, we test the validity of this assumption using micron-sized particle resuspension from the viscous sublayer. Analysis of direct numerical simulation (DNS) data reveals that while high- and low-drag events occur with Poissonian statistics, their internal dynamics is strongly persistent, with a Hurst exponent $H \approx 0.84$, indicating intrinsic non-Markovian behaviour. We therefore develop a non-Markovian resuspension model based on a fractional Ornstein–Uhlenbeck process, with physical parameters extracted directly from the DNS flow. Comparative simulations show that the empirical success of classical Markovian models arises not from an accurate description of the near-wall dynamics, but from their free parameter $C_{0}$ acting as a phenomenological surrogate for unresolved flow memory. We further identify a critical regime transition controlled by the event decay rate $\lambda$: strong intermittency ($\lambda \lt 0.2$) invalidates the Markovian approximation, whereas weak intermittency ($\lambda \gt 0.2$) renders it physically justifiable. These results define quantitative limits on stochastic modelling in near-wall turbulence.