The effect of Stokes number on turbulence modulation in particle-laden channel flow is investigated through four-way coupled point-particle direct numerical simulations, with the mass loading fixed at 0.6 and the friction Stokes number $St^+$ varying from 3 to 300. A full transition pathway is observed, from a drag-enhanced to a drag-reduced regime, eventually approaching the single-phase state as $St^+$ increases towards 300. A set of transport equations for the particle phase is derived analytically to characterise the interphase coupling, within the framework of the point-based statistical description of particle-laden turbulence. By virtue of this, two dominant mechanisms are identified and quantitatively characterised: a positive, particle-induced extra transport that decreases monotonically with increasing $St^+$, and a negative, particle-induced extra dissipation that varies non-monotonically with $St^+$. The coupling of these two mechanisms leads to a direct contribution of the particle phase to the shear stress balance, the turbulent kinetic energy budgets and the Reynolds stress budgets. Consequently, as $St^+$ increases, the self-sustaining cycle of near-wall turbulence transitions from being augmented to being suppressed and, eventually, returns to the single-phase state. This gives rise to an indirect effect, manifested as a non-monotonic modulation of Reynolds shear stress and turbulence production rate. Taken together, complex interplays between particle-modified turbulent transport, particle-induced extra transport and extra dissipation are analysed and summarised, providing a holistic physical picture composed of consistent interpretations of turbulence modulation induced by small heavy particles.

Flapping-based propulsive systems rely on fluid–structure interactions to produce thrust. At intermediate and high Reynolds numbers, vortex formation and organisation in the wake of such systems are crucial for the generation of a propulsive force. In this work, we experimentally investigate the wake produced by a tethered robotic fish immersed in a water tunnel. By systematically varying the amplitude and frequency of the fish tail as well as the free stream speed, we are able to observe and characterise different vortex streets as a function of the Strouhal number. The produced wakes are three-dimensional and exhibit a classical V-shape, mainly with two oblique trains of vortex rings convecting outward. Using two-dimensional particle image velocimetry in the mid-span plane behind the fish and through extensive data processing of the velocity and vorticity fields, we demonstrate the strong couplings at place between vortex dynamics, thrust production and wake structure. The main results are twofold. First, by accounting for the obliqueness of the vortex trains, we quantify in experiments the evolution of vortex velocity components in both streamwise and transverse directions. We also measure key geometrical and dynamical properties such as wake angle, vortex ring orientation, diameter and vorticity. Remarkably, all of these quantities collapse onto master curves that also encompass data from previous studies. Second, we develop a quasi-two-dimensional model that incorporates both components of the momentum balance equation and introduces an effective spanwise thickness of the wake structure. This additional dimension, which scales with the physical thickness of the fish, captures the fine features of the three-dimensional wake. The model successfully explains the experimental master curves and highlights the links between vortex dynamics, thrust and wake geometry. Together, this framework offers a comprehensive understanding of the influence of the Strouhal number, providing universal insights relevant for both biological locomotion and bio-inspired propulsion systems.

Depth-averaged systems of equations describing the motion of fluid–sediment mixtures have been widely adopted by scientists in pursuit of models that can predict the paths of dangerous overland flows of debris. As models have become increasingly sophisticated, many have been developed from a multi-phase perspective in which separate, but mutually coupled sets of equations govern the evolution of different components of the mixture. However, this creates the opportunity for the existence of pathological instabilities stemming from resonant interactions between the phases. With reference to the most popular approaches, analyses of two- and three-phase models are performed, which demonstrate that they are more often than not ill posed as initial-value problems over physically relevant parameter regimes – an issue which renders them unsuitable for scientific applications. Additionally, a general framework for detecting ill posedness in models with any number of phases is developed. This is used to show that small diffusive terms in the equations for momentum transport, which are sometimes neglected, can reliably eliminate this issue. Conditions are derived for the regularisation of models in this way, but they are typically not met by multi-phase models that feature diffusive terms.

Eddies within the meso/submeso-scale range are prevalent throughout the Arctic Ocean, playing a pivotal role in regulating the freshwater budget, heat transfer and sea ice transport. While observations have suggested a strong connection between the dynamics of sea ice and the underlying turbulent flows, quantifying this relationship remains an ambitious task due to the challenges of acquiring concurrent sea ice and ocean measurements. Recently, an innovative study using a unique algorithm to track sea ice floes showed that ice floes can be used as vorticity-meters of the ocean. Here, we present a numerical and analytical evaluation of this result by estimating the kinematic link between free-drifting ice floes and underlying ocean eddies using idealised vortex models. These analyses are expanded to explore local eddies in quasi-geostrophic turbulence, providing a more realistic representation of eddies in the Arctic Ocean. We find that in both flow fields, the relationship between floe rotation rates and ocean vorticity depends on the relative size of the ice floe to the eddy. As the floe size approaches and exceeds the eddy size, the floe rotation rates depart from half of the ocean vorticity. Finally, the effects of ice floe thickness, atmospheric winds and floe collisions on floe rotations are investigated. The derived relations and floe statistics set the foundation for leveraging remote sensing observations of floe motions to characterise eddy vorticity at small to moderate scales. This innovative approach opens new possibilities for quantifying Arctic Ocean eddy characteristics, providing valuable inputs for more accurate climate projections.

We study experimentally the starting vortices shed by airfoils accelerating uniformly from rest in superfluid helium-4 (He II). The vortices behave apparently as if they were moving in a classical Newtonian fluid, such as air or water. Specifically, the starting vortex positions obtained from the experimental data are found to be very close to those computed numerically in a Newtonian fluid, at sufficiently small times, when self-similar behaviour is expected to occur, and for Reynolds numbers ranging between approximately $5 \times 10^2$ and $5 \times 10^5$. The result indicates neatly that turbulent flows of He II can be very similar to classical flows of Newtonian fluids, when thermal effects can be neglected and at sufficiently large flow scales, i.e. the study demonstrates that He II could also be employed to study classical Newtonian flows.

In rotating fluids, the viscous smoothing of inviscid singular inertial waves leads to the formation of internal shear layers. In previous works, we analysed the internal shear layers excited by a viscous forcing (longitudinal libration) in a spherical shell geometry (He et al., 2022 J. Fluid Mech. 939, A3; He et al., 2023 J. Fluid Mech. 974, A3). We now consider the stronger inviscid forcing corresponding to the vertical oscillation of the inner boundary. We limit our analysis to two-dimensional geometries but examine three different configurations: freely propagating wave beams in an unbounded domain and two wave patterns (a periodic orbit and an attractor) in a cylindrical shell geometry. The asymptotic structures of the internal shear layers are assumed to follow the similarity solution of Moore & Saffman (1969 Phil. Trans. R. Soc. Lond. A, 264, 597–634) in the small viscous limit. The two undefined parameters of the similarity solution (singularity strength and amplitude) are derived by asymptotically matching the similarity solution with the inviscid solution. For each case, the derivation of the latter is achieved either through separation of variables combined with analytical continuation or the method of characteristics. Global inviscid solutions, when obtained, closely match numerical solutions for small Ekman numbers far from the critical lines, while viscous asymptotic solutions show excellent performance near those lines. The amplitude scalings of the internal shear layers excited by an inviscid forcing are found to be divergent as the Ekman number $E$ decreases, specifically $O(E^{-1/6})$ for the critical-point singularity and $O(E^{-1/3})$ for attractors, in contrast to the convergent scalings found for a viscous forcing.

We study buoyant miscible injections of dense viscoplastic fluids into lighter Newtonian fluids in inclined closed-end pipes, at the high-Péclet-number regime. We integrate experiments involving camera imaging and ultrasound Doppler velocimetry, and computational fluid dynamics simulations, to provide a detailed analysis of interfacial dynamics, flow phases/regimes, velocity field, yielded and unyielded zones, and interfacial arrest mechanisms. The flow dynamics is governed by Reynolds ($Re$), Froude ($Fr$) and Bingham ($B$) numbers, the viscosity ratio ($M$), inclination angle ($\beta$), or their combinations, such as $\chi \equiv 2Re/Fr^2$. As the interface evolves, our results reveal a transition from an inertial-dominated phase, characterised by linear front advancement at the injection velocity, to a viscoplastic-dominated phase, marked by deceleration and eventual interfacial arrest governed by the yield stress. The critical transition length between these phases $(\mathcal{L} \approx 1.26 Fr^{0.14})$ is determined by a balance between inertial and buoyant stresses. Experimental findings confirm buoyancy-driven slumping in our flows, consistent with the theoretical yield number criterion ($Y \equiv B/\chi$), with maximum interfacial arrest lengths scaling as $L_s \sim 1/Y$. These results also classify arrested and unhalted interfacial flow regimes on a plane involving ${\chi \cos (\beta )}/{B}$ and $Y$. Furthermore, we demonstrate that the interfacial arrest mechanism arises from interactions between buoyancy, rheology and geometry, as diminishing shear stresses promote unyielded zone expansion near the interface, progressively encompassing the viscoplastic layer and halting flow when stresses fall below the yield stress.

We consider the conceptual two-layered oscillating tank of Inoue & Smyth (2009 J. Phys. Oceanogr. vol. 39, no. 5, pp. 1150–1166), which mimics the time-periodic parallel shear flow generated by low-frequency (e.g. semi-diurnal tides) and small-angle oscillations of the density interface. Such self-induced shear of an oscillating pycnocline may provide an alternate pathway to pycnocline turbulence and diapycnal mixing in addition to the turbulence and mixing driven by wind-induced shear of the surface mixed layer. We theoretically investigate shear instabilities arising in the inviscid two-layered oscillating tank configuration and show that the equation governing the evolution of linear perturbations on the density interface is a Schrödinger-type ordinary differential equation with a periodic potential. The necessary and sufficient stability condition is governed by a non-dimensional parameter $\beta$ resembling the inverse Richardson number; for two layers of equal thickness, instability arises when $\beta \,{\gt}\,1/4$. When this condition is satisfied, the flow is initially stable but finally tunnels into the unstable region after reaching the time marking the turning point. Once unstable, perturbations grow exponentially and reveal characteristics of Kelvin–Helmholtz (KH) instability. The modified Airy function method, which is an improved variant of the Wentzel–Kramers–Brillouin theory, is implemented to obtain a uniformly valid, composite approximate solution to the interface evolution. Next, we analyse the fully nonlinear stages of interface evolution by modifying the circulation evolution equation in the standard vortex blob method, which reveals that the interface rolls up into KH billows. Finally, we undertake real case studies of Lake Geneva and Chesapeake Bay to provide a physical perspective.