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.

We investigate the energy transfer from the mean profile to velocity fluctuations in channel flow by calculating nonlinear optimal disturbances, i.e. the initial condition of a given finite energy that achieves the highest possible energy growth during a given fixed time horizon. It is found that for a large range of time horizons and initial disturbance energies, the nonlinear optimal exhibits streak spacing and amplitude consistent with direct numerical simulation (DNS) at least at ${Re}_\tau = 180$, which suggests that they isolate the relevant physical mechanisms that sustain turbulence. Moreover, the time horizon necessary for a nonlinear disturbance to outperform a linear optimal is consistent with previous DNS-based estimates using eddy turnover time, which offers a new perspective on how some turbulent time scales are determined.

In this study, changes in the mean flow of a compressible turbulent boundary layer spatially evolving from low to ‘moderate’ Reynolds numbers are examined. All discussions are based on literature data and a direct numerical simulation (DNS) of a supersonic boundary layer specifically designed to be effectively free of spurious inflow effects in the range $4000 \lessapprox Re_\theta \lessapprox 5000$, which enables discussion of sensitive properties such as the turbulent wake. Most noticeably, the DNS data show the formation of a distinct ‘bend’ in the friction coefficient distribution reflected in sudden deviation from established low-Reynolds-number correlations. As will be shown, the bend is related to the surprisingly abrupt saturation of the turbulent wake, marking the change from low- to moderate-Reynolds-number behaviour; in previous studies, this trend was potentially obscured by data scatter in experiments and/or insufficient domain length in DNS. Moreover, the influence of the wake saturation on the formation of the early logarithmic overlap layer is assessed, which, if fully developed, leads to the onset of high-Reynolds-number behaviour further downstream.

This study presents an experimental investigation on the drag reduction (DR) over air-fed hydrophobic surfaces (AFHS) with longitudinal grooves in a turbulent boundary layer (TBL). The AFHS, designed with longitudinal grooves and air supplement channels, enables active maintenance and reversible restoration of the plastron in TBL. The shear stress sensor, particle image velocimetry (PIV) and interfacial visualization are applied for simultaneous measurement of the skin friction drag, TBL velocity profiles and plastron coverage. The AFHS demonstrated the ability to control plastron shape and enhance its sustainability with friction Reynolds numbers up to 1723. Drag reductions ranging from 14.8–35.8 % are obtained over the AFHS. At same designed air fraction, the AFHS exhibits higher DR than the conventional hydrophobic surface. By minimizing influences of the degradation of plastron coverage and the shape, the monotonic increase in DR and slip velocity with Reynolds number is confirmed, which corroborates trends from direct numerical simulations. Turbulence statistics measured by PIV reveal an apparent decrease in near-wall viscous shear stress, and corresponding slip velocities both in the viscous sublayer and log-law region. The Reynolds shear stress and streamwise velocity fluctuations over the AFHS are larger than those over a smooth wall, where near-wall vortex cores of the AFHS are found to be shifted 10 % towards the wall. This study presents the first simultaneous experimental quantification of skin friction, plastron coverage and turbulence statistics under sustained plastron conditions in TBL. The results demonstrate the efficacy of the plastron control strategy on hydrophobic surfaces and address a critical gap in validating numerical predictions for turbulent flows in practical applications.

The Richtmyer–Meshkov instability at gas interfaces with controllable initial perturbation spectra under reshock conditions is investigated both experimentally and theoretically. A soap-film method is adopted to generate well-defined single-, dual- and triple-mode air/SF$_6$ interfaces. By inserting an acrylic block into the test section, a reflected shock with controllable reshock timing is created. The results reveal a complex relationship between the post-reshock perturbation growth rate and the pre-reshock interface morphology. For single-mode interfaces, the post-reshock growth rate exhibits a strong dependence on pre-reshock conditions. In contrast, for multi-mode interfaces, this dependence weakens significantly due to mode-coupling effects. It is found that, following reshock, each fundamental mode develops independently and later is significantly influenced by mode-coupling effects. Based on this finding, we propose an empirical model that matches the initial linear growth rate and the asymptotic growth rate, accurately predicting the evolution of fundamental modes from early to late stages across all three configurations. Furthermore, a theoretical formula is derived, linking the empirical coefficient in the model of Charakhch’An (2020 J. Appl. Mech. Tech. Phys. vol. 41, no. 1, pp. 23–31) to the initial perturbation. This provides a unified framework to explain the varying dependence of post-reshock growth rates on pre-reshock morphology observed in previous experiments.

A new model is presented for the decay of plane shock waves in equilibrium flows with an arbitrary equation of state. A fundamental challenge for the accurate prediction of shock propagation using analytical modelling is to account for the coupling between a shock’s motion and the post-shock flow. Our model accomplishes this by neglecting only higher-order perturbations to the second velocity gradient, $u_{xx}$, in the incident simple wave. The second velocity gradient is generally small and exactly zero for centred expansion waves in a perfect gas, so neglecting its effect on the shock motion provides an accurate closure criterion for a shock-change equation. This second-order shock-change equation is derived for a general equation of state. The model is tested by comparison with numerical simulations for three problems: decay by centred waves in a perfect gas, decay by centred waves in equilibrium air and decay by the simple wave generated from the constant deceleration of piston in a perfect gas. The model is shown to be exceptionally accurate for a wide range of conditions, including small $\gamma$ and large shock Mach numbers. For a Mach 15 shock in equilibrium air, model errors are less than 2 % in the first 60 % of the shock’s decay. The analytical results possess a simple formulation but are applicable to fluids with a general equation of state, enabling new insight into this fundamental problem in shock wave physics.

The nucleation of bubbles on rough substrates has been widely investigated in various applications such as electrolysis processes and fluid transportation in pipelines. However, the microscopic mechanisms underlying surface bubble nucleation are not fully understood. Using molecular dynamics simulations, we evaluate the probability of surface bubble nucleation, quantified by the magnitude of the nucleation threshold. Bubble nucleation preferentially occurs at the solid interfaces containing nanoscale defects or wells (nanowells), where reduced nucleation thresholds are observed. For the gas-entrapped nanowell, as the nanowell width decreases, the threshold of bubble nucleation around the nanowell gradually increases, eventually approaching a critical value close to that of a smooth surface. This results from a decrease in the amount of entrapped gas that promotes bubble nucleation, and the entrapped gas eventually converges to a critical state as the width decreases. For the liquid-filled nanowell, bubble nucleation initiates from the inner corner of the large nanowell. As the nanowell width decreases, the threshold is first kept constant and then decreases. This results from a decrease in the amount of filled liquid that inhibits bubble nucleation and from the enhanced confinement effect of the inner wall on the filled liquid as the width decreases. In this work, we propose a multiscale model integrating classical nucleation theory, van der Waals fluid theory and statistical mechanics to describe the relationship between nucleation threshold and nanowell width. Eventually, a unified phase diagram of bubble nucleation at the rough interface is summarised, offering fundamental insights for integrated system design.

This paper focuses on the concept of delaying laminar–turbulent transition in hypersonic boundary layers by stabilising fundamental resonance (FR), a key nonlinear mechanism in which finite-amplitude Mack modes support the rapid growth of oblique perturbations. As a pioneering demonstration of this control strategy, we introduce surface heating applied exclusively during the nonlinear phase. Unlike traditional control methods that target the linear phase, the suppressive effect of surface heating on secondary instability modes during FR is evident across various Reynolds numbers, wall temperatures and fundamental frequencies, as confirmed by direct numerical simulations (DNS) and secondary instability analyses (SIA). To gain deeper insights into this control concept, an asymptotic analysis is conducted, revealing an almost linear relationship between the suppression effect and the heating intensity. The asymptotic predictions align overall with the DNS and SIA calculations. The asymptotic theory reveals that the suppression effect of FR is primarily influenced by modifications to the fundamental-mode profile, while mean-flow distortion has a comparatively modest yet opposing impact on this process. This research presents a promising approach to controlling transition considering the nonlinear evolution of boundary-layer perturbations, demonstrating advantages over conventional methods that are sensitive to frequency variations.