Unsteady, non-equilibrium stagnation-point boundary layers are analysed using a newly developed engineering correlation that links the magnitude of atomic mass fraction fluctuations in the free stream to their corresponding values at the wall. Analytical solutions to the species conservation equation alongside empirical correlations are used to derive a generalised correlation, taking into account diffusive transport, finite-rate reactions and arbitrary surface catalycity. Fully coupled transient numerical simulations are performed to assess the accuracy of the approximate theory, resulting in an agreement of ${\lt } 12.5$ %. Four scaling parameters are identified: the Damkoehler number, and ratios of boundary-layer thickness, Stokes-layer thickness and wall catalycity. The magnitude of atomic-mass-fraction fluctuations at the wall is highest for frozen boundary layers and non-catalytic materials. Typical experimental operating conditions of high-enthalpy facilities are used to assess the relevance of oscillating mass fractions on gas–surface interaction. It is found that wall conditions can be severely affected by unsteadiness, leading to additional uncertainties in the interpretation of test results. The derived theory provides a first simple analytical framework, enabling improved analysis of transient high-enthalpy experiments and motivates future studies employing higher-fidelity models in order to remove uncertainty in the determination of gas–surface interaction rates.

High-resolution particle image velocimetry (PIV) particle-to-velocity analyses using small interrogation areas (IAs) often require substantial processing time. To overcome this limitation, a generative adversarial network (GAN)-based model is proposed to achieve spatio-temporal super-resolution (SR) reconstruction from low-resolution PIV data with large IAs, thereby significantly reducing post-processing time. Time-resolved PIV measurements of plasma-induced vortex flows, covering vortex formation, growth, transition and breakdown stages, are employed to train and evaluate the model with multi-scale vortical structures. By sequentially constructing spatial and temporal datasets, the GAN-based model enables reliable SR reconstruction at different scaling factors. Reconstruction accuracy is systematically assessed using time-averaged, instantaneous and phase-averaged velocity fields. At SR factors of $\times$4 and $\times$8, the reconstructed fields closely match high-resolution references, effectively capturing both fluctuating velocities and small-scale vortical structures. In contrast, $\times$16 reconstructions exhibit diminished accuracy due to the loss of fine-scale information from highly downsampled inputs. For time-averaged fields, high-resolution reconstructions reliably capture plasma jet characteristics at all SR factors. To enhance generalisation, transfer learning is introduced to fine tune the parameters of SR-related layers in the generator, enabling accurate reconstructions under varying vortex dynamics. In addition, the efficiency gains in PIV particle-to-velocity analysis and the fundamental limitations on achievable SR factors imposed by spatio-temporal data correlations are discussed. This study demonstrates that GAN-based spatio-temporal SR models offer a promising approach to accelerate PIV analyses while maintaining high reconstruction fidelity with diverse flow conditions.

Dispersion is a common phenomenon in miscible displacement flows. In the primary cementing process displacement takes place in a narrow eccentric annulus. Both turbulent Taylor dispersion and laminar advective dispersion occur, depending on flow regime. Since dispersion can cause mixing and contamination close to the displacement front, it is essential to understand and quantify. The usual modelling approach is a form of Hele-Shaw model in which quantities are averaged across the narrow annular gap: a so-called two-dimensional narrow gap (2DGA) model. Zhang & Frigaard (J. Fluid Mech., vol. 947, 2022, A732), introduced a dispersive two-dimensional gap-averaged (D2DGA) model for displacement of two Newtonian fluids, by modifying the earlier 2DGA model. This brings a significant improvement in revealing physical phenomena observed experimentally and in three-dimensional computations, but is limited to Newtonian fluids. In this study we adapt the D2DGA model approach for two Herschel–Bulkley fluids. We first obtain weak velocity solutions using the augmented Lagrangian method, while keeping the same two-layer flow assumption as the Newtonian D2DGA model. These solutions are then used to define closure relationships that are needed to compute the dispersive two-dimensional flows. Results reveal that the modified version of the D2DGA model can now predict expected frontal behaviours for two Herschel–Bulkley fluids, revealing dispersion, frontal shock, spike and static wall layer solutions. We then explore the displacement behaviour in more detail by investigating the impact of rheological properties and buoyancy on the mobility of fluids in a planar frontal displacement flow and their vulnerability to fingering-type instabilities. As the underlying flows are dispersive, our analysis reveals three distinct behaviours: (i) stable, (ii) partial penetration of the dispersing front, and (iii) unstable regimes. We explore these regimes and how they are affected by the two fluid rheologies.

We numerically investigate the cellular detonation dynamics in ethylene/oxygen/ozone/nitrogen mixtures considering detailed chemical kinetics. The aim is to elucidate emergent detonation structures and reveal the transition mechanism from single- to double-cellular structures. Ozone is used to induce two-stage reactions within the mixture. Through systematic initiation strength analysis, we demonstrate two distinct propagation regimes: (i) under strong initiation, a stable double-cellular detonation is established; (ii) weak initiation triggers a multi-stage evolutionary process, beginning with a low-speed single-cellular detonation in the initiation zone. During the initial weak stage, the detonation propagates at a quasi-steady velocity with uniform cellular patterning. The subsequent transition phase features spontaneous acceleration accompanied by structural bifurcation into double cells, ultimately stabilising in a normal stage with sustained double-cellular structures. Further analysis reveals that the weak-stage dynamics is governed exclusively by first-stage chemical reactions, resulting in a single-cellular structure propagating at a velocity much lower than the Chapman–Jouguet speed. In contrast, the double-cellular structure observed at the normal stage results from the two-stage exothermic reactions. Thermodynamic perturbations arising from cellular instability and fluid dynamic instability are identified as critical drivers for the transition from single- to double-cellular detonation. Besides, conditions for the formation of double-cellular detonation are explored, and two qualitative requirements are summarised: the reactions of the two stages must proceed as independently as possible, and both heat releases from the two stages must be high enough to sustain the triple-shock configurations.

Microswimming cells and robots exhibit diverse behaviours due to both their swimming and their environment. One key environmental feature is the presence of a background flow. While the influences of select flows, particularly steady shear flows, have been extensively investigated, these only represent special cases. Here, we examine inertialess swimmers in more general flows, specifically general linear planar flows that may possess rapid oscillations, and impose weak symmetry constraints on the swimmer (ensuring planarity, for instance). We focus on swimmers that are inefficient, in that the time scales of their movement are well separated from those associated with their motility-driving deformation. Exploiting this separation of scales in a multiple-time-scale analysis, we find that the behaviour of the swimmer is dictated by two effective parameter groupings, excluding mathematically precise edge cases. These systematically derived parameters measure balances between angular velocity and the rate of strain of the background flow. Remarkably, one parameter governs the orientational dynamics, whilst the other completely captures translational motion. Further, we find that the long-time translational dynamics is solely determined by properties of the flow, independent of the details of the swimmer. This illustrates the limited extent to which, and how, microswimmers may control their behaviours in planar linear flows.

Monitoring fluid flow and pollutant transport is important in many geophysical, environmental and industrial processes, such as geological $\textrm {CO}_2$ sequestration, waste water disposal, oil and gas recovery and sea water invasion. But it can also be challenging. Recent studies revealed a series of self-similar solutions to describe the interface shape evolution between the injecting and the ambient fluids during fluid injection into a confined porous layer. The present work focuses further on the pressure evolution. In particular, we present self-similar solutions for the pressure evolution at both the early and late times. Two dimensionless parameters are recognised, including the viscosity ratio $M$ and the rescaled buoyancy $G$, and their specific role on the pressure evolution is clarified. Laboratory experiments are also performed to measure the pressure evolution at two specific locations during the propagation of a viscous gravity current within a vertically placed Hele-Shaw cell, with a favourable comparison with the model prediction in the unconfined regime. The obtained pressure solutions are also used to explain the field data of bottom-hole-pressure (BHP) evolution from a geological $\textrm {CO}_2$ sequestration project, considering both fluid injection and shut-in operations. The model and solutions might also be of use to assess reservoir injectivity and develop pressure-based monitoring technologies at well bores.

Spatially evolving turbulent/turbulent interfaces (TTIs) in the absence of mean shear are studied using direct numerical simulation (DNS). To this end, a novel approach was developed, allowing for six different TTIs to be created with a Taylor-based Reynolds number in the range of $146 \lesssim {Re}_{\lambda }\lesssim 296$. The analysis of classical statistics of turbulence intensity, fluctuating vorticity and integral length scale clearly indicates that one of the two distinct turbulent regions bounding the interface tends to dominate the other one. The half-width thickness is found to be dependent on the turbulent properties of each layer, ultimately suggesting that the large-scale quantities dictate the spreading of each turbulent region. Small scale quantities, e.g. the enstrophy, exhibit an universal conditional mean profile when normalised by the local Kolmogorov (velocity and time) scales of motion. In contrast, the large-scale properties of the flow do not modify the enstrophy statistics. Additionally, when taking the difference of fluctuating vorticity levels on each layer ad extremum, profiles typical of turbulent/non-turbulent interfaces (TNTIs) are observed. The budget terms of enstrophy and rate-of-strain magnitude support these findings.

The Stokes boundary layer (SBL) is the oscillating flow above a flat plate. Its laminar flow becomes linearly unstable at a Reynolds number of $\textit{Re} = U_0 \sqrt {T_0/\nu } \approx 2511$, where $U_0$ is the amplitude of the oscillation, $T_0$ is the period of oscillation and $\nu$ is the fluid’s kinematic viscosity, but turbulence is observed subcritically for $\textit{Re} \gtrsim 700$. The state space consists of laminar and turbulent basins of attraction, separated by a saddle point (the ‘edge state’) and its stable manifold (the ‘edge’). This work presents the edge trajectories for the transitional regime of the SBL. Despite linear dynamics disallowing the lift-up mechanism in the laminar SBL, edge trajectories are dominated by coherent structures as in other canonical shear flows: streaks, rolls and waves. Stokes boundary layer structures are inherently periodic, interacting with the oscillating flow in a novel way: streaks form near the plate, migrate upward at a speed $2\sqrt {\pi }$ and dissipate. A streak-roll-wave decomposition reveals a spatiotemporally evolving version of the self-sustaining process (SSP): (i) rolls lift fluid near the plate, generating streaks (via the lift-up mechanism); (ii) streaks can only persist in regions with the same sign of laminar shear as when they were created, defining regions that moves upward at a speed $2 \sqrt {\pi }$; (iii) the sign of streak production reverses at a roll stagnation point, destroying the streak and generating waves; (iv) trapped waves reinforce the rolls via Reynolds stresses; (v) mass conservation reinforces the rolls. This periodic SSP highlights the role of flow oscillations in sustaining transitional structures in the SBL, providing an alternative picture to ‘bypass’ transition, which relies on pre-existing free stream turbulence and spanwise vortices.