The problem of axisymmetric supersonic laminar flow separation over a compression corner has not been considered within the framework of triple-deck theory for several decades, despite significant advances in both theoretical methods and numerical techniques. In this study, we revisit the problem considered by Gittler & Kluwick (J. Fluid Mech., vol. 179, 1987, pp. 469–487), using the numerical method of Ruban (Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, vol. 18, issue 5, 1978, pp. 1253–1265) and Cassel et al. (J. Fluid Mech., vol. 300, 1995, pp. 265–285), termed the Ruban–Cassel method (RCM). The solution shows good agreement with the results of Gittler & Kluwick (J. Fluid Mech., vol. 179, 1987, pp. 469–487) for a scale external radius of 1 and scale angles from 1 to 6. However, for scale angles above 6.8, a wave packet appears. This wave packet is similar to that reported by Cassel et al. (J. Fluid Mech., vol. 300, 1995, pp. 265–285) for two-dimensional supersonic flow. As the external scale radius increases (from 1 to 10), the axisymmetric solution converges towards the two-dimensional solution for equivalent scale angle values. For a scale external radius of 10, the wave packet appears at a scale angle of 3.8, compared with the value of 3.9 by Cassel et al. (J. Fluid Mech., vol. 300, 1995, pp. 265–285). Inspection of the velocity profiles reveals that inflection points, while ubiquitous in shear flow, do not seem to play a relevant role in the appearance of the wave packet for the axisymmetric flow. Axisymmetric effects become more important as the scale external radius decreases below 0.5. A larger scale angle is necessary to produce a flow structure equivalent to that of the two-dimensional case. For scale external radius 0.1, the pressure gradient is substantially diminished and the solution is devoid of a second shear-stress minimum.

Active flow control based on reinforcement learning has received much attention in recent years. Indeed, the requirement for substantial data for trial-and-error in reinforcement learning policies has posed a significant impediment to their practical application, which also serves as a limiting factor in the training of cross-case agents. This study proposes an in-context active flow control policy learning framework grounded in reinforcement learning data. A transformer-based policy improvement operator is set up to model the process of reinforcement learning as a causal sequence and autoregressively give actions with sufficiently long context on new unseen cases. In flow separation problems, this framework demonstrates the capability to successfully learn and apply efficient flow control strategies across various airfoil configurations. Compared with general reinforcement learning, this learning mode without the need for updating the network parameter has even higher efficiency. This study presents an effective novel technique in using a single transformer model to address the flow separation active flow control problem on different airfoils. Additionally, the study provides an innovative demonstration of incorporating reinforcement-learning-based flow control with aerodynamic shape optimization, leading to collective enhancement in performance. This method efficiently lessens the training burden of the new flow control policy during shape optimization, and opens up a promising avenue for interdisciplinary intelligent co-design of future vehicles.

We present a theory that quantifies the interplay between intrapore and interpore flow variabilities and their impact on hydrodynamic dispersion. The theory reveals that porous media with varying levels of structural disorder exhibit notable differences in interpore flow variability, characterised by the flux-weighted probability density function (PDF), $\hat {\psi }_\tau (\tau ) \sim \tau ^{-\theta -2}$, for advection times $\tau$ through conduits. These differences result in varying relative strengths of interpore and intrapore flow variabilities, leading to distinct scaling behaviours of the hydrodynamic dispersion coefficient $D_L$, normalised by the molecular diffusion coefficient $D_m$, with respect to the Péclet number $Pe$. Specifically, when $\hat {\psi }_\tau (\tau )$ exhibits a broad distribution of $\tau$ with $\theta$ in the range of $(0, 1)$, the dispersion undergoes a transition from power-law scaling, $D_L/D_m \sim Pe^{2-\theta }$, to linear scaling, $D_L/D_m \sim Pe$, and eventually to logarithmic scaling, $D_L/D_m \sim Pe\ln (Pe)$, as $Pe$ increases. Conversely, when $\tau$ is narrowly distributed or when $\theta$ exceeds 1, dispersion consistently follows a logarithmic scaling, $D_L/D_m \sim Pe\ln (Pe)$. The power-law and linear scaling occur when interpore variability predominates over intrapore variability, while logarithmic scaling arises under the opposite condition. These theoretical predictions are supported by experimental data and network simulations across a broad spectrum of porous media.

Gas-encapsulated drops, much like antibubbles, are drops enclosed in a bubble within a liquid. They show potential as payload carriers in fluid transport and mixing techniques where sound waves can be leveraged to induce the collapse of the gas core and the subsequent release of the drop. Here, the interaction of millimetre-sized gas-encapsulated drops with impulsive laser-induced shock waves is investigated to gain fundamental insights into the release process. Experimental synchrotron X-ray phase contrast imaging, which allows the drop dynamics to be visualised inside the encapsulating bubble, is complemented by numerical simulations to study the intricate physics at play. Three drop dynamical release regimes are discovered, namely the drop impact, partial deposition and jet impact regimes. The regime type is mainly dependent on the shape of the bubble interface impacting the drop and the associated Weber and Reynolds numbers. The drop dynamics of the drop impact and partial deposition regimes show similarities with the canonical configuration of drops impacting flat liquid surfaces, whereas the jet impact regime resembles binary drop collisions, which allows existing scaling laws to be applied to describe the underlying processes. The release of the drop is investigated numerically. The time evolution of the drop dissemination within the surrounding liquid discloses enhanced mixing for dynamics involving high Weber and Reynolds numbers such as the drop impact and jet impact regimes.

The lubricated motion of an object near a deformable boundary presents striking subtleties arising from the coupling between the elasticity of the boundary and lubricated flow, including but not limited to the emergence of a lift force acting on the object despite the zero Reynolds number. In this study, we characterize the hydrodynamic forces and torques felt by a sphere translating in close proximity to a fluid interface, separating the viscous medium of the sphere's motion from an infinitely more viscous medium. We employ lubrication theory and perform a perturbation analysis in capillary compliance. The dominant response of the interface owing to surface tension results in a long-ranged interface deformation, which leads to a modification of the forces and torques with respect to the rigid reference case, that we characterize in detail with scaling arguments and numerical integrations.

This paper derives the upper bound on heat transport in supergravitational turbulent thermal convection analytically and numerically. Using a piecewise background profile, the functional inequality analysis delivers a suboptimal bound $Nu\lesssim -({3\sqrt {3}}/{2})({\eta \ln (\eta )}/({1-\eta ^2}))\,Ra^{1/2}$ as $Ra\rightarrow \infty$, where $Nu$ is the Nusselt number, $\eta$ is the radius ratio of the inner cylinder to the outer cylinder ($0<\eta <1$), and $Ra$ is the Rayleigh number. A variational problem yielded from Doering–Constantin–Hopf formalism is solved asymptotically and numerically, which delivers a better upper bound than the piecewise background profile. The asymptotic analysis and numerical data indicate that the current best bound is given by $Nu\leqslant -0.106({\eta \ln (\eta )}/({(1-\eta )(1+\sqrt {\eta })^2}))\,Ra^{1/2}$. Both analytical and numerical results demonstrate that the upper bound can be significantly reduced by the curvature effect. Unlike the traditional Rayleigh–Bénard turbulence, in which the optimal perturbation yielded from the variational problem is always two-dimensional, the present study shows that three-dimensional perturbations, annular perturbations and axisymmetric perturbations can be induced by the curvature effect simultaneously. However, we show that the bound yielded from the three-dimensional variational problem is very close to the axisymmetric situation as $\eta$ increases and $Ra$ increases.

Surface roughness significantly modifies the liquid film thickness entrained when dip coating a solid surface, particularly at low coating velocity. Using a homogenization approach, we present a predictive model for determining the liquid film thickness coated on a rough plate. A homogenized boundary condition at an equivalent flat surface is used to model the rough boundary, accounting for both flow through the rough texture layer, through an interface permeability term, and slip at the equivalent surface. While the slip term accounts for tangential velocity induced by viscous shear stress, accurately predicting the film thickness requires the interface permeability term to account for additional tangential flow driven by pressure gradients along the interface. We find that a greater degree of slip and interface permeability signifies less viscous stress that would promote deposition, thus reducing the amount of free film coated above the textures. The model is found to be in good agreement with experimental measurements, and requires no fitting parameters. Furthermore, our model may be applied to arbitrary periodic roughness patterns, opening the door to flexible characterization of surfaces found in natural and industrial coating processes.

Hydrodynamic interactions between swimming or flying organisms can lead to complex flows on the scale of the group. These emergent fluid dynamics are often more complex than a linear superposition of individual organism flows, especially at intermediate Reynolds numbers. This paper presents an approach to estimate the flow induced by multiple swimmer wakes in proximity using a semianalytical model that conserves mass and momentum in the aggregation. The key equations are derived analytically, while the implementation and solution of these equations are carried out numerically. This model was informed by and compared with empirical measurements of induced vertical migrations of brine shrimp, Artemia salina. The response of individual swimmers to ambient background flow and light intensity was evaluated. In addition, the time-resolved three-dimensional spatial configuration of the swimmers was measured using a recently developed laser scanning system. Numerical results using the model found that the induced flow at the front of the aggregation was insensitive to the presence of downstream swimmers, with the induced flow tending towards asymptotic beyond a threshold aggregation length. Closer swimmer spacing led to higher induced flow speeds, in some cases leading to model predictions of induced flow exceeding swimmer speeds required to maintain a stable spatial configuration. This result was reconciled by comparing two different models for the near-wake of each swimmer. The results demonstrate that aggregation-scale flows result from a complex, yet predictable interplay between individual organism wake structure and aggregation configuration and size.

When they occur, azimuthal thermoacoustic oscillations can detrimentally affect the safe operation of gas turbines and aeroengines. We develop a real-time digital twin of azimuthal thermoacoustics of a hydrogen-based annular combustor. The digital twin seamlessly combines two sources of information about the system: (i) a physics-based low-order model; and (ii) raw and sparse experimental data from microphones, which contain both aleatoric noise and turbulent fluctuations. First, we derive a low-order thermoacoustic model for azimuthal instabilities, which is deterministic. Second, we propose a real-time data assimilation framework to infer the acoustic pressure, the physical parameters, and the model bias and measurement shift simultaneously. This is the bias-regularized ensemble Kalman filter, for which we find an analytical solution that solves the optimization problem. Third, we propose a reservoir computer, which infers both the model bias and measurement shift to close the assimilation equations. Fourth, we propose a real-time digital twin of the azimuthal thermoacoustic dynamics of a laboratory hydrogen-based annular combustor for a variety of equivalence ratios. We find that the real-time digital twin (i) autonomously predicts azimuthal dynamics, in contrast to bias-unregularized methods; (ii) uncovers the physical acoustic pressure from the raw data, i.e. it acts as a physics-based filter; (iii) is a time-varying parameter system, which generalizes existing models that have constant parameters, and capture only slow-varying variables. The digital twin generalizes to all equivalence ratios, which bridges the gap of existing models. This work opens new opportunities for real-time digital twinning of multi-physics problems.

Developed in this study is a theoretical description of squeeze-film lubrication systems that involve the flexural oscillation of a thin plate near a parallel wall. Such systems were discovered in recent experiments to produce load-bearing attractive forces that are a thousandfold stronger than those generated by rigid oscillators, which typically favour repulsion. Analyses of squeeze-film gas flow driven by a presumed plate deformation reproduce the observed magnification of attractive load capacity, but exhibit serious discrepancies with crucial aspects of the experimental measurements – most importantly, the precise distribution of air pressure along the film. The discrepancies are resolved in this study by accounting for the presence of two-way-coupled fluid–structure interactions whereby the undulations of the plate, modelled here with use of the classical Kirchhoff–Love equation, are affected non-negligibly by the evolving pressure, described by a modified Reynolds lubrication equation that accounts for compressibility. The resulting problem of elastohydrodynamic lubrication is solved with use of perturbation methods that exploit the limit of small oscillation amplitudes. The analysis ultimately provides an explicit expression specifying the attractive load capacity of a squeeze-film system as a function of relevant operating parameters – including, in particular, the amplitude and frequency of the localized excitation force exerted on the plate. The rudimentary theory derived here may be readily generalized to guide the analysis and development of a wide variety of emerging engineering systems that exploit the vibration-induced squeeze-film effect – such as wall-climbing soft robots and contactless grippers.