A deep reinforcement learning method for training a jellyfish-like swimmer to effectively track a moving target in a two-dimensional flow was developed. This swimmer is a flexible object equipped with a muscle model based on torsional springs. We employed a deep Q-network (DQN) that takes the swimmer’s geometry and dynamic parameters as inputs, and outputs actions that are the forces applied to the swimmer. In particular, an action regulation was introduced to mitigate the interference from complex fluid–structure interactions. The goal of these actions is to navigate the swimmer to a target point in the shortest possible time. In the DQN training, the data on the swimmer’s motions were obtained from simulations using the immersed boundary method. During tracking a moving target, there is an inherent delay between the application of forces and the corresponding response of the swimmer’s body due to hydrodynamic interactions between the shedding vortices and the swimmer’s own locomotion. Our tests demonstrate that the swimmer, with the DQN agent and action regulation, is able to dynamically adjust its course based on its instantaneous state. This work extends the application scope of machine learning in controlling flexible objects within fluid environments.

In this study, the statistical properties and formation mechanisms of particle clusters that consider the influence of particle–wall interactions in particle-laden wall turbulence are systematically investigated through wind tunnel experiments. In the experiments, two particle release modes, including particle top-releasing mode (Case 1) and particle locally laying mode (Case 2), were adopted to establish varying conditions with different particle–wall interaction strengths. The Voronoï diagram method was employed to identify the particle clusters, and the impact of particle–wall interactions on the characteristics of the clusters was analysed. The results indicate that particle–wall interaction is the predominant factor in the formation of particle clusters in the near-wall region. Under Case 1 and Case 2, the maximum concentration of particles in the clusters could reach nearly five times the average particle concentration; however, the clusters with large particle numbers ($N_C\gt 5$) in Case 1 tended to form near the wall and the vertical velocities of these clusters were greater than the average velocities of all particles. In contrast, under Case 2, clusters with large particle numbers exhibited a higher probability of occurrence further from the wall and the vertical velocities of these clusters were lower than the average velocity of all particles. Furthermore, this study found that the presence of particle clusters in these flows significantly alters the flow field properties surrounding them, implying that a region of high strain and low vorticity constitutes an essential but non-sufficient condition for the generation of particle clusters in wall turbulence.

We theoretically investigate the small-amplitude broadside oscillations of an annular disk within an unbounded fluid domain. Specifically, we formulate a semi-analytical framework to examine the effects of the oscillation frequency and pore radius on the disk’s added mass and damping coefficients. By leveraging the superposition principle, we decompose the complex original problem into two simpler ones. The force exerted on the disk by the fluid is linked to the solutions of these sub-problems through the reciprocal theorem; the first solution is readily available, while the second is derived asymptotically, assuming a small inner radius. Both solutions are evaluated by transforming dual integral equations into systems of algebraic equations, which are then solved numerically. Building on these solutions, we extract asymptotic expressions for the variations of the quantities of interest in the limits of low and high oscillatory Reynolds numbers. Notably, at high frequencies, we uncover a previously overlooked logarithmic term in the force coefficient expansions, absent in prior scaling analyses of oscillating solid (impermeable) disks. Our findings indicate that, when viscosity plays a dominant role, an annular (porous) disk behaves similarly to a solid one, with reductions in the force coefficients scaling with the cube of the pore radius. We also discover, perhaps surprisingly, that, as inertial effects intensify, the damping coefficient initially increases with the pore radius, reaches a maximum and subsequently declines as the disk’s inner hole enlarges further; at its peak, it can exceed the value for an equivalent solid disk by up to approximately 62 % in the asymptotic limit of extremely high oscillatory Reynolds number. Conversely, the added mass coefficient decreases monotonically with increasing porosity. The decay rate of the added mass in the inertial regime initially scales with the cube of the pore radius before transitioning to linear scaling when the pore radius is no longer extremely small. Although our analysis assumes a small pore radius, direct numerical simulations confirm that our asymptotic formulation remains accurate for inner-to-outer radius ratios up to at least $1/2$.

Elastoviscoplastic (EVP) fluid flows are driven by a non-trivial interplay between the elastic, viscous and plastic properties, which under certain conditions can transition the otherwise laminar flow into complex flow instabilities with rich space–time-dependent dynamics. We discover that under elastic turbulence regimes, EVP fluids undergo dynamic jamming triggered by localised polymer stress deformations that facilitate the formation of solid regions trapped in local low-stress energy wells. The solid volume fraction $\phi$, below the jamming transition $\phi\lt\phi_J$, scales with $\sqrt {\textit{Bi}}$, where $\textit{Bi}$ is the Bingham number characterising the ratio of yield to viscous stresses, in direct agreement with theoretical approximations based on the laminar solution. The onset of this new dynamic jamming transition $\phi \geqslant \phi _J$ is marked by a clear deviation from the scaling $\phi \sim \sqrt {\textit{Bi}}$, scaling as $\phi \sim \exp {\textit{Bi}}$. We show that this instability-induced jamming transition – analogous to that in dense suspensions – leads to slow, minimally diffusive and rigid-like flows with finite deformability, highlighting a novel phase change in elastic turbulence regimes of complex fluids.

Recent studies reveal the central role of chaotic advection in controlling pore-scale processes including solute mixing and dispersion, chemical reactions, and biological activity. These dynamics have been observed in porous media (PM) with a continuous solid phase (such as porous networks) and PM comprising discrete elements (such as granular matter). However, a unified theory of chaotic advection across these continuous and discrete classes of PM is lacking. Key outstanding questions include: (i) topological unification of discrete and continuous PM; (ii) the impact of the non-smooth geometry of discrete PM; (iii) how exponential stretching arises at contact points in discrete PM; (iv) how fluid folding arises in continuous PM; (v) the impact of discontinuous mixing in continuous PM; and (vi) generalised models for the Lyapunov exponent in both PM classes. We address these questions via a unified theory of pore-scale chaotic advection. We show that fluid stretching and folding (SF) in discrete and continuous PM arise via the topological complexity of the medium. Mixing in continuous PM manifests as discontinuous mixing through a combination of SF and cutting and shuffling (CS) actions, but the rate of mixing is governed by SF only. Conversely, discrete PM involves SF motions only. These mechanisms are unified by showing that continuous PM is analogous to discrete PM with smooth, finite contacts. This unified theory provides insights into the pore-scale chaotic advection across a broad class of porous materials and points to design of novel porous architectures with tuneable mixing and transport properties.

The pressure effects on the mixing fields of non-reacting and reacting jets in cross-flow are studied using large eddy simulation (LES). A hydrogen jet diluted with 30 % helium is injected perpendicularly into a cross-stream of air at four different pressures: 1, 4, 7 and 15 bar. The resulting interaction and the mixing fields under non-reacting and reacting conditions are simulated using LES. The subgrid scale combustion is modelled using a revised flamelet model for the partially premixed combustion. Good agreement of computed and measured velocity fields for reacting and non-reacting conditions is observed. Under non-reacting conditions, the mixing field shows no sensitivity to the pressure, whereas notable changes are observed for reacting conditions. The lifted flame at 1 bar moves upstream and attaches to the nozzle as the pressure is increased to 4 bar and remains so for the other elevated pressures because of the increasing burning mass flux with pressure. This attached flame suppresses the fuel–air mixing in the near-nozzle region. The premixed and non-premixed contributions to the overall heat release in the partially premixed combustion are analysed. The non-premixed contribution is generally low and occurs in the near-field region of the fuel jet through fuel-rich mixtures in the shear layer regions, and decreases substantially further with the increase in pressure. Hence, the predominant contributions are observed to come from premixed modes and these contributions increase with pressure.

A block of ice in a box heated from below and cooled from above can (partially) melt. Vice versa, a box of water with less heating from below or more cooling from above can (partially) re-solidify. This study investigates the asymmetric behaviours between such melting and freezing processes in this Rayleigh–Bénard geometry, focusing on differences in equilibrium flow structures, solid–liquid interface morphology, and equilibrium mean interface height. Our findings reveal a robust asymmetry across a range of Rayleigh numbers and top cooling temperature (i.e. hysteretic behaviour), where the evolution of freezing shows a unique ‘splitting event’ of convection cells that leads to a non-monotonic height evolution trend. To characterise the differences between melting and freezing, we introduce an effective Rayleigh number and the aspect ratio for the cellular structures, and apply the heat flux balance and the Grossmann–Lohse theory. Based on this, we develop a unifying model for the melting and freezing behaviour across various conditions, accurately predicting equilibrium states for both phase-change processes. This work provides insights into the role of convective dynamics in phase-change symmetry-breaking, offering a framework applicable to diverse systems involving melting and freezing.

The shape of a free-surface slump of viscoplastic material supported by an oblique barrier on an inclined plane is investigated theoretically and experimentally. The barrier is sufficiently tall that it is not surmounted by the viscoplastic fluid, and a focus of this study is the largest volume of rigid viscoplastic fluid that can be supported upstream of it. A lubrication model is integrated numerically to determine the transient flow as the maximal rigid shape is approached. Away from the region supported by the barrier, the viscoplastic layer attains a uniform thickness in which the gravitational stresses are in balance with the yield stress of the material. However, closer to the barrier, the layer thickens and the barrier bears the additional gravitational loading. An exact solution for the rigid shape of the viscoplastic material is constructed from the steady force balance and computed by integrating Charpit’s equations along characteristics that emanate from the barrier wall. The characteristics represent the late-time streamlines of the flow as it approaches the rigid shape. The exact solution depends on a single dimensionless group, which incorporates the slope inclination, the barrier width and the fluid’s yield stress. It is shown that the shape is insensitive to the transient flow from which it originates. The force exerted by the slump is calculated for different barrier shapes. The results of new laboratory experiments are reported; these show that although convergence to the final rigid state is slow, there is good agreement with the experimental measurements at long times.

This study examines the similarity properties of hypersonic turbulent boundary layers using direct numerical simulations within a two-species mixture, composed of molecular and atomic oxygen. A dissociation–recombination mechanism is considered, at varying reaction rates. The results show that while the hydrodynamic field remains largely unaffected by changes in reaction rates, temperature profiles are slightly altered, with faster reactions leading to lower temperature peaks. The chemical mechanisms significantly influence the wall heat flux, with frozen chemistry overestimating the flux. The reference simulations are compared with companion calculations, where chemical reactions are activated downstream within the fully turbulent region. These calculations represent set-ups in which the computational domain effectively starts with an inflow in a fully turbulent state, where hydrodynamic and thermal quantities are accurately described at the boundary and the chemical inflow profile is derived from a frozen-chemistry assumption. In this set-up, chemical source terms rapidly relax towards the baseline downstream of the chemistry activation location. This behaviour is due to an approximate global self-similarity shown by the chemical species transport in the fully turbulent region. Unlike laminar boundary layers where streamwise fluxes are relevant, source terms are balanced only by wall-normal transport in the turbulent region. A chemical relaxation length scale is introduced to collapse the results of all mechanisms.

Accurately predicting the mean flow properties of wall-bounded turbulence is essential for both fundamental research and engineering applications. In atmospheric boundary layers, the mean flow within the surface layer is typically described by Monin–Obukhov similarity theory (MOST). However, beyond the surface layer, MOST no longer applies as the Coriolis effect becomes significant. To address this issue, this study introduces a novel analytical model for the mean turbulent momentum fluxes and geostrophic wind deficits in nocturnal stable atmospheric boundary layers (NSBLs), which are stably stratified near the surface and transition to neutrally stratified flow above. The model solutions are derived from the Ekman equations using the eddy viscosity approach and a new parametrisation of the flux Richardson number. The solutions show that the geostrophic wind deficits scale with $u_*^2/(hf)$, where $u_*$ is the friction velocity, $h$ is the boundary layer height, and $f$ is the Coriolis parameter. The model’s predictions align closely with recent large-eddy simulation studies, confirming the model’s accuracy. Combined with the geostrophic drag law, the model can reliably predict the wind speed profile above the surface layer of NSBLs. This work marks a significant step in modelling atmospheric turbulence and its fundamental dynamics.

The reactivity of transverse waves in detonations of methane, oxygen and nitrogen are experimentally assessed using MHz rate schlieren and chemiluminescence imaging. In these highly unstable mixtures, the mode of wave propagation is more complex than what is described by the cellular instability model that is conventionally used for weakly unstable mixtures. Behind the low-speed leading shock in unstable waves, the processed gas remains essentially unreacted until transverse waves reach this region. In highly unstable waves, the transverse waves have a range of reactivity, that is rates of reaction in the flow immediately behind the wave. In this study, we present examples of transverse waves for near-limit detonations and analyse four cases in detail. In some cases, these waves appear to be essentially non-reactive or cause very slow reaction. In other cases, the transverse waves can be highly reactive. In the most extreme example, the transverse wave is propagating at the Chapman–Jouguet speed with a small reaction zone, i.e. a transverse detonation. A reactive oblique shock model is used to approximate the triple-point configuration of this case as a double-Mach reflection, which shows good agreement with the images. The reaction evolution along path lines is analysed using detailed reaction mechanisms and considerations about flow-field unsteadiness. Length scales of the energy release and expansion processes within the reaction zone region are used to explain the observed modes of wave propagation and interaction.