The measurement of lift on symmetrically shaped obstacles immersed in low Reynolds number flow is the quintessential way to signal odd viscosity. For flow past cylinders, such a lift force does not arise if incompressibility and no-slip boundary conditions are fulfilled, whereas for spheres, a lift force has been found in Stokes flow, which is valid for cases where the Reynolds numbers are negligible and convection can be ignored. When considering the role of convection at low but non-zero Reynolds numbers, two hurdles arise, the Whitehead paradox and the breaking of axial symmetry, which are overcome by the method of matched asymptotic expansions and the Lorentz reciprocal theorem, respectively. We also consider the case where axial symmetry is preserved because the translation of the sphere is aligned with the axis of chirality of odd viscosity. We find that while lift vanishes, the interplay between odd viscosity and convection gives rise to a stream-induced torque.

Consider the flow through a channel with grooved edges on one (or both) side(s). If heating is applied to the boundaries, thermal drift is the flow generated by the interaction of the groove and heating patterns. It is known that, if one side of a channel is smooth while the other is grooved, the application of heating forms a so-called ‘thermal drift engine’. Two thermal drift engines are activated if both surfaces are grooved, and these may reinforce or oppose each other. Carefully choosing these engines can lead to an intensification of the thermal drift. The interplay of two drift engines is explored using a horizontal slot with grooves that have a sinusoidal profile with a prescribed wavenumber $\alpha $. It is shown that the strength of the flow decreases proportional to $\alpha $ as $\alpha \to 0$ and proportional to ${\alpha ^{ - 1}}$ as $\alpha \to \infty $. We determine the value of $\alpha $ corresponding to the strongest flow and characterize how the conclusions should be modified if a uniform heating component is added to the heating pattern.

Direct numerical simulations of oscillatory flow over a bed made of ripples have been performed. Two oscillatory flow forcing mechanisms have been compared: (i) a sinusoidal external pressure gradient (pressure-driven flow); and (ii) a sinusoidal velocity boundary conditions on the rippled bed (shear-driven flow). In the second case, the oscillations of the bed are such that when observed from a reference frame fixed with the bed, the free stream follows the same harmonic oscillation as in the pressure-driven case. While the outer layers have the same dynamics in the two cases, close to the bed differences are observed during the cycle, mostly because the large form drag across the ripples cannot be reproduced in the shear-driven case. A comparison against experimental data from an oscillating tray apparatus provides a relatively good agreement for the phase-averaged flow when the same forcing is considered (i.e. a shear-driven flow). The pressure-driven case has a comparable error to the shear-driven numerical results over the crest of the ripples, whereas the discrepancy is larger at the troughs. The discrepancies between the two cases are more limited for time-averaged flow quantities, such as the mean flow pattern and the time-averaged Reynolds stress distribution. This suggests that numerical or experimental shear-driven configurations may capture well the net effects of coastal transport processes (which occur in pressure-driven oscillatory flow), but care should be exercised in interpreting phase-dependent dynamics near the troughs. More work is needed to fully assess the sensitivity to the forcing mechanisms in different flow regimes.

We investigate exact nonlinear waves on surfaces locally approximating the rotating sphere for two-dimensional inviscid incompressible flow. Our first system corresponds to a $\beta$-plane approximation at the equator, and the second to a $\gamma$ approximation, with the latter describing flow near the poles. We find exact wave solutions in the Lagrangian reference frame that cannot be written down in closed form in the Eulerian reference frame. The wave particle trajectories, contours of potential vorticity and Lagrangian mean velocity take relatively simple forms. The waves possess a non-trivial Lagrangian mean flow that depends on the amplitude of the waves and on a particle label that characterizes values of constant potential vorticity. The mean flow arises due to potential vorticity conservation on fluid particles. Solutions over the entire space are generated by assuming that the flow far from the origin is zonal and there is a region of uniform potential vorticity between this zonal flow and the waves. In the $\gamma$ approximation, a class of waves is found that, based on analogous solutions on the plane, we call Ptolemaic vortex waves. The mean flow of some of these waves, which we can describe in highly nonlinear scenarios due to the exact nature of the solutions, resembles polar jet streams. Several illustrative solutions are used as initial conditions in the fully spherical rotating Navier–Stokes equations, where integration is performed via the numerical scheme presented in Salmon & Pizzo (Atmosphere, vol. 14, issue 4, 2023, 747). The potential vorticity contours found from these numerical experiments vary between stable permanent progressive form and fully turbulent flows generated by wave breaking.

The orientation dynamics of inertialess prolate and oblate spheroidal particles in a directly simulated spanwise-rotating turbulent channel flow has been investigated by means of an Eulerian–Lagrangian point-particle approach. The channel rotation and the particle shape were parameterized using a rotation number Ro and the aspect ratio λ, respectively. Eleven particle shapes 0.05 ≤ λ ≤ 20 and four rotation rates 0 ≤ Ro ≤ 10 have been examined. The spheroidal particles retained their almost isotropic orientation in the core region of the channel, despite the significant mean shear rate set up by the Coriolis force. Irrespective of channel rotation rate Ro, rod-like spheroids tend to align in the streamwise direction, while disk-like particles are oriented in the wall-normal direction. These trends were accentuated with increasing departure from sphericity λ = 1. The changeover from the isotropic orientation mode in the centre to the highly anisotropic near-wall orientation mode commenced further away from the suction-side wall with increasing Ro, whereas the particle orientations on the pressure side of the rotating channel remained essentially unaffected by Ro. We observed that the alignments of the fluid rotation vector with the Lagrangian stretching direction were similarly unaffected by the imposed system rotation, except that the de-alignment set in deeper into the core at high Ro. This contrasts with the well-known substantial impact of system rotation on the velocity and vorticity fields. Similarly, slender rods and flatter disks were aligned with the Lagrangian stretching and compression directions, respectively, for all Ro considered, except in the vicinity of the walls. The typical near-wall de-alignment extended considerably further away from the suction-side wall at high Ro. We conjecture that this phenomenon reflects a change in the relative importance of mean shear and small-scale turbulence caused by the Coriolis force. Preferential particle alignment with Lagrangian stretching and compression directions are known from isotropic and anisotropic turbulence in inertial reference systems. The present results demonstrate the validity of this principle also in a non-inertial system.

Self-sustained thermoacoustic oscillations as observed in low-emission combustion- involved gas turbines and aero-engines involve complicated thermal fluid–acoustics interaction and rich nonlinear dynamics. Such pulsating oscillations are known as thermoacoustic instability. When it occurs, large-amplitude limit cycle oscillations (LCOs) of thermodynamic parameters are frequently observed. These LCOs could cause overheating, flame flashback, and even engine failures. Thus it is critical to understand and predict the generation mechanisms and nonlinear dynamics behaviours, and then develop corresponding control approaches to prevent or control the onset of such instabilities. In this work, we develop and extend the classical van der Pol oscillators by integrating a physics-informed neural networks (PINNs) algorithm with a modelled nonlinear Rijke-type thermoacoustic combustor. The theoretical Rijke tube system (with Galerkin expansion and modified King's law implemented) and a CFD simulation model are applied to provide ‘training/calibration data’ for the extended van der Pol (EVDP)-PINNs model. The optimized EVDP oscillators are confirmed to be capable of capturing the key nonlinear characteristics by comparing the transient growth behaviours of thermodynamic perturbations and LCO amplitude and frequency. Further investigations are conducted to obtain Hopf bifurcation and amplitude death (AD) characteristics. Comparison is then made to the coupled EVDP systems. Quite similar Hopf bifurcation features, but differences in regions of AD, are observed. In general, we demonstrate an applicable approach to intelligently ‘learn’ a nonlinear thermoacoustic system and to create reliable EVDP oscillator systems, which have great potential to contribute to the development and testing of control approaches, such as the coupling described in this work, which may replace costly experimental tests.

Flying insects exhibit remarkable capabilities in coordinating their olfactory sensory system and flapping wings during odour plume-tracking flights. While observations have indicated that their flapping wing motion can ‘sniff’ up the incoming plumes for better odour sampling range, how flapping motion impacts the odour concentration field around the antennae is unknown. Here, we reconstruct the body and wing kinematics of a forwards-flying butterfly based on high-speed images. Using an in-house computational fluid dynamics solver, we simulate the unsteady flow field and odourant transport process by solving the Navier–Stokes and odourant advection-diffusion equations. Our results show that, during flapping flight, the interaction between wing leading-edge vortices and antenna vortices strengthens the circulation of antenna vortices by over two-fold compared with cases without flapping motion, leading to a significant increase in odour intensity fluctuation along the antennae. Specifically, the interaction between the wings and antennae amplifies odour intensity fluctuations on the antennae by up to 8.4 fold. This enhancement is critical in preventing odour fatigue during odour-tracking flights. Further analysis reveals that this interaction is influenced by the inter-antennal angle. Adjusting this angle allows insects to balance between resistance to odour fatigue and the breadth of odour sampling. Narrower inter-antennal angles enhance fatigue resistance, while wider angles extend the sampling range but reduce resistance. Additionally, our findings suggest that while the flexibility of the wings and the thorax's pitching motion in butterflies do influence odour fluctuation, their impact is relatively secondary to that of the wing–antenna interaction.

The spatio-temporal scales, as well as a comprehensive self-sustained mechanism of the reattachment unsteadiness in shock wave/boundary layer interaction, are investigated in this study. Direct numerical simulations reveal that the reattachment unsteadiness of a Mach 7.7 laminar inflow causes over $26\,\%$ variation in wall friction and up to $20\,\%$ fluctuation in heat flux at the reattachment of the separation bubble. A statistical approach, based on the local reattachment upstream movement, is proposed to identify the spanwise and temporal scales of reattachment unsteadiness. It is found that two different types, i.e. self-induced and random processes, dominate different regions of reattachment. A self-sustained mechanism is proposed to comprehend the reattachment unsteadiness in the self-induced region. The intrinsic instability of the separation bubble transports vorticity downstream, resulting in an inhomogeneous reattachment line, which gives rise to baroclinic production of quasi-streamwise vortices. The pairing of these vortices initiates high-speed streaks and shifts the reattachment line upstream. Ultimately, viscosity dissipates the vortices, triggering instability and a new cycle of reattachment unsteadiness. The temporal scale and maximum vorticity are estimated with the self-sustained mechanism via order-of-magnitude analysis of the enstrophy. The advection speed of friction, derived from the assumption of coherent structures advecting with a Blasius-type boundary layer, aligns with the numerical findings.

We use direct numerical simulations to study convection in rotating Rayleigh–Bénard convection in horizontally confined geometries of a given aspect ratio, with the walls held at fixed temperatures. We show that this arrangement is unconditionally unstable to flow that takes the form of wall-adjacent convection rolls. For wall temperatures close to the temperatures of the upper or lower boundaries, we show that the base state undergoes a Hopf bifurcation to a state comprised of spatiotemporal oscillations – ‘wall modes’ – precessing in a retrograde direction. We study the saturated nonlinear state of these modes, and show that the velocity boundary conditions at the upper and lower boundaries are crucial to the formation and propagation of the wall modes: asymmetric velocity boundary conditions at the upper and lower boundaries can lead to prograde wall modes, while stress-free boundary conditions at both walls can lead to wall modes that have no preferred direction of propagation.

Turbulent shear flows driven by a combination of a pressure gradient and buoyancy forcing are investigated using direct numerical simulations. Specifically, we consider the set-up of a differentially heated vertical channel subject to a Poiseuille-like horizontal pressure gradient. We explore the response of the system to its three control parameters: the Grashof number $Gr$, the Prandtl number $Pr$, and the Reynolds number $Re$ of the pressure-driven flow. From these input parameters, the relative strength of buoyancy driving to the pressure gradient can be quantified by the Richardson number $Ri=Gr/Re^2$. We compare the response of the mixed vertical convection configuration to that of mixed Rayleigh–Bénard convection, and find a nearly identical behaviour, including an increase in wall friction at higher $Gr$, and a drop in the heat flux relative to natural convection for $Ri=O(1)$. This closely matched response is despite vastly different flow structures in the systems. No large-scale organisation is visible in visualisations of mixed vertical convection – an observation that is confirmed quantitatively by spectral analysis. This analysis, combined with a statistical description of the wall heat flux, highlights how moderate shear suppresses the growth of small-scale plumes and reduces the likelihood of extreme events in the local wall heat flux. Vice versa, starting from a pure shear flow, the addition of thermal driving enhances the drag due to the emission of thermal plumes.

Shock refraction in a gas–liquid interface is ubiquitous in nature and engineering. This study investigates the shock refraction phenomena in air–water interfaces for various inclination angles. The interface inclination angles are achieved using a tiltable vertical shock tube. The time-resolved schlieren images are compared with numerical simulations performed using the BlastFoam solver in the OpenFOAM software. The stiffened gas equation of state is used to model water in the simulations. The shock polar analysis using modified shock relations for a stiffened gas is used to elucidate the refraction patterns. A regular refraction pattern with a reflected shock wave and a bound precursor refraction with a regular reflection are observed experimentally for the first time in an air–water system. Further, a new free precursor refraction pattern with a Mach reflection is observed. The transition criteria and the corresponding boundaries for each refraction pattern are demarcated in the ($M_S, \theta _w^c$)-plane. The refraction sequence and the range for various incident shock strength regimes are also identified.

We study liquid plugs in the pulmonary airways based on the two-phase axisymmetric weighted residual integral boundary-layer model of Dietze et al. (J. Fluid Mech., vol. 894, 2020, A17), which was originally developed to study liquid films coating the inner surface of a cylindrical tube in interaction with a core gas flow. The augmented form of this model, which was never applied beyond a proof of concept, allows for the representation of liquid pseudo-plugs. Here, we demonstrate its predictive power vs experiments and direct numerical simulations, in terms of the dynamics of plug formation and the characteristics of developed liquid plugs, such as their shape, flow field, speed and length, as well as the associated wall stresses and their spatial derivatives. In particular, we show that the augmented model allows us to establish a direct continuation path from travelling-wave solutions (TWS) to travelling-plug solutions (TPS). We then apply the model to predict mucus plugs in the conducting zone of the tracheobronchial tree, based on the lung architecture model of Weibel. We proceed by numerical continuation of travelling-state solutions in terms of the airway generation, whereby we impose the wavelength of the linearly most-amplified convective instability (CI) mode or that of the absolute instability (AI) mode. We identify the critical airway generation for liquid-plug formation (TWS/TPS transition), maximum potential for wall-stress-induced epithelial cell damage and CI/AI transition, and investigate how these phenomena are affected by the main control parameters, i.e. airway orientation vs gravity, air flow rate, mucus properties and airway size.

This work experimentally investigates the flow structure around a rectangular cylinder with an aspect ratio of 2 under varying incidence angles to examine how acoustic perturbations modify and modulate the unsteady flow instabilities. In the absence of acoustic excitation, the angle of incidence is found to markedly influence the flow topology and the natural shedding pattern altering the vortex formation length and wake dynamics. With acoustic perturbations, it is observed that for incidence angles $\alpha = 0^{\circ }$ and $\alpha = 5^{\circ }$, the masked impinging leading-edge vortex (ILEV)/trailing-edge vortex shedding (TEVS) instability modes of $n= 1$ and $n= 2$ become evident when their frequencies coincide with the frequencies of the acoustic perturbations (i.e. resonant condition). Both trailing-edge and leading-edge vortices were found to be modulated by the acoustic pressure cycle. These instability modes, which are naturally present under non-resonant conditions for significantly higher aspect ratios, highlight the role of incidence angle and self-excited acoustic resonance in virtually augmenting the streamwise length of the cylinder, thereby facilitating the emergence and sustenance of the ILEV/TEVS shedding pattern.

In the generalized quasilinear approximation (GQLA) (Marston et al., Phys. Rev. Lett., vol. 116, 2016, 214501), a threshold wavenumber ($k_0$) in the direction of translational symmetry segregates the total into large- ($l$) and small-scale ($h$) fields. While the governing equation for the large-scale field is fully nonlinear, that for the small scales is linearized with respect to the large-scale field. In addition, some nonlinear triad interactions are omitted in the GQLA. Herein, the GQLA is applied to two-dimensional planar Rayleigh–Bénard convection (RBC). A scale separation between the large-scale convection rolls and small-scale turbulent fluctuations is typical in RBC. The present work explores the efficacy of GQLA in capturing the scale-by-scale energy transfer processes in RBC. The initial condition for the GQLA simulations was either the statistically stationary state obtained in direct numerical simulation (DNS) or random fluctuations superimposed on the linear conductive temperature profile and $\boldsymbol {u}=0$. The GQLA simulations can capture the convection rolls for $k_0$ larger than or equal to the dominant wavenumber for thermal driving of the flow ($k_0 \ge k_{\hat {Q}}$). Additionally, the GQLA emulates the fully nonlinear dynamics for $k_0$ larger than or equal to the first harmonic of the convection-roll wavenumber ($k_0 \ge 2k_{roll}$). In the intermediate regime with $2k_{roll} > k_0 \ge k_{\hat {Q}}$, the dynamics captured in GQLA simulations is different from the DNS. In DNS, two primary energy transfer processes dominate: (i) the energy transfer to/from the convection rolls and (ii) the scale-by-scale inverse kinetic energy and forward thermal energy cascades mediated by the convection rolls. The fully nonlinear dynamics is emulated by GQLA when these energy transfer processes are faithfully reproduced. Utilizing the framework of altering the triad interactions in GQLA, an additional intrusive calculation, including target triad interactions, is performed here to study their influence. This intrusive calculation shows that the convection rolls are not captured in GQLA for $k_0 < k_{\hat {Q}}$ because of the exclusion of the $h \to l \to l$ and $l \to h \to h$ triad interactions in GQLA. The inclusion of these triad interactions in the intrusive calculation yields the convection rolls, and the reproduced dynamics is similar to that of the intermediate GQLA regime with $2k_{roll} > k_0 \ge k_{\hat {Q}}$.

Supersonic shear layers experience instabilities that generate significant adverse effects; in complex configurations, these instabilities have global impacts as they foster compounding complications with other independent flow features. We consider the flow near the exit of a dual-stream rectangular nozzle. The supersonic core and sonic bypass streams mix downstream of a splitter plate trailing edge (SPTE) just above an adjacent deck. We perform two-dimensional direct numerical simulations with laminar inflow conditions to parametrically explore the influence of active flow control, considering various actuation angles and locations. The goal is to alleviate the prominent tone associated with vortices shed at the SPTE; these vortices initiate an unsteady shock system that affects the entire flow field through a shock-induced separation and the downstream evolution of plume shear layers. Resolvent analysis is performed on the baseline flow. The identified optimal response guides the placement of steady-blowing actuators. Since the resolvent analysis fundamentally investigates the input–output dynamics of a system, it is also utilized to uncover actuation-induced changes in the forcing–response dynamics. Spectral analysis shows that the baseline flow fluctuating energy is concentrated in the shedding instability. Actuating at optimal angles based on location disperses this energy into various flow features; this affects the shedding itself, and the structure and unsteadiness of the shock system, and thus the response of the deck and nozzle wall boundary layers and the plume. The resolvent analysis indicates, and Navier–Stokes solutions confirm, that favourable control is obtained by either indirectly or directly mitigating the baseline instability.

Interface-resolved direct numerical simulations (DNS) of clustered settling suspensions in a periodic domain are performed to study the filtered drag force for clustered particle-laden flows. Our results show that, for the homogeneous system, the filtered drag is independent of the filter size, whereas for the clustered particle-laden flows, the averaged drag becomes smaller than the homogeneous drag at the filter size above 4 particle diameters. The drag reduction saturates at the filter size being comparable to the cluster size in the horizontal direction in our simulations. A new correlation is proposed to account for the mesoscale effect on the filtered drag force by using drift velocity and variance of the solid volume fraction, based on the modification of existing subgrid drag models for the inhomogeneous system. The existing models for the drift velocity and the variance of the solid volume fraction are assessed using our DNS data. A new model for the drift velocity and the variance of the solid volume fraction is proposed, based on the combination and modification of the previous models. All mesoscale models considered can predict well the filtered drag with comparable accuracy, and are superior to the homogeneous drag model for the clustered system. Our models with the same parameter values obtained from the large-scale system can also predict well the filtered drag for smaller computational domain sizes.

Shear-induced self-diffusion is a fundamental mode of transport in granular flows. Yet its critical behaviour and dependence on the particle solid fraction are still unclear. Here, we rationalize these dependencies by performing two-dimensional pressure-imposed numerical simulations of dense non-Brownian frictional suspensions. Our results, combined with existing numerical data on inertial granular flows, show that the shear-induced diffusion coefficients of both systems can be captured by a single function of the distance to jamming. They further show that the grain diffusive behaviour is underpinned by a specific random walk process, having a constant elementary step length driven at a frequency that increases with the solid fraction. The proposed scaling laws pave the way for a better understanding of mixing processes in granular media.

A novel selective mode decomposition, proper orthogonal decomposition and dynamic mode decomposition methods are used to analyse large-eddy simulation data of the flow field about a NACA0012 airfoil at low Reynolds numbers of $5\times 10^4$ and $9\times 10^4$, and at near-stall conditions. The objective of the analysis is to investigate the structure of the laminar separation bubble (LSB) and its associated low-frequency flow oscillation (LFO). It is shown that the flow field can be decomposed into three dominant flow modes: two low-frequency modes (LFO-Mode-1 and LFO-Mode-2) that govern an interplay of a triad of vortices and sustain the LFO phenomenon, and a high-frequency oscillating (HFO) mode featuring travelling Kelvin–Helmholtz waves along the wake of the airfoil. The structure and dynamics of the LSB depend on the energy content of these three dominant flow modes. At angles of attack lower than the stall angle of attack and above the angle of a full stall, the flow is dominated by the HFO mode. At angles of attack above the stall angle of attack the LFO-Mode-2 overtakes the HFO mode, triggers instability in the LSB and initiates the LFO phenomenon. Previous studies peg the structure, stability and bursting conditions of the separation bubble to local flow parameters. However, the amplitude of these local flow parameters is dependent on the energy content of the three dominant flow modes. Thus, the present work proposes a more robust bursting criterion that is based on global eigenmodes.

We present a thin-film viscoplastic fluid model of a mountain range, where a uniform fluid layer is deformed by a vertical backstop moving at constant speed. This represents a simplification of the geometry in subduction zones, where an overlying tectonic plate scrapes sediments off the underthrusting plate, thereby forming an accretionary wedge. By using a viscoplastic rheology, we aim to generalise Newtonian models that capture the effective viscous behaviour of rock at large length scales. The model system is characterised by the dimensionless Bingham number, which is the ratio of the yield stress to characteristic shear stress. At low and high Bingham numbers and at early and late times the system is found to be asymptotically self-similar, which we confirm by solving the governing equations numerically. In addition, we test the high-Bingham-number results experimentally using ultrasound gel as the working fluid. The experiments reproduce many features of the theoretically predicted behaviour. The size of the observed wedge grows in the manner predicted, and the fluid surface profile is found to collapse to a universal shape. The viscoplastic fluid wedge exhibits features of both viscous continuum and Coulomb models of accretionary wedges, suggesting that a viscoplastic rheology may provide quantitative insights into the dynamics of real accretionary wedges found in convergent tectonic settings.

A hydrodynamic theory of premixed flame propagation within closed vessels is developed assuming the flame is much thinner than all other fluid dynamic lengths. In this limit, the flame is confined to a surface separating the unburned mixture from burned combustion products, and propagates at a speed determined from the analysis of its internal structure. Unlike freely propagating flames that propagate under nearly isobaric conditions, combustion in a closed vessel results in continuous increases in pressure, burning rate and flame temperature, and a progressive decrease in flame thickness. The flame speed is shown to depend on the voluminal stretch rate, which measures the deformation of a volume element of the flame zone, and on the rate of pressure rise. Both effects are modulated by pressure-dependent Markstein numbers that depend on heat release and mixture properties while capturing the effects of temperature-dependent transport and stoichiometry. The model applies to flames of arbitrary shape propagating in general flows, laminar or turbulent, within vessels of general configurations. The main limitation of hydrodynamic flame theories is the assumption that variations inside the flame zone due to chemistry or turbulence, which could potentially alter its internal structure, are physically unresolved. Nonetheless, the theory, deduced from physical first principles, identifies the various mechanisms involved in the combustion process as demonstrated in detailed discussions of planar flames propagating in rectangular channels and spherically expanding flames in spherical vessels. It also enables the construction of instructive models to numerically simulate the evolution of multi-dimensional and corrugated flames under confinement.