We investigate the spreading of axisymmetric Newtonian gravity currents (GCs) propagating within an infinite, saturated porous medium bounded below by a horizontal impermeable surface. The flow is driven by buoyancy, and the intruding fluid advances due to its higher density relative to the lighter, stationary saturating fluid. Different injection scenarios are considered, depending on the exponent gamma γ $\gamma$ : gamma equals 0 γ = 0 $\gamma =0$ and gamma equals 1 γ = 1 $\gamma =1$ correspond to instantaneous and constant injection, respectively, while gamma less than 1 γ < 1 $\gamma \lt 1$ and gamma greater than 1 γ > 1 $\gamma \gt 1$ describe waning and waxing inflow conditions, respectively. The temporal evolution of the current volume therefore follows upper V tilde upper T Superscript gamma V ∼ T γ $V\sim T^{\gamma }$ . The flow is assumed to obey the Darcy–Forchheimer law, which extends Darcy’s model by introducing a nonlinear inertial correction that scales quadratically with the seepage velocity. The resulting nonlinear problem is solved numerically to determine the temporal evolution of the GC profiles. A special regime, referred to as the high-Forchheimer regime, also admits a similarity solution, valid when the local Forchheimer number is much greater than unity. This condition depends on a dimensionless group upper N N $N$ , which controls the relative importance of nonlinear resistance and may vary widely around unity in practical applications. Theoretical predictions are validated through an extensive laboratory investigation, involving 18 experiments performed with porous media of different particle size ranges and under different injection conditions. The experimental results show good agreement with the theoretical predictions, both in terms of front propagation and current profiles. Finally, a simplified subsurface application is presented to illustrate the range of conditions under which inertial effects may become non-negligible.
To minimise the required length of supersonic-combustion ramjets (scramjets), injected fuel should mix rapidly with the supersonic cross-flow. Tandem dual-jet injection has shown improved mixing performance over single-jet injection. The present study comprises experimental work of tandem dual-jet injection, using schlieren flow visualisation in a supersonic wind tunnel, as well as numerical simulations of this flow inside the wind tunnel channel, both at Mach number 1.6. The numerical simulations are based on the Reynolds-averaged Navier–Stokes (RANS) equations for the time-averaged flow, and the time-resolved hybrid unsteady RANS-Large-Eddy Simulation, i.e. Delayed Detached Eddy Simulations (DDES), to assess the need of time-resolved solutions for capturing the time-averaged behaviour of the jets. From the wind-tunnel schlieren images, the time-averaged location in the cross-flow of the upper boundary of the main jet plume is found to obey an empirical similarity relation, providing for a given jet-to-cross-flow momentum flux ratio upper J J $J$ the value of the dimensionless distance upper S S $S$ between the jets for which plume penetration into the cross-flow is maximal. Numerical simulations facilitated the detailed analysis of the time-dependent flow, and numerical schlieren images in the midplane are used for comparison with wind-tunnel schlieren images. The numerical results, also for other cross-sections, are used to increase insight into the flow phenomena that occur in the interaction of the jet plume with the supersonic cross-flow, i.e. the experiments are complemented by numerics. These numerical results also validate the empirical similarity relation for the penetration depth of the jet plume determined from wind-tunnel schlieren images.
We explored the collective sedimentation of non-convex ring-shaped particles in viscous suspensions using direct numerical simulations based on the smoothed profile method. The toroidal particle geometry introduces an internal flow pathway that allows fluid penetration, fundamentally altering disturbance–flow interactions relative to convex particles. Simulations are performed at italic Re equals 0.1 Re = 0.1 $\textit{Re}=0.1$ over volume fractions 0.001 less than or equals phi less than or equals 0.1 0.001 ≤ ϕ ≤ 0.1 $0.001 \le \phi \le 0.1$ . For an isolated particle, the drag coefficient scales with Stokes law but remains systematically larger than that of convex particles, consistent with enhanced viscous dissipation associated with flow penetrating through the ring opening. In suspensions, the mean settling velocity exhibits enhanced hindered settling, following a Richardson–Zaki-type scaling with exponent n almost equals 7 n ≈ 7 $n \approx 7$ . Velocity fluctuations display anisotropic behaviour and follow a phi Superscript 1 divided by 3 ϕ 1 / 3 $\phi ^{1/3}$ scaling in dilute regimes, consistent with hydrodynamic screening governed by a finite correlation length. Spatial correlations and correlation times reveal persistent streamwise coherence associated with gravity-aligned wake interactions, while the suspension microstructure exhibits multiple preferred separation distances imposed by the ring topology. The results show that particle topology, beyond conventional shape descriptors, constitutes a key control parameter governing hydrodynamic interactions, microstructure, and transport in particulate suspensions.
This study examines anomalous thermal transport in confined liquid metal Rayleigh–Bénard convection via direct numerical simulations over Rayleigh numbers italic Ra element of left bracket 10 Superscript 5 Baseline comma 10 Superscript 8 Baseline right bracket Ra ∈ [ 10 5 , 10 8 ] $\textit{Ra} \in [10^5, 10^8]$ . A phenomenological hybrid model is introduced to capture the full transition from the near-wall boundary layer to the non-monotonic core, and the presence of an inverse mean temperature gradient in the bulk is shown to originate from the spatial organization of dynamic thermal blobs. For temperature fluctuations, a spatial characterization of the temperature standard-deviation profile ( sigma Subscript upper T σ T $\sigma _T$ ) reveals a distinctive bimodal structure, with a secondary peak emerging away from the wall. Through variation of spanwise confinement, no-slip sidewalls are found to constrain the development of corner vortices, reorganizing them into a coherent spiral-like precession. This three-dimensional flow topology induces intense spanwise velocity fluctuations, which are associated with the transport and trapping of boundary-layer thermal plumes in the core region, thereby supporting the formation of the anomalous near-core sigma Subscript upper T σ T $\sigma _T$ peak. At the largest Rayleigh numbers considered, the strengthening of turbulent mixing and large-scale circulation weakens this coherent corner-vortex activity, leading to the attenuation of the bimodal signature. Furthermore, we show that such quasi-two-dimensional confinement modifies the macroscopic heat transfer scaling, producing a steeper effective exponent ( italic Nu tilde italic Ra Superscript 0.332 Nu ∼ Ra 0.332 $\textit{Nu} \sim \textit{Ra}^{0.332}$ ) compared with classical predictions – a phenomenon closely tied to the morphological condensation of thermal plumes.
New experiments with particle-driven, finite-volume gravity currents show that some of the ambient fluid displaced up and over the head of the current becomes mixed into the current. Measurements show that this leads to an increase in volume of the current at a similar rate to that in a single-phase current. Experiments also show that particles gradually settle from the top surface of the current, releasing fluid from the current. Eventually, this begins to dominate the entrainment through the head, and the volume of the current then decreases. Meanwhile, particles continuously sediment from the base of the flow, reducing the particle load. A simplified integral box model is developed to illustrate the evolving balance between these processes as a function of upper S 0 S 0 $S_0$ , the ratio of the current speed, based on the initial buoyancy, to the particle fall speed, for 30 less than upper S 0 less than 300 30 < S 0 < 300 $30\lt S_0\lt 300$ . The model combines the entrainment law proposed by Sher and Woods ( J. Fluid Mech. , 2015, vol. 784, pp. 130–162) for single-phase gravity currents, the sedimentation law proposed by Bonnecaze et al. ( J. Fluid Mech. , 1993, vol. 250, pp. 339–369) for a constant-volume gravity current, and a new model for the release of fluid from the top surface of the current through particle settling. We show that the maximum volume of the current and the position of the nose when reaching this maximum volume both increase nearly linearly with upper S 0 S 0 $S_0$ . We discuss the importance of these results for particle-driven gravity currents, especially where the effects of fluid entrainment can lead to a change in fluid chemistry, promoting flocculation and hence sedimentation, or a change in fluid buoyancy through fluid–particle interaction.
This study develops a general theory for analysing a three-dimensional (3-D) acoustofluidic system, which consists of a cavity sandwiched by parallel piezoelectric substrates. The cavity is filled with a fluid and microparticle mixture, whose movements are actuated by surface acoustic waves (SAW) generated by the piezoelectric substrates. In contrast to the formulations based on the velocity potential and streamfunction, we developed a frequency-domain perturbation method to solve the compressible Navier–Stokes equations to obtain the acoustofluidic fields for both inviscid and viscous fluids. These solutions allow for the accurate prediction of the pressure nodal positions within the sandwiched cavity, and the effects of the microfluidic cavity geometry on the pressure nodal position are examined. Our analysis shows that the in-plane pressure-node distribution is controlled by phase modulation, whereas the out-of-plane distribution is governed by the amplitude ratio of the standing SAWs produced by the two parallel substrates. For viscous fluids, a coordinated amplitude–phase modulation strategy is proposed to achieve the desirable wave node distribution. The present theoretical derivations are validated against numerical simulations and laboratory experiments, in terms of both the velocity and pressure fields. This work provides guidelines for the fabrication and operation of acoustofluidic devices, extending current 2-D acoustic control to fully 3-D manipulation of microparticles suspended in the fluid.
A widely cited experimental dataset (Cleve et al. , J. Fluid Mech. , 2019, vol. 875, pp. 597–621) on non-spherical acoustic cavitation dynamics provides a valuable benchmark for model validation, yet its use is hindered by large uncertainties in the two key parameters: the equilibrium bubble radius and the acoustic pressure amplitude. This study introduces a robust parameter-identification framework to resolve these discrepancies and enable meaningful comparison with models. Using an in-house graphics processing unit-accelerated solver for solving the second-order perturbation model developed by Shaw ( Phys. Fluids , 2006, vol. 18, issue 7, p. 072104), the dataset is systematically re-examined. A Fourier coefficient-based error metric is developed to quantify the pronounced mismatch between simulations and measurements. The proposed method reliably corrects the vast majority of the experimental parameters, yielding excellent agreement between numerical predictions and observations. The outcome is a validated dataset with accurately identified parameters that can serve as a reliable benchmark for validating advanced computational fluid dynamics simulations and theoretical models. In addition, the approach offers a general tool for future experiments where direct measurements of local acoustic pressure remain difficult.
We perform a comprehensive linear non-modal stability analysis of plane Poiseuille flow in Oldroyd-B fluids, employing the recently proposed geometric decomposition of the polymer conformation tensor (Hameduddin et al. , J. Fluid Mech ., 2018, vol. 842, 395–427; J. Fluid Mech ., 2019, vol. 858, 377–406), where perturbation elastic energy has an appropriate definition. In the presence of weak shear flow, e.g. Reynolds number Re = 1, the spanwise-uniform disturbance with a large wavenumber exhibits the largest transient growth, and perturbation elastic energy is the most amplified, proportional to W 2 (where W denotes the Weissenberg number), which is mainly attributed to the combination of different modes in the continuous spectrum (CS). Elastic energy analysis suggests that this growth is physically due to the energy transfer from the perturbation wall-normal velocity to the normal components of the perturbation polymer conformation tensor. As Re increases to Re = 1000, transient growth has a significant increase, and its maximum appears in the oblique disturbance with perturbation kinetic energy dominating amplification instead of elastic energy, which is still induced by the spanwise-uniform components of the input perturbation conformation tensor, just as in the Re = 1 case. Mathematically, this energy growth is caused by the combination of CS and the remaining discrete modes, and it is remarkably larger than that merely caused by CS. Kinetic energy analysis suggests that this significant kinetic energy growth is physically due to the fact that elastic effects enhance energy transfer from the base flow field and the perturbed conformation tensor field to the perturbed hydrodynamic field.
A forced rotation applied to a circular cylinder elastically mounted in quiescent fluid can cause the body to vibrate. The present work explores the rotation-induced vibrations (RIV) occurring when the cylinder is free to translate, with two degrees of freedom, in the plane normal to its axis. The exploration is conducted numerically for ranges of the four governing parameters. The Reynolds number and the reduced velocity (inverse of the non-dimensional natural frequency of the oscillator), based on the surface velocity of the rotating body and its diameter, are varied up to 100 100 $100$ and 200 200 $200$ , respectively, and the structural damping ratio up to 50 percent sign 50 % $50\,\%$ . The structure to displaced fluid mass ratio ranges from 1 1 $1$ to 100 100 $100$ . RIV arise over a vast region of the parameter space, including for substantially damped oscillators. They develop through three regimes, characterised by different forms of responses: periodic circular orbits oriented either in the sense of the imposed rotation, or in the opposite sense, and quasi-periodic orbits combining two incommensurable components associated with circular trajectories of opposite orientations. The system may reach distinct states depending on the initial condition, e.g. the emergence of RIV for low mass ratios requires a large initial perturbation, and two vibratory regimes can coexist over wide regions of the parameter space. The orbit radius, which tends to increase with the reduced velocity, may exceed 100 100 $100$ body diameters, while the revolution frequency may drastically deviate from the oscillator natural frequency. The mechanism driving the two-degree-of-freedom RIV is examined in light of a quasi-steady modelling of fluid forces, i.e. assuming that the time scales of the flow and moving body are decoupled, which is found to predict the three forms of responses uncovered in this work.
The low-Reynolds-number flow near the sharp corner of a wedge-shaped obstacle is reconsidered. For flow round the corner, the velocity is zero (and the vorticity infinite) at the vertex, yet it is shown that fluid particles accelerate as their distance r r $r$ from the vertex decreases, i.e. as they approach the point of zero velocity. By contrast, for symmetric flow towards the corner, fluid particles decelerate as the corner region is approached. The limiting case in which the wedge collapses to a flat plate is given special consideration. For flow round the edge of the plate (with symmetric streamfunction), the streamlines are parabolic. In this flat-plate limit, a family of asymmetric flows is determined.
We perform the acoustic characterization of a model-scale wind turbine, including the tower and a fully reflective ground surface. The study constitutes the natural extension of the research presented in Rismondo et al. ( J. Fluid Mech. , 2025, vol. 1024, p. A33), where the isolated rotor (IR) was analysed. We use large-eddy simulation and acoustic analogy. The analysis of pressure over the solid surfaces shows that the rotor produces broadband trailing-edge fluctuations modulated at the blade passing frequency (BPF) by the blade–tower interaction, while the tower exhibits predominantly tonal behaviour at the BPF and its harmonics, as well as low-frequency tower vortex shedding. The tower increases wake asymmetry and turbulent mixing, producing a less coherent wake compared with the IR case. Two main mechanisms rule the near-to-far wake transition: tip-vortex instability and nonlinear interactions between the rotor and the tower induced wakes, enhancing asymmetry and mixing. These dynamics reduce the nonlinear low-frequency acoustic levels in the near wake compared with the IR case, while increasing the sound pressure level and the tonal character in the lateral direction, related to the tower pressure field. In addition, the presence of the tower shapes distinct directivity patterns: radiation in the horizontal plane is nearly isotropic, whereas the rotor-plane directivity is more dipole-shaped, related to the tower, and becomes more pronounced considering the reflective surfaces. Overall, the complete configuration differs significantly from the IR, with measurable differences in surface pressure, wake development and acoustic radiation, emphasizing the role of the tower in both aerodynamics and aeroacoustics.
This study investigates the genesis and temporal evolution of turbulent eddies in violent-sloshing flows using a fully meshless computational framework. A quasi-Lagrangian delta δ $\delta$ -large-eddy simulation–smoothed particle hydrodynamics formulation is employed to solve the weakly compressible Navier–Stokes equations, together with a novel methodology to quantify slosh-induced energy dissipation, where delta δ $\delta$ denotes the density-diffusion operator introduced in the delta δ $\delta$ -SPH formulation. Under violent periodic forcing, the flow exhibits a strongly nonlinear free-surface dynamics, characterised by recurrent wave breaking and energetic impacts against the tank walls. By decomposing the total viscous dissipation into enstrophy-related and deformation-related contributions, we find that the enstrophy fraction remains nearly constant, at around 30 percent sign 30 % $30\,\%$ , across the investigated regimes. Moreover, in the absence of surface tension, the enstrophy-related dissipation does not converge under grid refinement; the inclusion of surface tension regularises this behaviour and promotes a shift of the vortex population towards larger coherent structures. High-resolution two-dimensional simulations, spanning a wide range of spatial resolutions, are complemented by fully three-dimensional simulations and by reduced-width three-dimensional configurations, in which the spanwise direction is fully resolved over a limited extent. This combined analysis shows that, for this class of bounded violent free-surface flows, global loads and energy dissipation are primarily governed by free-surface fragmentation and reconnection, rather than by fully three-dimensional turbulent cascade mechanisms. As a result, two-dimensional simulations provide an accurate description of the dynamics controlling the integral quantities of interest. These findings offer new physical insight into the coupling between free-surface fragmentation, vortex dynamics and dissipation mechanisms in violent sloshing, and establish a reference framework for future studies of turbulence generation in confined free-surface flows.
We numerically investigate the propulsion of a two-dimensional compliant membrane executing prescribed harmonic heave in the near wake of a stationary circular cylinder at Reynolds number italic Re equals 3000 Re = 3000 $\textit{Re}=3000$ . Using a partitioned high-fidelity fluid–structure interaction solver with nonlinear iterative force correction, we map the coupled response over upper A Superscript asterisk Baseline element of left bracket 0.05 comma 0.5 right bracket A ∗ ∈ [ 0.05 , 0.5 ] $A^* \in [0.05,0.5]$ and f Superscript asterisk Baseline element of left bracket 0.1 comma 0.6 right bracket f ∗ ∈ [ 0.1 , 0.6 ] $f^* \in [0.1,0.6]$ , where upper A Superscript asterisk A ∗ $A^*$ is dimensionless flapping amplitude and f Superscript asterisk f ∗ $f^*$ is dimensionless flapping frequency. The parameter sweep reveals a sharp transition in the force maps from weakly forced, wake-following behaviour to a high-performance regime in which cycle-averaged lift and lift-to-drag increase abruptly. This transition coincides with intermittent exposure of the membrane to higher-momentum fluid and a pronounced amplification of deformation. A frequency-resolved analysis, combined with a body-frame Fourier mode decomposition of the flow, identifies four distinct flapping states, namely a wake-dominated state, two flapping-dominated states associated with lift reduction and lift gain and a two-way lock-in state. In the latter, vortex shedding locks onto the imposed actuation, while the first fluid-loaded structural mode approaches the actuation frequency, producing selective amplification of low-order deformation. The resulting curvature-induced camber intensifies leading-edge suction and increases the cross-membrane pressure difference, establishing feedback that reorganises upstream shedding. Motivated by these mechanisms, we derive scaling relations for the cycle-averaged lift, drag and power that separate quasi-steady motion, added-mass effects, curvature-induced contributions, wake-momentum deficit and transverse shear. For the present reference compliance, the scaling clarifies how flexibility is detrimental when the membrane remains fully immersed within the wake core, yet beneficial when intermittent wake exposure permits passive camber amplification to offset momentum deficit with limited drag penalty. These results provide a mechanistic framework for the present reference-compliance configuration and identify how wake exposure, imposed heaving and membrane response combine to produce two-way lock-in.
Rapidly rotating Rayleigh–Bénard convection on an f f $f$ -plane at colatitude theta Subscript f ϑ f $\vartheta _{\!f}$ is investigated numerically using an asymptotically reduced equation set valid in the limit of very rapid rotation. The equations provide a non-hydrostatic but quasi-geostrophic description in a non-orthogonal coordinate system. The tilt changes the structure of the large-scale barotropic condensate from large-scale vortices to zonal flows as the colatitude of the f f $f$ -plane increases, with bistable states present for certain parameter ranges, extending prior work to a geophysically significant parameter regime. This behaviour is understood through the impact of broken rotation symmetry on the barotropic source terms resulting from baroclinic vorticity stresses and baroclinic torque. As the tilt angle theta Subscript f ϑ f $\vartheta _{\!f}$ increases, global heat and momentum transport is reduced relative to upright-polar convection, a result that is explained through linear theory and nonlinear power maps both of which demonstrate increased attenuation of the domain of dynamically active spatial scales as the convective modes depart from a north–south alignment in the horizontal plane. A key finding is that the predominance of lateral thermal mixing allows for the maintenance of a persistent unstable mean temperature gradient that saturates at increasing forcing levels and remains insensitive to the colatitude.
Multiscale vortex structures significantly influence inertial particle dynamics, contributing to clustering in turbulent flows – a phenomenon common in many applications. In this study, our primary objective is to investigate how particle clustering is influenced by vortex effects while accounting for particle feedback. Using a two-way coupled numerical method, we identify novel particle dynamics characteristics, as localised particle clustering triggers periodic leakage, even in a dilute particle-laden unequal-strength counter-rotating vortex pair (CVP). Small, heavy, dilute inertial particles are considered. In particular, the initial particle volume fraction and the particle Stokes number are set to upper Phi Subscript p comma 0 Baseline less than 1.0 times 10 Superscript negative 3 Φ p , 0 < 1.0 × 10 − 3 $\varPhi _{p,0}\lt 1.0\times 10^{-3}$ and italic St element of left parenthesis 0 comma 0.1 right parenthesis St ∈ ( 0 , 0.1 ) ${\textit{St}}\in (0,0.1)$ , respectively. The particle dynamics is governed by two critical Stokes numbers: the trapping critical Stokes number italic St Subscript italic cr comma t St cr,t ${\textit{St}}_{\textit{cr,t}}$ and the stability critical Stokes number italic St Subscript italic cr comma s St cr,s ${\textit{St}}_{\textit{cr,s}}$ . The critical Stokes number italic St Subscript italic cr comma t St cr,t ${\textit{St}}_{\textit{cr,t}}$ governs particle trapping. For italic St less than italic St Subscript italic cr comma t Baseline St < St cr,t ${\textit{St}} \lt {\textit{St}}_{\textit{cr,t}}$ , particles are trapped, forming a localised particle clustering ring (PCR) that induces substantial particle feedback on the flow. Furthermore, italic St Subscript italic cr comma s St cr,s ${\textit{St}}_{\textit{cr,s}}$ determines the stability of the PCR, which varies with upper Phi Subscript p comma 0 Φ p , 0 $\varPhi _{p,0}$ . A stable PCR forms when italic St less than italic St Subscript italic cr comma s Baseline St < St cr,s ${\textit{St}} \lt {\textit{St}}_{\textit{cr,s}}$ . At italic St Subscript italic cr comma s Baseline less than upper S t less than italic St Subscript italic cr comma t St cr,s < S t < St cr,t ${\textit{St}}_{\textit{cr,s}} \lt St \lt {\textit{St}}_{\textit{cr,t}}$ , a PCR forms and then periodic temporal leakage of particles occurs. The significant feedback from the PCR creates a morphologically similar positive vorticity region (PVR) through the baroclinic source. The periodic transport of vorticity within the PVR modulates the critical streamlines upper S Subscript italic max S max $S_{\textit{max}}$ and upper S 0 S 0 $S_0$ , which play decisive roles in particle trapping. These modulations directly reduce the stable region of the PCR and displace its location, enabling particles to escape.
The dynamics of Lagrangian particles dispersed in rotating turbulence differ fundamentally from those observed in classical homogeneous isotropic turbulence (HIT). Rotation induces a pronounced two dimensionalisation of the carrier flow, governed by inertial waves and coherent columnar vortices, while particles experience additional Coriolis and centrifugal accelerations that compete with the standard Stokes drag. In this study, high-fidelity direct numerical simulations of HIT and rotating turbulence in a triply periodic domain are used to investigate the clustering and Lagrangian dynamics of millions of sub-Kolmogorov point particles. Increasing rotation reorganises both the flow and the dispersed phase: moderate rotation produces a domain-scale columnar vortex that expels inertial particles via drag-Coriolis coupling, while further increasing rotational effects amplifies centrifugal segregation and promotes anisotropic organisation, ultimately leading to the formation of slender, particle columns representative of a limiting clustering regime. Rotation significantly enhances particle clustering and anisotropy, shifting the maximum preferential concentration toward larger Stokes numbers. These trends are quantified using a new diagnostic based on the gyration tensor, which provides a unified description of cluster concentration, morphology and orientation across scales. To link these static signatures to their dynamical origin, the geometry and acceleration of Lagrangian trajectories are analysed. Increasing rotation suppresses vertical acceleration component while amplifying the planar one, steering particle dispersion toward an effectively two-dimensional regime. This transition is reflected in curvature and torsion statistics, which reveal more strongly bent trajectories and a reduced decorrelation from large-scale vortical structures.
Direct numerical simulations of the flow over a compound delta-wing model reveal a novel receptivity mechanism for the second-mode instability in hypersonic boundary layers. This mechanism involves disturbances that propagate obliquely upward from the wall, interact with the shock wave and reflect back into the boundary layer. Detailed analysis indicates that this process strongly modulates high-frequency instabilities, such as the second mode, while exerting minimal influence on low-frequency cross-flow and first-mode disturbances. Upon re-entry into the boundary layer, the reflected disturbances cause rapid, stepwise amplification of the internal second mode, demonstrating that the mechanism modulates and enhances boundary-layer instability. Further analysis shows that a phase-locked mechanism is involved in these interactions. The identification of this receptivity mechanism offers new insights into hypersonic boundary-layer transition.
Acoustic liners are passive sound-absorbing materials widely used in engineering applications and are commonly characterised by their acoustic impedance. In the presence of high sound pressure levels or grazing flows, the impedance is modified by local nonlinear effects. Conventional impedance measurements are typically obtained through frequency-domain eduction techniques, which infer impedance from its effect on measurable acoustic quantities and therefore rely on assumptions regarding wave propagation and near-wall acoustic–flow interactions. In this paper, a time-domain impedance eduction approach based on instantaneous wall-normal velocity measurements is developed to investigate the nonlinear response of acoustic liners under grazing-flow conditions. Unlike conventional methods, the proposed approach does not rely on a wave-propagation model and reconstructs the liner impedance directly from the local velocity field. The method is assessed using both laser Doppler velocimetry measurements and high-fidelity numerical simulations. The resulting impedance estimates show good agreement with classical predictions while revealing that a significant part of the flow effect originates from turbulence-induced wall-normal velocity fluctuations acting through the same nonlinear mechanisms as high-amplitude acoustic excitation. Furthermore, the commonly reported upstream–downstream impedance mismatch largely disappears when wave-propagation modelling is removed from the eduction process, suggesting that this discrepancy primarily arises from modelling assumptions rather than from an intrinsic dependence of the liner impedance on the direction of acoustic propagation.
This study combines linear stability analysis (LSA) and direct numerical simulations (DNS) to investigate the coupling mechanisms of rotation, stratification and shear in two flow geometries: spanwise rotating stratified plane Couette flow (between two infinite parallel plates) and sheared annular centrifugal Rayleigh–Bénard convection (between two concentric cylinders). First, LSA reveals a universal scaling law with respect to left parenthesis 1 minus eta right parenthesis ( 1 − η ) $(1-\eta )$ , where eta η $\eta$ denotes the radius ratio, for the deviation between annular and planar system results, quantitatively establishing the dynamical connection between annular and planar geometries. Building on this, DNS results indicate that the breakdown of the twin-force analogy in the turbulent regime originates from mode competition: buoyancy tends to drive three-dimensional chaotic plumes via baroclinic effects, whereas the Coriolis force tends to sustain quasi-two-dimensional longitudinal vortices. The Prandtl number determines the dominant mechanism in the near-wall region by regulating the relative thicknesses of the thermal and momentum boundary layers, thereby leading to a systematic dissimilarity between heat and momentum transport. Furthermore, this study provides a new theoretical basis for transport prediction in complex flows from the perspectives of enstrophy and mode competition.
Topographic roughness, defined as irregular variability of ocean depth on lateral scales of 1–10 km, has recently been shown to substantially impact the dynamics of large-scale and mesoscale ocean flows, including eddies, Rossby waves and baroclinic instability. This suggests that accurate modelling of roughness-induced forcing is critical for representing large-scale ocean behaviour. A recent multi-scale analysis of flows affected by small-scale bathymetry has produced the ‘sandpaper theory’, an explicit parametrisation of the roughness-induced bottom drag. This model accurately captures the impact of small-scale topography on large-scale flows without the need to resolve it in general circulation models. A peculiar facet of the sandpaper theory is that the drag is a non-monotonic function of the flow speed above the bottom boundary layer, which results in an instability. We characterise this non-monotonic drag instability for a series of barotropic and baroclinic systems, and explore a dynamically rich variety of scenarios that can produce stable jets, overstable Rossby waves, mesoscale eddy streets and self-amplifying hetons. We describe and quantify the properties of each flow type as they pertain to this non-monotonic drag regime.
