Whilst surface-stress integration remains the standard approach for fluid force evaluation, control-volume integral methods provide deeper physical insights through functional relationships between the flow field and the resultant force. In this work, by introducing a second-order tensor weight function into the Navier–Stokes equations, we develop a novel weighted-integral framework that offers greater flexibility and enhanced capability for fluid force diagnostics in incompressible flows. Firstly, in addition to the total force and moment, the weighted integral methods establish, for the first time, rigorous quantitative connections between the surface-stress distribution and the flow field, providing potential advantages for flexible body analyses. Secondly, the weighted integral methods offer alternative perspectives on force mechanisms, through vorticity dynamics or pressure view, when the weight function is set as divergence-free or curl-free, respectively. Thirdly, the derivative moment transformation (DMT)-based integral methods (Wu et al., J. Fluid Mech. vol. 576, 2007, 265–286) are generalised to weighted formulations, by which the interconnections among the three DMT methods are clarified. In the canonical problem of uniform flow past a circular cylinder, weighted integral methods demonstrate advantages in yielding new force expressions, improving numerical accuracy over original DMT methods, and enhancing surface-stress analysis. Finally, a force expression is derived that relies solely on velocity and acceleration at discrete points, without spatial derivatives, offering significant value for experimental force estimation. This weighted integral framework holds significant promise for flow diagnostics in fundamentals and applications.

Asymptotic flow states with limiting drag modification are explored via direct numerical simulations in a moderate-curvature viscoelastic Taylor–Couette flow of the FENE-P fluid. We show that asymptotic drag modification (ADM) states are achieved at different solvent-to-total viscosity ratios ($\beta$) by gradually increasing the Weissenberg number from 10 to 150. As $\beta$ decreases from 0.99 to 0.90, for the first time, a continuous transition pathway is realised from the maximum drag reduction to the maximum drag enhancement, revealing a complete phase diagram of the ADM states. This transition originates from the competition between Reynolds stress reduction and polymer stress development, namely, a mechanistic change in angular momentum transport. Reduced $\beta$ has been found to effectively enhance elastic instability, suppressing large-scale Taylor vortices while promoting the formation of small-scale elastic Görtler vortices. The enhancement and in turn dominance of small-scale structures result in stronger incoherent transport, facilitating efficient mixing and substantial polymer stress development that ultimately drives the AMD state transition. Further analysis of the scale-decomposed transport equation of turbulent kinetic energy reveals an inverse energy cascade in the gap centre, which is attributed to the polymer-induced energy redistribution: polymers extract more energy from large scales than they can dissipate, with the excess energy redirected to smaller scales. However, the energy accumulating at smaller scales cannot be dissipated immediately and is consequently transferred back to larger scales via nonlinear interactions, thereby unravelling a novel polymer-mediated cycle for the reverse energy cascade. Overall, this study unravels the challenging puzzle of the existence of distinct dynamically connected ADM states and paves the way for coordinated experimental, simulation and theoretical studies of transition pathways to desired ADM states.

Wall pressure fluctuations (WPFs) over aerodynamic surfaces contribute to the physical origin of noise generation and vibrational loading. Understanding the generation mechanism of WPFs, especially those exhibiting extremely high amplitudes, is important for advancing design and control in practical applications. In this work, we systematically investigate extreme events of WPFs in turbulent boundary layers and the compressibility effects thereon. The compressibility effects, encompassing extrinsic and intrinsic ones, ranging from weak to strong, are achieved by varying Mach numbers and wall temperatures. A series of datasets at moderate Reynolds numbers obtained from direct numerical simulation are analysed. It is found that the intermittency of WPFs depends weakly on extrinsic compressibility effects, whereas intrinsic compressibility effects significantly enhance intermittency at small scales. Coherent structures related to extreme events are identified using volumetric conditional average. Under extrinsic compressibility effects, extreme events are associated with the weak dilatation structures induced by interactions of high- and low-speed motions. When intrinsic compressibility effects dominate, these events are associated with the strong alternating positive and negative dilatation structures embedded in low-speed streaks. Furthermore, Poisson-equation-based pressure decomposition is performed to partition pressure fluctuations into components governed by distinct physical mechanisms. By analysing the proportion of each pressure component in extreme events, it is found that the contributions of the slow pressure and viscous pressure exhibit weak dependence on the compressibility effects, especially the extrinsic ones, and the varying trend of contributions of the rapid pressure with compressibility effects is opposite to that of the compressible pressure component.

Large-scale circulation (LSC) dynamics have been studied in thermal convection driven by heat-releasing particles via the four-way coupled Euler–Lagrange approach. We consider a wide range of Rayleigh–Robert number (${\textit{Rr}}=4.97\times 10^{5} - 4.97 \times 10^{8}$) and density ratio ($\hat {\rho }_r=1- 1000$) that characterize the thermal buoyancy and the particle inertia, respectively. An intriguing flow transition has been found as $\hat {\rho }_r$ continuously increases, involving in sequence three typical LSC regimes, i.e. the bulk-flow-up regime, the marginal regime and the bulk-flow-down (BFD) regime. The comprehensive influence of the LSC regime transition is demonstrated by examining the key flow statistics. As integral flow responses, the heat transfer efficiency and flow intensity change substantially when the LSC regime transition happens, and the thermal boundary layer thicknesses at the top and bottom walls exhibit similar alterations. Significant local accumulation of particles occurs as $\hat {\rho }_r$ increases to a sufficiently high value, resulting in a great modification in the flow dynamics. Specifically, particles aggregate near the sidewalls and heat the local surrounding fluid to generate rising warmer plumes that drive the LSC regime transition. Of interest, well-patterned cellular structures of particles take place near the top wall and obtain notable deviation from the thermal convection cells for the BFD regimes. A mechanical interpretation is proposed and substantiated based on a conceptual vortex–particle model, namely, the centrifugal motion of heat-releasing particles that is confirmed to play a driving role for the LSC regime transition.

The evolution of the mixing layer in rotation-driven Rayleigh–Taylor (RT) turbulence is investigated theoretically and numerically. It is found that the evolution of the turbulent mixing layer in rotation-driven RT turbulence is self-similar, but the width of the mixing layer does not follow the classical quadratic growth observed in planar RT turbulence induced by constant external acceleration. Based on the approach used in cylindrical RT turbulence without rotation (Zhao et al. 2021, Phys. Rev. E, vol. 104, 055104), a theoretical model is established to predict the growth of mixing widths in rotation-driven RT turbulence, and the model’s excellent agreement with direct numerical simulations (DNS) serves to validate its reliability. The model proposes a rescaled time that allows for the unification of the evolutions of the mixing layers in rotation-driven RT turbulence with various Atwood numbers and rotation numbers. It is further identified that the growth law described by the model of rotation-driven RT turbulence can be recovered to quadratic growth when the effects of geometrical curvature, radial inhomogeneity of the centrifugal force, and Coriolis force become negligible. Moreover, based on the DNS results, we find that turbulent mixing layers in rotation-driven RT turbulence cover a wide range of length scales. The strong rotation at the same Atwood number enhances the generation of fine-scale structures but is not conducive to overall fluid mixing within the mixing layer.

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.

Yaw control can effectively enhance wind farm power output, but the vorticity distribution and coherent structures in yawed turbine wakes remain poorly understood. We propose a physical model capable of accurately predicting tip vortex dynamics from their generation to destabilisation. This model integrates a point vortex framework with advanced blade element momentum theory and vortex cylinder theory for yawed turbines. Comparisons with large eddy simulations demonstrate that the model effectively predicts the vorticity distribution of tip vortices and the wake profile of yawed turbines. Finally, we employ sparsity-promoting dynamic mode decomposition to analyse the dynamics of the far wake. Our analysis reveals four primary mode types: (i) the averaged mode; (ii) shear modes; (iii) harmonic modes; and (iv) merging modes. Under yawed conditions, these modes become asymmetric, leading to interactions between the tip and root vortex modes. This direct interaction plays a critical role during the formation process of the counter-rotating vortex pair observed in yawed wakes.

The effect of Stokes number on turbulence modulation in particle-laden channel flow is investigated through four-way coupled point-particle direct numerical simulations, with the mass loading fixed at 0.6 and the friction Stokes number $St^+$ varying from 3 to 300. A full transition pathway is observed, from a drag-enhanced to a drag-reduced regime, eventually approaching the single-phase state as $St^+$ increases towards 300. A set of transport equations for the particle phase is derived analytically to characterise the interphase coupling, within the framework of the point-based statistical description of particle-laden turbulence. By virtue of this, two dominant mechanisms are identified and quantitatively characterised: a positive, particle-induced extra transport that decreases monotonically with increasing $St^+$, and a negative, particle-induced extra dissipation that varies non-monotonically with $St^+$. The coupling of these two mechanisms leads to a direct contribution of the particle phase to the shear stress balance, the turbulent kinetic energy budgets and the Reynolds stress budgets. Consequently, as $St^+$ increases, the self-sustaining cycle of near-wall turbulence transitions from being augmented to being suppressed and, eventually, returns to the single-phase state. This gives rise to an indirect effect, manifested as a non-monotonic modulation of Reynolds shear stress and turbulence production rate. Taken together, complex interplays between particle-modified turbulent transport, particle-induced extra transport and extra dissipation are analysed and summarised, providing a holistic physical picture composed of consistent interpretations of turbulence modulation induced by small heavy particles.

The extracellular matrices, such as the haemolymph, in insects are at the centre of most physiological processes and are protected from oxidative stress by the extracellular antioxidant enzymes. In this study, we identified two secreted superoxide dismutase genes (PxSOD3 and PxSOD5) and investigated the oxidative stress induced by chlorpyrifos (CPF) in the aquatic insect Protohermes xanthodes (Megaloptera: Corydalidae). PxSOD3 and PxSOD5 contain the signal peptides at the N-terminus. Structure analysis revealed that PxSOD3 and PxSOD5 contain the conserved CuZn-SOD domain, which is mainly composed of β-sheets and has conserved copper and zinc binding sites. Both PxSOD3 and PxSOD5 are predicted to be soluble proteins located in the extracellular space. After exposure to different concentrations of sublethal CPF, MDA content in P. xanthodes larvae were increased in a dose-dependent manner; SOD and CAT activities were also higher in CPF-treated groups than that in the no CPF control, indicating that sublethal CPF induces oxidative stress in P. xanthodes larvae. Furthermore, PxSOD3 and PxSOD5 expression levels and haemolymph SOD activity in the larvae were downregulated by sublethal CPF at different concentrations. Our results suggest that the PxSOD3 and PxSOD5 are putative extracellular antioxidant enzymes that may play a role in maintaining the oxidative balance in the extracellular space. Sublethal CPF may induce oxidative stress in the extracellular space of P. xanthodes by reducing the gene expression and catalytic activity of extracellular SODs.

Direct numerical simulations in a low-curvature viscoelastic turbulent Taylor vortex flow, with Reynolds numbers ranging from 1500 to 8000 and maximum chain extensibility ($L$) from 50 to 200, reveal a maximum drag reduction (MDR) asymptote. Compared with the classical MDR observed in planar wall-bounded shear flows, that is, drag reduction (DR) is $\sim -80\, \%$, this MDR state achieves only moderate levels of DR ($\sim -60\,\%$). This is due to the existence of large-scale structures (LSSs). A careful examination of the flow structures reveals that the polymer–turbulence interaction suppresses small-scale vortices and stabilizes the LSSs. These structural changes in turn lead to a reduction of Reynolds stress, and consequently to a DR flow state. Although Reynolds stress does not vanish as observed in classical MDR states, the small-scale vortices that heavily populate the near-wall region are also almost completely eliminated in this flow state. Concurrently, significant polymer stresses develop as a consequence of the interaction between polymer chains and LSSs that partially offset the magnitude of DR, leading to MDR asymptotes with moderate levels of DR. Moreover, we demonstrate that polymer deformation, i.e. deviation from the equilibrium state, is directly correlated with the LSSs dynamics, while the polymer deformation fluctuation displays a universal property in the MDR state. Hence, it is not surprising that the extent of DR exhibits a non-monotonic dependence on the maximum chain extensibility. Specifically, the variation in $L$ alters the incoherent and coherent angular momentum transport by small- and large-scale flow structures, respectively. To that end, the most DR flow state occurs at a moderate value $L=100$. Overall, this study further supports the universal property of polymer-induced asymptotic states in wall-bounded turbulence and paves the way for mechanistic understanding of drag modification that arises from the interaction of polymers with small- and large-scale flow structures.

The stability of Taylor–Couette flow modulated by oscillatory wall suction/blowing is investigated using Floquet linear stability analysis. The growth rate and stability mode are obtained by numerical calculation and asymptotic expansion. By calculating the effect of wall suction/blowing on the critical mode of steady Taylor–Couette flow, it is found that for most suction/blowing parameters, the maximum disturbance growth rate of the critical mode decreases and the flow becomes more stable. Only in a very small parameter region, wall suction/blowing increases the maximum disturbance growth rate of the critical mode, resulting in flow instability when the gap between the cylinders is large. The asymptotic results for small suction/blowing amplitudes indicate that the change of flow instability is mainly due to the steady correction of the basic flow induced by the modulation. A parametric study of the critical inner Reynolds number and the associated critical wavenumber is performed. It is found that the flow is stabilized by the modulation for most of the parameter ranges considered. For a wide gap between the cylinders, it is possible for the system to be mildly destabilized by weak suction/blowing.

This study is dedicated to achieving efficient active noise control in a supersonic underexpanded planar jet, utilizing control parameters informed by resolvent analysis. The baseline supersonic underexpanded jet exhibits complex wave structures and substantial high-amplitude noise radiations. To perform the active control, unsteady blowing and suction are applied along the nozzle inner wall close to the exit. Employing both standard and acoustic resolvent analyses, a suitable frequency and spanwise wavenumber range for the blowing and suction is identified. Within this range, the control forcing can be significantly amplified in the near field, effectively altering the original sound-producing energetic structure while minimizing far-field amplification to prevent excessive noise. A series of large-eddy simulations are further conducted to validate the control efficiency, demonstrating an over 10 dB reduction in upstream-propagated screech noise. It is identified that the present unsteady control proves more effective than steady control at the same momentum coefficient. The controlled jet flow indicates that the shock structures become more stable, and the stronger the streamwise amplification of the forcing, the more likely it is to modify the mean flow characteristics, which is beneficial for reducing far-field noise radiation. Spectral proper orthogonal decomposition analysis of the controlled flow confirms that the control redistributes energy to higher forcing frequencies and suppresses large-scale antisymmetric and symmetric modes related to screech and its harmonics. The findings of this study highlight the potential of resolvent-guided control techniques in reducing noise in supersonic underexpanded jets and provide a detailed understanding of the inherent mechanisms for effective noise reduction through active control strategies.

Turbulent flow induced by elastorotational instability in viscoelastic Taylor–Couette flow (TCF) with Keplerian rotation is analogous to a turbulent accretion disk destabilized by magnetorotational instability. We examine this novel viscoelastic Keplerian turbulence via direct numerical simulations (DNS) for the shear Reynolds number ($Re$) ranging from $10^2$ to $10^4$. The observed characteristic flow structure consists of penetrating streamwise vortices with axial length scales much smaller than the gap width, distinct from the classic centrifugally induced Taylor vortices, which have axial lengths of the gap width. These intriguing vortices persist for the wide $Re$ range considered and give rise to intriguing scaling behaviour in key flow quantities. Specifically, the characteristic axial length of the penetrating vortices is shown to scale as $Re^{-0.22}$; the angular momentum transport scales as $Re^{0.42}$; the kinetic and elastic boundary-layer thicknesses based on angular velocity and hoop stress near the inner cylinder wall scale as $Re^{-0.48}$ and $Re^{-0.49}$, respectively. This implies that the viscoelastic Keplerian turbulence belongs to the classical turbulent regime of TCF with the Prandtl–Blasius-type boundary layer. Furthermore, we present an analytical relation between the viscous and elastic dissipation rates of kinetic energy and the angular momentum transport and in turn demonstrate its validity using our DNS data. This study has paved the way for future research to explore astrophysics-related Keplerian turbulence and angular momentum transport via the scaling relations of the analogous TCF of dilute polymeric solutions.

Developing a model to describe the shock-accelerated cylindrical fluid layer with arbitrary Atwood numbers is essential for uncovering the effect of Atwood numbers on the perturbation growth. The recent model (J. Fluid Mech., vol. 969, 2023, p. A6) reveals several contributions to the instability evolution of a shock-accelerated cylindrical fluid layer but its applicability is limited to cases with an absolute value of Atwood numbers close to $1$, due to the employment of the thin-shell correction and interface coupling effect of the fluid layer in vacuum. By employing the linear stability analysis on a cylindrical fluid layer in which two interfaces separate three arbitrary-density fluids, the present work generalizes the thin-shell correction and interface coupling effect, and thus, extends the recent model to cases with arbitrary Atwood numbers. The accuracy of this extended model in describing the instability evolution of the shock-accelerated fluid layer before reshock is confirmed via direct numerical simulations. In the verification simulations, three fluid-layer configurations are considered, where the outer and intermediate fluids remain fixed and the density of the inner fluid is reduced. Moreover, the mechanisms underlying the effect of the Atwood number at the inner interface on the perturbation growth are mainly elucidated by employing the model to analyse each contribution. As the Atwood number decreases, the dominant contribution of the Richtmyer–Meshkov instability is enhanced due to the stronger waves reverberated inside the layer, leading to weakened perturbation growth at initial in-phase interfaces and enhanced perturbation growth at initial anti-phase interfaces.

The scaling relations mapping the turbulence statistics in compressible turbulent boundary layers (TBLs) onto their incompressible counterparts are of fundamental significance for turbulence modelling, such as the Morkovin scaling for velocity fields, while for pressure fluctuation fields, a corresponding scaling relation is currently absent. In this work, the underlying scaling relations of pressure fluctuations about Mach number ($M$) contained in their generation mechanisms are explored by analysing a series of direct numerical simulation data of compressible TBLs over a wide Mach number range $(0.5\leq M \leq 8.0)$. Based on the governing equation of pressure fluctuations, they are decomposed into components according to the properties of source terms. It is notable that the intensity of the compressible component, predominantly originating from the acoustic mode, obeys a monotonic distribution about the Mach number and wall distance; further, the intensity of the rest of the pressure components, which are mainly generated by the vorticity mode, demonstrates a uniform distribution consistent with its incompressible counterpart. Moreover, the coupling between the two components is negligibly weak. Based on the scaling relations, semiempirical models for the fluctuation intensity of both pressure and its components are constructed. Hence, a mapping relation is obtained that the profiles of pressure fluctuation intensities in compressible TBLs can be mapped onto their incompressible counterparts by removing the contribution from the acoustic mode, which can be provided by the model. The intrinsic scaling relation can provide some basic insight for pressure fluctuation modelling.

The efficacy of steady large-amplitude blowing/suction on instability and transition control for a hypersonic flat plate boundary layer with Mach number 5.86 is investigated systematically. The influence of the blowing/suction flux and amplitude on instability is examined through direct numerical simulation and resolvent analysis. When a relatively small flux is used, the two-dimensional instability critical frequency that distinguishes the promotion/suppression mode effect closely aligns with the synchronisation frequency. For the oblique wave, as the spanwise wavenumber increases, the suppression effects would become weaker and the mode suppression bandwidth diminishes/increases in general in the blowing/suction control. Increasing the blowing/suction flux can effectively broaden the frequency bandwidth of disturbance suppression. The influence of amplitude on disturbance suppression is weak in a scenario of constant flux. To gain a deeper insight into disturbance suppression mechanism, momentum potential theory (MPT) and kinetic energy budget analysis are further employed in analysing disturbance evolution with and without control. When the disturbance is suppressed, the blowing induces the transport of certain acoustic components along the compression wave out of the boundary layer, whereas the suction does not. The velocity fluctuations are derived from the momentum fluctuations of the MPT. Compared with the momentum fluctuations, the evolutions indicated by each component's velocity fluctuations greatly facilitate the investigations of the acoustic nature of the second mode. The rapid variation of disturbance amplitude near the blowing is caused by the oscillations of the acoustic component and phase speed differences between vortical and thermal components. Kinetic energy budget analysis is performed to address the non-parallel effect of the boundary layer introduced by blowing/suction, which tends to suppress disturbances near the blowing. Moreover, viscous effects leading to energy dissipation are identified to be stronger in regions where the boundary layer is rapidly thickening. Finally, it is demonstrated that a flat plate boundary layer transition triggered by a random disturbance can be delayed by a blowing/suction combination control. The resolvent analysis further demonstrates that disturbances with frequencies that dominate the early transition stage are dampened in the controlled base flow.

Mineral-microbe interactions are widespread in a number of environmental processes such as mineral weathering, decomposition, and transformation. Both clay minerals and silicate-weathering bacteria are widely distributed in nature, and the latter contribute to weathering, diagenesis, and mineralization of major rock-forming minerals. The purpose of this study was to observe changes in the chemical composition and structure, especially the phase transformation, of smectite after processing by a silicate-weathering bacterium. The interaction between Bacillus mucilaginosus and bentonite was studied using custom culture media. Results from Inductively Coupled Plasma-Atomic Emission Spectrometry revealed that the bacterium promoted release of Si and Al from solid bentonite to solution. Concomitantly, the Ka nd Fe contents of the mineral increased as shown by X-ray photoelectron spectroscopy results. After interaction with the bacterium, the montmorillonite underwent a possible structure transformation to smectite, as indicated by the emergence of a new weak peak (d = 9.08 Å) shown by X-ray diffraction patterns. The mineralogical changes were also demonstrated by the decrease in the specific surface area of the mineral from 33.0 to 24.0 m2/g (these lower values for SSA of bentonite are related to the particle size of the smectite examined (120-160 mesh) and the weakened absorption bands in Al-O-H and Si-O-Si vibrations by Micro Fourier-transform infrared spectroscopy. The morphology changes in the bacteria observed by environmental scanning electron microscopy and atomic force microscopy revealed an obvious growth of the flagella in the presence of bentonite.