The statistical characteristics and the evolution of the backflow structures are investigated in wall-bounded flows at Reynolds numbers up to $Re_{\tau }=1000$. The backflow is caused by the joining of large-scale high- and low-speed structures in the vicinity of the wall and is formed at the tail tip of the low-speed structure. The distribution density of the backflow structures and the percentage area of the backflow region on the wall both increase with the Reynolds number. The backflow structures have an average lifespan of 8 wall units which is found to be slightly longer in the pipe than the channel, and they are convected downstream at the average velocities of the buffer region of approximately 10 wall units, similar to Cardesa et al. (J. Fluid Mech., vol. 880, 2019, R3). The backflow structures occasionally split and merge, and can form detached from the wall. Evidence shows that the split, merged and wall-detached backflow structures are caused by the near-wall structures. The split backflow structures are on average, larger and more spanwise-elongated which are split due to the spanwise shearing of the near-wall streaks. A backflow structure is formed detached from the wall when the trailing end of its carrier low-speed structure ‘sits’ on the near-wall high-speed streaks. The wall-detached backflow structures tend to become wall-attached by approaching the wall when undergoing a similar life cycle to the normal backflow of growth and decay with spanwise elongation because the backflow region at the tail of the low-speed structure is continuously pressed down to the wall by the high-speed structure driven by persistent vortical structures in the buffer region.

As is known, the presence of surfactants can profoundly influence the dynamics of Newtonian viscous threads. Also, it is known that non-Newtonian viscoelastic threads behave differently from Newtonian ones, particularly in the nonlinear regime. A naturally arising question is how surfactants affect the dynamic behaviour of non-Newtonian viscoelastic threads. To gain some insights into it, we build a one-dimensional model for an Oldroyd-B/finitely extensible nonlinear elastic-Peterlin approximation (FENE-P) viscoelastic liquid thread covered with an insoluble surfactant monolayer based on the slender body theory. A parametric study is performed to examine the effects of the dimensionless numbers related to the surfactant, including the initial concentration, the Marangoni number, the surface Péclet number, the shear Boussinesq number and the dilatational Boussinesq number. It is found that the formation of the beads-on-a-string structure can be greatly delayed by the surfactant. At large values of the surface Péclet number, the exponential thinning of the Oldroyd-B viscoelastic thread is little influenced, but the surfactant may lead to the disappearance of secondary droplets. At moderate values of the surface Péclet number, the surfactant induces the formation of secondary droplets. The primary droplets are axially stretched by the Marangoni or surface viscous stresses and evolve into a prolate or a more singular shape eventually. The surfactant can delay the pinch-off of the FENE-P viscoelastic thread to a great extent, but it affects little the decrease in the minimum thread radius prior to pinch-off when the surface Péclet number is large.

The present paper simplifies the naturally formed dunes (riverbeds) as large-scale three-dimensional staggered wavy walls to investigate the features of the accompanying secondary flows and streamwise vortices via large-eddy simulation. A comparison between the swirling strength and the mean velocities suggests where a secondary flow induces upwash or downwash motions. Moreover, we propose a pseudo-convex wall mechanism to interpret the directionality of the secondary flow. The centrifugal instability criterion is then used to reveal the generation of the streamwise vortices. Based on these analytical results, we found that the streamwise vortices are generated in the separation and reattachment points on both characteristic longitudinal–vertical and horizontal cross-sections, which is related to the curvature effect of the turbulent shear layer. Furthermore, the maximum Görtler number characterized by the ratio of centrifugal to viscous effects suggests that, for fixed ratio of spanwise- to streamwise-wavelength cases, the strongest centrifugal instability occurring on the longitudinal–vertical cross-section gradually dominates with the increases in amplitude. A similar trend for the cases with varied spanwise wavelength can also be found. It is also found that the streamwise vortices are generated more readily via transverse flow around the crest near the separation and reattachment points when the ratio of spanwise- to streamwise-wavelength equals 1.

We numerically investigated the global linear instability and bifurcations in electro-thermo-convection (ETC) of a dielectric liquid confined in a two-dimensional (2-D) concentric annulus subjected to a strong unipolar injection. Seven kinds of solutions exist in this ETC system due to the complex bifurcations, i.e. saddle-node, subcritical and supercritical Hopf bifurcations. These bifurcation routes constitute at most four solution branches. Global linear instability analysis and energy analysis were conducted to explain the instability mechanism and transition of different solutions and to predict the local instability regions. The linearized lattice Boltzmann method (LLBM) for global linear instability analysis, first proposed by Pérez et al. (Theor. Comput. Fluid Dyn., vol. 31, 2017, pp. 643–664) to analyse incompressible flows, was extended here to solve the whole set of coupled linear equations, including the linear Navier–Stokes equations, the linear energy equation, Poisson's equation and the linear charge conservation equation. A multiscale analysis was also performed to recover the macroscopic linearized Navier–Stokes equations from the four different discrete lattice Boltzmann equations (LBEs). The LLBM was validated by calculating the linear critical value of 2-D natural convection; it has an error of 1.39% compared with the spectral method. Instability with global travelling wave behaviour is a unique behaviour in the annulus configuration electrothermohydrodynamic system, which may be caused by the baroclinity. Finally, the chaotic behaviour was quantitatively analysed through calculation of the fractal dimension and Lyapunov exponent.

A novel experiment was performed in rotating Rayleigh–Bénard convection (RRBC), wherein the convection cell with radius $R$ was shifted away from the rotation axis by a distance $d$. In this case, the centrifugal force felt by a fluid parcel (characterized by the Froude number $Fr$) can be decomposed into an axisymmetrical part $Fr_R$ and a directed one $Fr_d$. It has been reported that the global heat transport enhances at $Fr_{d,c}$ and then reaches an optimal state at $Fr_{d,max}$ (Hu et al., Phys. Rev. Lett., vol. 127, 2021, 244501). In this paper, the local properties after the offset effects set in are investigated further, which show different features before and after $Fr_{d,max}$. The local temperature measurements at the cell centre reveal that the bulk flow turns from a turbulent state into a laminar state at $Fr_{d,max}$, which is consistent with the particle image velocimetry results. This transition can be qualitatively understood by an equivalent tilted RRBC system. As for the hot and cold coherent structures near the sidewall, their vertical temperature variations reach a minimum at $Fr_{d,max}$, implying that these structures are mostly uniform in the vertical direction at $Fr_{d,max}$. Their temperature contrasts show a linear dependence on $Fr_d$ and start to deviate from this linear behaviour when $Fr_d>Fr_{d,max}$. Besides the dominant effects of $Fr_d$, the secondary effects of $Fr_R$ are also investigated. Due to the positive effect of $+Fr_R$ on the cold structure and the negative effect of $-Fr_R$ on the hot one, the cold structure is more coherent than the hot one, but its size is smaller. The shift of the cold cluster centre from the farthest point is also larger than the shift of the hot one from the nearest point.

Many microorganisms use cilia to propel themselves in low Reynolds number ($Re$) environments. In this work, we study the dynamics of a composite cilium consisting of an elastic filament and a spherical particle attached at the filament tip driven by an external time-periodic force acting on the particle. The elastic filament is modelled numerically using a slender body theory with hydrodynamic interactions. When tilted at a large angle from the normal direction of the wall, the filament buckles, and the induced velocity field by the cilium shows a large net flux. By varying the tilt angle or the force amplitude, the particle trajectory and the net flux display abrupt changes along with a reversal of the buckling direction. We further demonstrate through a segmental model that the abrupt changes arise from the deviation of the cilium orientation at the start of the recovery stroke from the natural orientation. Our results suggest a simple approach to engineering particle motions and designing artificial cilia for fluid pumping in low $Re$ environments.

A novel data-driven modal analysis method, reduced-order variational mode decomposition (RVMD), is proposed, inspired by the Hilbert–Huang transform and variational mode decomposition (VMD), to resolve transient or statistically non-stationary flow dynamics. First, the form of RVMD modes (referred to as an ‘elementary low-order dynamic process’, ELD) is constructed by combining low-order representation and the idea of intrinsic mode function, which enables the computed modes to characterize the non-stationary properties of space–time fluid flows. Then, the RVMD algorithm is designed based on VMD to achieve a low-redundant adaptive extraction of ELDs in flow data, with the modes computed by solving an elaborate optimization problem. Further, a combination of RVMD and Hilbert spectral analysis leads to a modal-based time-frequency analysis framework in the Hilbert view, providing a potentially powerful tool to discover, quantify and analyse the transient and non-stationary dynamics in complex flow problems. To provide a comprehensive evaluation, the computational cost and parameter dependence of RVMD are discussed, as well as the relations between RVMD and some classic modal decomposition methods. Finally, the virtues and utility of RVMD and the modal-based time-frequency analysis framework are well demonstrated via two canonical problems: the transient cylinder wake and the planar supersonic screeching jet.

In this work, we investigate the characteristics of wind turbine wakes for three different blade designs (i.e. the NREL-Ori, NREL-Root and NREL-Tip designs, where the NREL-Ori refers to the baseline offshore 5 MW wind turbine designed by the US National Renewable Energy Laboratory) under turbulent inflows using large-eddy simulations with the actuator surface model. The load on the blade is higher near the blade root/tip for the NREL-Root/NREL-Tip designs when compared with the NREL-Ori design, while their thrust coefficients are the same. The results show that the blade designs influence the velocity deficit in the near wake, turbulence kinetic energy and wake meandering (both amplitude and frequency). In the near-wake region, the magnitude of the velocity deficit from the NREL-Root design is higher. As for the turbulence kinetic energy, its maximum in the near wake is higher for the NREL-Tip design, while in the far wake, it is higher for the NREL-Root design. Analyses of the instantaneous spanwise wake centre positions show higher meandering amplitude for the NREL-Root design, with the magnitudes of the low-frequency components approximately the same as the other two designs under the same inflow. The dominant meandering frequencies from different designs are different, with lower values for the NREL-Root design for which the vortex structures near the hub of low frequency play leading roles, and higher values for the NREL-Tip design for which the flow structures of high frequency in the tip shear layer are more important.

We report the first shock-tube experiments on two-dimensional dual-mode air–SF$_6$ interfaces with different initial spectra subjected to a convergent shock wave. The convergent shock tube is specially designed with a tail opening to highlight the Bell–Plesset (BP) and mode-coupling effects on amplitude development of fundamental mode (FM). The results show that the BP effect promotes the occurrence of mode coupling, and the feedback of high-order modes to the FM also arises earlier in convergent geometry than that in its planar counterpart. Relatively, the amplitude growth of the FM with a higher mode number is inhibited by the feedback, and saturates earlier. The FM with a lower mode number is affected more heavily by the BP effect, and finally dominates the flow. A new model is proposed to well predict the amplitude growths of the FM and high-order modes in convergent geometry. In particular, for FM that reaches its saturation amplitude, the post-saturation relation is introduced in the model to achieve a better prediction.

Two kinetic models are proposed for high-temperature rarefied (or non-equilibrium) gas flows with internal degrees of freedom and radiation. One of the models uses the Boltzmann collision operator to model the translational motion of gas molecules, which has the ability to capture the influence of intermolecular potentials, while the other adopts the relaxation time approximations, which has higher computational efficiency. In our kinetic model equations, not only the transport coefficients such as the shear/bulk viscosity and thermal conductivity but also their underlying relaxation processes are recovered. The non-equilibrium dynamics of gas flow and radiation are tightly coupled, where the transport properties of gas molecules and photons are correlatively dependent. The proposed kinetic models are validated by the direct simulation Monte Carlo method in several non-radiative rarefied gas flows (e.g. the normal shock wave, Fourier flow, Couette flow and the creep flow driven by the Maxwell demon), and the experimental data of planar heat transfer and normal shock waves in nitrogen. Then, the rarefied gas flows with strong radiation are studied based on the kinetic models, not only in the above one-dimensional gas flows, but also in the two-dimensional radiative hypersonic flow passing a cylinder. The characteristics of heat transfer in the tightly coupled fields of gas and radiation are systematically investigated, particularly the influence of the non-equilibrium photon transport and their interactions with gas molecules are revealed. It is found that the radiation makes a profound contribution to the total heat transfer in radiative hypersonic flow at an intermediate photon Knudsen number.

The three-dimensional flow over a low-aspect-ratio (low-$A\!R$) trapezoidal plate is investigated experimentally with a focus on how the tip effects impact the structure and dynamics of the separation bubble. The chord-based Reynolds number is $5800$, and the angle of attack varies from $4^\circ$ to $10^\circ$. Once the flow separates, the separation bubble emerges and features a swallow-tailed structure that shrinks near the midspan, which is first found for the flows over low-$A\!R$ plates. This structure develops into the conventional single-tailed structure as the angle of attack increases. Moreover, the vortex shedding within the swallow-tailed separation bubble is restored from multiple asynchronously measured local velocity fields. It is revealed that the leading-edge vortex undergoes the novel transformation from a C-shape vortex into an M-shape vortex. This vortex transformation stems from the mass transport of the near-wall spanwise flow, which affects the fluid motion on the windward side of the C-shape vortex head, strengthening and accelerating the vortex head. The strengthened vortex head facilitates the entrainment of high-momentum fluid from the outer flow. This is responsible for the formation of the swallow-tailed structure. These findings help to fill the gaps left by the downwash at low angles of attack for low-$A\!R$ wings, and are of value in improving the cruising and gliding performance of micro-air vehicles.

The Reynolds number and wall cooling effects on correlations between the thermodynamic variables are systematically investigated in hypersonic turbulent boundary layers by direct numerical simulations. The correlations between the thermodynamic variables and the streamwise velocity are also analysed. The Kovasznay decomposition is introduced to decompose the fluctuating density and temperature into the acoustic and entropic modes. It is found that in the strongly cooled wall cases, the travelling-wave-like alternating positive and negative structures (TAPNSs) are found in the fluctuating pressure and the acoustic modes of density and temperature, and the streaky entropic structures (SESs) are identified in the fluctuating entropy and the entropic modes of density and temperature near the wall. Furthermore, both the acoustic and the entropic modes of density and temperature give significant contributions to the correlations involving density and temperature in the near-wall region, while these correlations are almost totally contributed by the entropic modes in the far-wall region. The entropic modes of the density and temperature are almost linearly correlated with the fluctuating entropy. Therefore, the fact that the fluctuating entropy is strongly correlated with the fluctuating density and temperature far from the wall is mainly due to the dominance of the entropic modes in the fluctuating density and temperature. Moreover, the fluctuating temperature is strongly positively correlated with the fluctuating streamwise velocity near the wall in strongly cooled wall cases, which can be ascribed to the appearance of the TAPNSs and SESs.

Drag force acting on a particle is vital for the accurate simulation of turbulent multiphase flows, but the robust drag model is still an open issue. Fully resolved direct numerical simulation (DNS) with an immersed boundary method is performed to investigate the drag force on saltating particles in wall turbulence over a sediment bed. Results show that, for saltating particles, the drag force along the particle trajectories cannot be estimated accurately by traditional drag models originally developed for an isolated particle that depends on the particle-wall separation distance or local volume fraction in addition to the particle Reynolds number. The errors between the models and DNS are especially clear during the descending phase of the particles. Through simple theoretical analysis and DNS data fitting, we present a corrected factor using the classical, particle Reynolds number dependent drag force model as the benchmark model. The new drag model, which takes the particle vertical velocity into account, can reasonably predict the mean drag force obtained by DNS along a particle trajectory.

Due to the curvature of the droplet surface, the propagation of transmitted waves is complex inside a droplet impacted by an incident shock wave. The wave converging phenomena inside a two-dimensional water column impacted by different curved shock waves are explored in this paper by means of theoretical ray analysis and high-resolution numerical simulations. An analytical method describing the wave structure evolution characteristics inside the shocked water column is established. Hence, the morphological pattern and focus locations of these waves are theoretically obtained. The analysis shows that both the first and the second reflected waves focus inside the water column regardless of the convergent, planar or divergent nature of the incident shock wave shape. The dimensionless distances from focusing points to the column centre are derived as ${\kappa }/{( 3\kappa -{{M}_{0}}{{f}_{s}} )}$ for the former and ${\kappa }/{( 5\kappa -{{M}_{0}}{{f}_{s}})}$ for the latter, respectively. Here, $\kappa$, $M_0$ and $f_s$ represent the sound-speed ratio of the two phases, the incident shock wave strength and a function characterising the shock wave shape effect, respectively. Moreover, highly negative pressures due to the first reflected wave focusing and significant pressure oscillations due to the second reflected wave focusing are numerically tracked for three shapes of the incident shock. The effects of the incident shock wave intensity on the pressure variations at focus points are further studied. As the incident shock wave intensity increases, stronger negative pressure and higher pressure oscillation are induced. The converged incident shock wave can enhance the above phenomena, but the diverged one can weaken them.

Body-force modelling in the lattice Boltzmann method (LBM) has been studied extensively in the incompressible limit but rarely discussed for thermal compressible flows. Here we present a systematic approach of incorporating body force in the LBM which is valid for thermal compressible and non-equilibrium flows. In particular, a LBM forcing scheme accurate for the energy equation with second-order time accuracy is given. New and essential in this scheme is the third-moment contribution of the force term. It is shown via Chapman–Enskog analysis that the absence of this contribution causes an erroneous heat flux quadratic in Mach number and linear in temperature variation. The theoretical findings are verified and the necessity of the third-moment contribution is demonstrated by numerical simulations.

It is generally believed that the temperature and the velocity fields are highly coupled in compressible wall-bounded turbulence. In the present study, we employ a linear model, i.e. the two-dimensional spectral linear stochastic estimation (SLSE), to study this coupling from the perspective of the multi-scale energy-containing eddies. Particular attention is paid to the relevant statistical characteristics of the temperature field. The connections of the two fields are found to be varied with the wall-normal position in the boundary layer. In a nutshell, their entanglement is strongest in the near-wall region, and only the extreme thermal events cannot be captured by SLSE. In the logarithmic region, only the scales that correspond to the attached eddies and the very large-scale motions (VLSMs) are firmly coupled. The near-wall footprints of the former are organized in an additive manner and fulfil the predictions of the celebrated attached-eddy model. In the outer region, the two fields are linearly coupled only at the scales corresponding to VLSMs. These findings are demonstrated to be insensitive to the Mach number effects and ascribed to the similarity between the momentum and the heat transfer in compressible wall turbulence. It is also shown that it is the Reynolds number rather than Mach number that acts as a key similarity parameter in constructing their coupling. The framework built in the present study may pave a way for investigating the multi-physics coupling in turbulence, and reinforcing our analysing and modelling capability to the interrelated problems.

We perform a two-dimensional numerical study on the thermal effect of porous media on global heat transport and flow structure in Rayleigh–Bénard (RB) convection, focusing on the role of thermal conductivity $\lambda$ of porous media, which ranges from $0.1$ to $50$ relative to the fluid. The simulation is carried out in a square RB cell with the Rayleigh number $Ra$ ranging from $10^7$ to $10^9$ and the Prandtl number $Pr$ fixed at $4.3$. The porosity of the system is fixed at $\phi =0.812$, with the porous media modelled by a set of randomly displayed circular obstacles. For a fixed $Ra$, the increase of conductivity shows a small effect on the total heat transfer, slightly depressing the Nusselt number. The limited influence comes from the small number of obstacles contacting with thermal plumes in the system as well as the counteraction of the increased plume area and the depressed plume strength. The study shows that the global heat transfer is insensitive to the conduction effect of separated porous media in the bulk region, which may have implications for industrial designs.

Dust storms are typical dispersed two-phase atmospheric turbulence involving electrified charged dust particles. Previous observations have demonstrated that clean-air atmospheric turbulence is strongly intermittent. However, the intermittency of the wind velocity, concentration of dust particles with a diameter smaller than $10\ \mathrm {\mu }{\rm m}$ (PM10) and electric fields, known as multifield intermittency, has not been reported or characterized yet. Here, we quantify the small-scale multifield intermittency of dust storms using datasets obtained from the Qingtu Lake Observation Array and a wavelet-based data analysis technique. The results indicate that the probability density functions of the multifield increments are scale dependent, and the scaling exponents of the multifield structure functions exhibit anomalous scaling, suggesting that the multiple fields in dust storms are also highly intermittent. Specifically, the wind velocity during dust storms appears to be more intermittent as compared with clean-air conditions. Among the multiple fields, the small-scale intermittency is strongest for PM10 dust concentration, moderate for electric fields and weakest for wind velocity. Furthermore, the anomalous scaling of multiple fields is well described by the hierarchical structure theory of turbulence. It is theoretically predicted that the wind velocity displays a one-dimensional filamentary structure, while the PM10 dust concentration and electric fields display two-dimensional sheet-like structures. Finally, after removing the coherent components of the observed time series by the proposed wavelet conditioning statistics, Kolmogorov linear scaling is recovered for the multiple fields, suggesting that small-scale multifield intermittency is caused by the presence of small-scale coherent structures.

This work proposes a machine-learning or artificial intelligence (AI) control of a low-drag Ahmed body with a rear slant angle φ = 35° with a view to finding strategies for efficient drag reduction (DR). The Reynolds number Re investigated is 1.7 × 105 based on the square root of the body cross-sectional area. The control system comprises of five independently operated arrays of steady microjets blowing along the edges of the rear window and vertical base, twenty-six pressure taps on the rear end of the body and a controller based on an ant colony algorithm for unsupervised learning of a near-optimal control law. The cost function is designed such that both DR and control power input are considered. The learning process of the AI control discovers forcing that produces a DR up to 18 %, corresponding to a drag coefficient reduction of 0.06, greatly exceeding any previously reported DR for this body. Furthermore, the discovered forcings may provide alternative solutions, i.e. a tremendously increased control efficiency given a small sacrifice in DR. Extensive flow measurements performed with and without control indicate significant alterations in the flow structure around the body, such as flow separation over the rear window, recirculation bubbles and C-pillar vortices, which are linked to the pressure rise on the window and base. The physical mechanism for DR is unveiled, along with a conceptual model for the altered flow structure under the optimum control or biggest DR. This mechanism is further compared with that under the highest control efficiency.

Turbulence modulation by finite-size particles in homogeneous isotropic turbulence (HIT) has been investigated numerically and experimentally in many studies, but its controlling parameters are not fully clear. In this work, four non-dimensional parameters governing the turbulent modulation by non-settling particles, i.e. $Re_\lambda$ of the background HIT, the particle-to-fluid density ratio $\rho _p/\rho _f$, the relative particle size $d_p/\eta$ and the particle volume fraction $\phi _v$, are identified through dimensional analysis. Then, a parameterization study is conducted based on results from fully resolved direct numerical simulations to investigate the influence of the above non-dimensional parameters on the modulation of turbulent kinetic energy (TKE) and viscous dissipation rate. Empirical models that quantitatively predict the modulation of TKE and dissipation rate are then developed by fitting in the simulation results. These models are used to examine the turbulence modulation results reported in the literature. The model predictions and the data points of TKE modulation show reasonable agreement, but the model predicting the modulation of dissipation rate needs further deliberation as the credibility of the available data points is currently difficult to assess. The generality and the physics behind these empirical models also require further investigation.