Instability evolutions of shock-accelerated thin cylindrical SF$_6$ layers surrounded by air with initial perturbations imposed only at the outer interface (i.e. the ‘Outer’ case) or at the inner interface (i.e. the ‘Inner’ case) are numerically and theoretically investigated. It is found that the instability evolution of a thin cylindrical heavy fluid layer not only involves the effects of Richtmyer–Meshkov instability, Rayleigh–Taylor stability/instability and compressibility coupled with the Bell–Plesset effect, which determine the instability evolution of the single cylindrical interface, but also strongly depends on the waves reverberated inside the layer, thin-shell correction and interface coupling effect. Specifically, the rarefaction wave inside the thin fluid layer accelerates the outer interface inward and induces the decompression effect for both the Outer and Inner cases, and the compression wave inside the fluid layer accelerates the inner interface inward and causes the decompression effect for the Outer case and compression effect for the Inner case. It is noted that the compressible Bell model excluding the compression/decompression effect of waves, thin-shell correction and interface coupling effect deviates significantly from the perturbation growth. To this end, an improved compressible Bell model is proposed, including three new terms to quantify the compression/decompression effect of waves, thin-shell correction and interface coupling effect, respectively. This improved model is verified by numerical results and successfully characterizes various effects that contribute to the perturbation growth of a shock-accelerated thin heavy fluid layer.

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.

The highly nonlinear evolution of the single-mode stratified compressible Rayleigh–Taylor instability (RTI) is investigated via direct numerical simulation over a range of Atwood numbers ($A_T=0.1$–$0.9$) and Mach numbers ($Ma=0.1$–$0.7$) for characterising the isothermal background stratification. After the potential stage, it is found that the bubble is accelerated to a velocity which is well above the saturation value predicted in the potential flow model. Unlike the bubble re-acceleration behaviour in quasi-incompressible RTI with uniform background density, the characteristics in the stratified compressible RTI are driven by not only vorticity accumulation inside the bubble but also flow compressibility resulting from the stratification. Specifically, in the case of strong stratification and high $A_T$, the flow compressibility dominates the bubble re-acceleration characters. To model the effect of flow compressibility, we propose a novel model to reliably describe the bubble re-acceleration behaviours in the stratified compressible RTI, via introducing the dilatation into the classical model that takes into account only vorticity accumulation.

Three-dimensional elastic turbulence in Taylor–Couette flows of dilute polymer solutions has been realized and thoroughly investigated via direct numerical simulations. A novel flow transition pathway from elastically dominated turbulence to solitary vortex pairs (or diwhirls) and eventually to elastic turbulence is observed by decreasing the fluid inertia ($Re$) over seven orders of magnitude, i.e. from $Re=1000$ to $0.0001$. The dominant spatio-temporal flow features in the elastic turbulence regime are those of large-scale unsteady diwhirls and small-scale axial and azimuthal travelling waves in the outer and inner halves of the gap, respectively. Moreover, it is conclusively shown that production of turbulent kinetic energy in purely elastic turbulence solely arises due to the stochastic nature of polymer stretch/relaxation. Overall, based on this comprehensive numerical investigation, the differences in the underlying fluid physics that give rise to turbulent fluctuations in elastically dominated and purely elastic turbulence have been delineated.

The width effect on contact angle hysteresis in a microchannel with patterned heterogeneous surfaces is systematically investigated. In the model, identical defects periodically appear on the background surface. To this end, a droplet's evaporation and condensation processes inside the microchannel are studied by theoretical analysis and numerical simulation based on a diffuse-interface lattice Boltzmann method. The microchannel width effect on the system's equilibrium properties is studied. The results demonstrate that the number of equilibrium configurations increases linearly with the microchannel width ($b$), and has a quadratic relationship with the cosine of the reference contact angle and the heterogeneity strength ($\varepsilon$). The average most stable contact angle is independent of $b$ and is always equal to the contact angle predicted by the Cassie–Baxter equation. For contact angle hysteresis ($H$), when the microchannels are narrow and wide, there are individual-effect-dominated hysteresis (IDH) and collective-effect-dominated hysteresis (CDH), respectively. The IDH and CDH are hysteresis modes corresponding to the jumping behaviour of contact lines affected by individual defects and two neighbouring defects, respectively. Based on the graphical force balance approach, we establish a scaling law to quantify the connection between $H$, $b$ and $\varepsilon$. Specifically, in the IDH mode, $H\sim b \varepsilon ^2$, while in the CDH mode, $H$ increases linearly with $\varepsilon$ but nonlinearly with $b$.

Pressure fluctuations play an essential role in the transport of turbulent kinetic energy and vibrational loading. This study focuses on examining the effect of wall cooling on pressure fluctuations in compressible turbulent boundary layers by high-fidelity direct numerical simulations. Pressure fluctuations result from the vorticity mode and the acoustic mode that are both closely dependent on compressibility. To demonstrate the effects of wall cooling at various compressibility intensities, three free-stream Mach numbers are investigated, i.e. $M_\infty =0.5$, 2.0 and 8.0, with real gas effects being absent for $M_\infty =8.0$ due to a low enthalpy inflow. Overall, opposite effects of wall cooling on pressure fluctuations are found between the subsonic/supersonic cases and the hypersonic case. Specifically, the pressure fluctuations normalized by wall shear stress $p^\prime _{rms}/\tau _w$ are suppressed in the subsonic and supersonic cases, while enhanced in the hypersonic case near the wall. Importantly, travelling-wave-like alternating positive and negative structures (APNS), which greatly contribute to pressure fluctuations, are identified within the viscous sublayer and buffer layer in the hypersonic cases. Furthermore, generating mechanisms of pressure fluctuations are explored by extending the decomposition based on the fluctuating pressure equation to compressible turbulent boundary layers. Pressure fluctuations are decomposed into five components, in which rapid pressure, slow pressure and compressible pressure are dominant. The suppression of pressure fluctuations in the subsonic and supersonic cases is due to both rapid pressure and slow pressure being suppressed by wall cooling. In contrast, wall cooling strengthens compressible pressure for all Mach numbers, especially in the hypersonic case, resulting in increased wall pressure fluctuations. Compressible pressure plays a leading role in the hypersonic case, mainly due to the APNS. Essentially, the main effects of wall cooling can be interpreted by the suppression of the vorticity mode and the enhancement of the acoustic mode.

Trailing-edge serrations inspired by owls are capable of reducing broadband noise. In this study, the wall-resolved large-eddy simulations (LES) are carried out on the flow over NACA-0012 airfoil with additional serrated trailing edges. The computations are conducted with the high-order flux reconstruction method on unstructured meshes. Three kinds of serrations with different lengths are studied and compared with the straight trailing-edge case, and all three types of serration achieved a certain degree of noise reduction. Presently, the medium-length serration achieves the best noise reduction effect. The maximum decrease of overall sound pressure level is approximately 2.4 dB, implying that the length of serration has a substantial impact on the noise reduction effect. The serration has no significant effect on the upstream turbulence statistics, but it changes the flow structure near the serration, such as inducing side vortex pairs attached to the serration edges. Moreover, dynamic mode decomposition shows that the pressure structures vary with the serration length. For the most unstable hydrodynamic wave, the spanwise coherence of the mode structure of pressure in the upstream boundary layer is weakened. In addition, serrations can redistribute the dipole sources on the surfaces of airfoil and serrations. The destructive interference is enhanced to some extent, which is favourable for noise reduction. In contrast with LES simulations, the pure dipole analysis shows that the longest serration case seems to be the best. Furthermore, a recently developed noise theory is used to evaluate the influence of serrations on the flow noise sources qualitatively and quantitatively. It is found that the serrations can mitigate noise source intensity near the serration edges but increase the source intensity in the near wake. The combined effect of serration on the dipole source and flow noise source determines the overall noise reduction effect. To conclude, destructive interference plays a primary role in suppressing noise radiation by serrated trailing edges, and the dual effect of flow noise sources should be considered in future serration designs. As the influence of turbulence structure will make it more difficult to find the optimal serration parameters, the position of high-fidelity simulation will become increasingly important.

A direct numerical simulation database of a weakly compressible turbulent channel flow with bulk Mach number 1.56 is studied in detail, including the geometrical relationships between the pressure-Hessian tensor and the vorticity/strain-rate tensor, as well as the mechanism of the pressure-Hessian tensor contributing to the evolution of invariants of the velocity gradient tensor. The results show that the geometrical relationships between the pressure-Hessian tensor and the vorticity/strain-rate tensor in the central region of the channel are consistent with that of isotropic turbulence. However, in the buffer layer with relatively stronger inhomogeneity and anisotropy, the vorticity tends to be aligned with the first or second eigenvector of the pressure-Hessian tensor in the unstable focus/compressing topological region, and tends to be aligned with the first eigenvector of the pressure-Hessian tensor in the stable focus/stretching topological region. In the unstable node/saddle/saddle and stable node/saddle/saddle topological regions, the vorticity prefers to lie in the plane of the first and second eigenvectors of the pressure-Hessian tensor. The strain-rate and the pressure-Hessian tensors tend to share their second principal direction. Moreover, for the coupling between the pressure-Hessian tensor and the principal strain rates, we clarify the influence on dissipation, the nonlinear generation of dissipation and the enstrophy generation. The decomposition of the pressure-Hessian tensor further shows that the slow pressure-related term dominates the pressure-Hessian tensor's contribution, and the influence of inhomogeneity and anisotropy mainly originates from the inhomogeneity and anisotropy of the fluctuating velocity. These statistical properties would be instructive in formulating dynamical models of the velocity gradient tensor for wall turbulence.

The stability of the two-layer film flow driven by an oscillatory plate under long-wave disturbances is studied. The influence of key factors, such as thickness ratio ($n$), viscosity ratio ($m$), density ratio ($r$), oscillatory frequency ($\beta$) and insoluble surfactants on the stability behaviours is studied systematically. Four special Floquet patterns are identified, and the corresponding growth rates are obtained by solving the eigenvalue problem of the fourth-order matrix. A small viscosity ratio ($m\le 1$) may stabilize the flow but it depends on the thickness ratio. If the viscosity ratio is not very small ($m>0.1$), in the $(\beta ,n)$-plane, stable and unstable curved stripes appear alternately. In other words, under the circumstances, if the two-layer film flow is unstable, slightly adjusting the thickness of the upper film may make it stable. In particular, if the upper film is thin enough, even under high-frequency oscillation, the flow is always stable. The influence of density ratio is similar, i.e. there are curved stable and unstable stripes in the $(\beta ,r)$-planes. Surface surfactants generally stabilize the flow of the two-layer oscillatory membrane, while interfacial surfactants may stabilize or destabilize the flow but the effect is mild. It is also found that gravity can generally stabilize the flow because it narrows the bandwidth of unstable frequencies.

A high-order transition route from inertial to elasticity-dominated turbulence (EDT) in Taylor–Couette flows of polymeric solutions has been discovered via direct numerical simulations. This novel two-step transition route is realized by enhancing the extensional viscosity and hoop stresses of the polymeric solution via increasing the maximum chain extension at a fixed polymer concentration. Specifically, in the first step inertial turbulence is stabilized to a laminar flow much like the modulated wavy vortex flow. The second step destabilizes this laminar flow state to EDT, i.e. a spatially smooth and temporally random flow with a $-3.5$ scaling law of the energy spectrum reminiscent of elastic turbulence. The flow states involved are distinctly different to those observed in the reverse transition route from inertial turbulence via a relaminarization of the flow to elasto-inertial turbulence in parallel shear flows, underscoring the importance of polymer-induced hoop stresses in realizing EDT that are absent in parallel shear flows.

The flow physics of inertio-elastic turbulent Taylor–Couette flow for a radius ratio of $0.5$ in the Reynolds number ($Re$) range of $500$ to $8000$ is investigated via direct numerical simulation. It is shown that as $Re$ is increased the turbulence dynamics can be subdivided into two distinct regimes: (i) a low $Re \leqslant 1000$ regime where the flow physics is essentially dominated by nonlinear elastic forces and the main contribution to transport and mixing of momentum, stress and energy comes from large-scale flow structures in the bulk region and (ii) a high $Re \geqslant 5000$ regime where inertial forces govern the flow physics and the flow dynamics is mainly governed by small-scale flow structures in the near-wall region. Flow–microstructure coupling analysis reveals that the elastic Görtler instability in the near-wall region is triggered via significant polymer extension and commensurately high hoop stresses. This instability gives rise to small-scale elastic vortical structures identified as elastic Görtler vortices which are present at all $Re$ considered. In fact, these vortices develop herringbone streaks near the inner wall that have a longer average life span than their Newtonian counterparts due to their elastic origin. Examination of the budgets of mean streamwise enstrophy, mean kinetic energy, turbulent kinetic energy and Reynolds shear stress demonstrates that increasing fluid inertia hinders the generation of elastic stresses, leading to a monotonic reduction of the elastic-related effects on the flow physics.

Kinetic energy and enstrophy transfer in compressible Rayleigh–Taylor (RT) turbulence were investigated by means of direct numerical simulation. It is revealed that compressibility plays an important role in the kinetic energy and enstrophy transfer based on analyses of transport and large-scale equations. For the generation and transfer of kinetic energy, some findings have been obtained as follows. The pressure-dilatation work dominates the generation of kinetic energy in the early stage of flow evolution. The baropycnal work and deformation work handle the kinetic energy transfer from large to small scales on average for RT turbulence. The baropycnal work is mainly responsible for the kinetic energy transfer on large scales, and the deformation work for the kinetic energy transfer on small scales. The baropycnal work is also disclosed to be related to the compressibility from the finding that the expansion motion enhances the positive baropycnal work and the compression motion strengthens the negative baropycnal work. For the generation and transfer of enstrophy, the horizontal enstrophy is generated by the baroclinic effect and the vertical enstrophy by vortex stretching and tilting. Then the enstrophy is strengthened by the vortex stretching and tilting during the evolution of RT turbulence and the vorticity tends to be isotropic in the turbulent mixing region. The large-scale enstrophy equation in compressible flow has also been derived to deal with the enstrophy transfer. It is identified that the enstrophy is transferred from large to small scales on average and tends to stabilize for RT turbulence.

We present an experimental study on controlling the number of vortices and the torque in a Taylor–Couette flow of water for Reynolds numbers from 660 to 1320. Different flow states are achieved in the annulus of width $d$ between the inner rotating and outer stationary cylinders through manipulating the initial height of the water annulus. We show that the torque exerted on the inner cylinder of the Taylor–Couette system can be reduced by up to 20 % by controlling the flow at a state where fewer than the nominal number of vortices develop between the cylinders. This flow state is achieved by starting the system with an initial water annulus height $h_0$ (which nominally corresponds to $h_0/d$ vortices), then gradually adding water into the annulus while the inner cylinder keeps rotating. During this filling process the flow topology is so persistent that the number of vortices does not increase; instead, the vortices are greatly stretched in the axial (vertical) direction. We show that this state with stretched vortices is sustainable until the vortices are stretched to around 2.05 times their nominal size. Our experiments reveal that by manipulating the initial height of the liquid annulus we are able to generate different flow states and demonstrate how the different flow states manifest themselves in global momentum transport.

The subgrid effects on the dynamics of the filtered velocity gradient tensor (VGT) in compressible turbulence are studied by means of statistical analysis of the invariants of the filtered VGT in compressible mixing layers. The evolution of the filtered VGT is determined by the interaction among the invariants, the pressure effects, the viscous effects and the subgrid effects. Based on the probability fluxes in the plane of the second ($Q$) and the third ($R$) invariants of the filtered VGT, it is found that the flux for the subgrid effect term changes most with the dilatation compared to the other terms. Further, a Schur decomposition of the filtered VGT into its normal part and non-normal part, which represent the local effect and the non-local effect of the flow dynamics, respectively, is used to deal with their effects of the velocity gradient. It is revealed that the compressibility is mainly related to the normal effect while the behaviour of the subgrid-scale (SGS) energy dissipation is mainly associated with the non-normal effect. A backscattering region of the SGS energy dissipation in the $Q$–$R$ plane is identified in the locally expanded regions, which is determined by the non-normal effect. Further, an SGS model with the non-local effect is proposed to give a better prediction of the SGS energy dissipation.

The effect of trailing-edge shape on the self-propulsive performance of three-dimensional flexible plates is studied numerically. In our study, the trailing edges of the plates are symmetric chevron shapes, and the trailing-edge angle $\unicode[STIX]{x1D719}$ varies from $30^{\circ }$ (concave plate) to $150^{\circ }$ (convex plate). Under different bending stiffnesses $K$, three regimes of the propulsive performance in terms of propulsive velocity $U$ and efficiency $\unicode[STIX]{x1D702}$ as a function of $\unicode[STIX]{x1D719}$ are identified. When $K$ is small, moderate and large, the square, convex and concave plate achieves the best performance, respectively. Analyses of vortical structures and velocity fields show that usually the jet behind the plate with the best performance is longest. Besides, the inclination angle of the jet may be small. The different propulsive performances at small and moderate $K$ are mainly attributed to the phase lag of the trailing edge. The force acting on the plate is analysed and it is found that the thrust force is mainly contributed by the normal force. If $U$, $\unicode[STIX]{x1D702}$ and $K$ are rescaled by the normal force and the area moment of the plate, the curves for different $\unicode[STIX]{x1D719}$ almost collapse into a single curve when the bending stiffness coefficient is small or moderate. The scaling confirms that the normal force should be the characteristic fluid force at small or moderate $K$ and the $\unicode[STIX]{x1D719}$ effect is governed by the area moment. The findings may shed some light on the propulsive performance of aquatic animals.

We report direct numerical simulation results that clearly elucidate the mechanism that leads to curvature dependence of drag enhancement (DE) in viscoelastic turbulent Taylor–Couette flow. Change in the angular momentum transport and its inherent link to transitions in vortical flow structures have been explored to depict the influence of the curvature of the flow geometry on DE. Specifically, it has been demonstrated that a transition in vortical structures with increasing radius ratio leads to weakening and elimination of the small-scale Görtler vortices and development and better organization (occupying the entire gap) of large-scale Taylor vortices as also evinced by the patterns of angular momentum current. The commensurate change in DE and its underlying mechanism are examined by contributions of convective flux and polymeric stress to the angular momentum current. The present finding paves the way for capturing highly localized elastic turbulence structures in direct numerical simulation by increasing geometry curvature in traditional turbulent curvilinear flows.

Liquid films can be entrained when the dewetting velocity attains a threshold, and this dynamical wetting transition has been well studied in the situation of plane substrates. We investigate the forced dewetting in a capillary tube using diffuse-interface simulations and lubrication analysis, focusing on the onset of wetting transition and subsequent interface evolution. Results show that the meniscus remains stable when the displacing rate is below a threshold, beyond which film entrainment occurs and eventually leads to the formation of Taylor bubbles separated by liquid slugs, as has also been observed in the recent experiments of Zhao et al. (Phys. Rev. Lett., vol. 120, 2018, 084501). We derive an analytical solution of the critical capillary number, and demonstrate that the wetting transition is accompanied by a vanishing apparent contact angle and an abrupt drop of the contact-line velocity. Both the bubble and slug lengths are found to depend on the capillary number and the wettability of the wall. A theoretical formula for the bubble length is also proposed and compares favourably with numerical and experimental results.

While hydrodynamic interactions for aggregates of swimmers have received significant attention in the low Reynolds number realm ($Re\ll 1$), there has been far less work at higher Reynolds numbers, in which fluid and body inertia are involved. Here we study the collective behaviour of multiple self-propelled plates in tandem configurations, which are driven by harmonic flapping motions of identical frequency and amplitude. Both fast modes with compact configurations and slow modes with sparse configurations were observed. The Lighthill conjecture that orderly configurations may emerge passively from hydrodynamic interactions was verified on a larger scale with up to eight plates. The whole group may consist of subgroups and individuals with regular separations. Hydrodynamic forces experienced by the plates near their multiple equilibrium locations are all springlike restoring forces, which stabilize the orderly formation and maintain group cohesion. For the cruising speed of the whole group, the leading subgroup or individual plays the role of ‘leading goose’.

Energetic benefit and enhanced performance are considered among the most fascinating achievements of collective behaviours, e.g. fish schools and flying formations. The collective locomotion of two self-propelled flapping plates initially in a side-by-side arrangement is investigated numerically. Both in-phase and antiphase oscillations for the two plates are considered. It is found that the plates will spontaneously form some stable configurations as a result of the flow-mediated interaction, specifically, the staggered-following (SF) mode and the alternate-leading (AL) mode for the in-phase scenario and the moving abreast (MA) mode and the AL mode for the antiphase scenario. In the SF mode, the rear plate follows the front one with a staggered configuration. In the AL mode, the plates chase each other side-by-side alternately. In terms of propulsive speed and efficiency, the performance of the plates in the SF mode with small lateral spacing $H$ is found to be better than those in the tandem following case ($H=0$) and the side-by-side case (i.e. the AL mode). To achieve higher propulsive efficiency, no matter in-phase or antiphase oscillations, the two plates with moderate bending stiffness, e.g. $K\approx O(1)$, are preferred and they should be close enough in the lateral direction. For the side-by-side configuration, the performance of each plate in the antiphase and in-phase scenarios is enhanced and weakened in comparison with that of the isolated plate, respectively. Besides the pressure and vorticity contours, the normal force and thrust acting on the plates are also analysed. It is revealed that the thrust is mainly contributed by the normal force at moderate bending stiffness. The normal force and thrust are critical to the propulsive speed and efficiency. For two self-propelled plates, in view of hydrodynamics, to achieve higher performance the in-phase SF mode and antiphase flappings in the side-by-side configuration are preferred.

We numerically investigate the mechanism leading to the entrapment of spheres at the gas–liquid interface after impact. Upon impact onto a liquid pool, a hydrophobic sphere is seen to follow one of the three regimes identified in the experiment (Lee & Kim, Langmuir, vol. 24, 2008, pp. 142–145): sinking, bouncing or being entrapped at the interface. It is important to understand the role of wettability in this process of flow–structure interaction with dynamic wetting, and in particular, to what extent the wettability can determine whether the sphere is entrapped at the interface. For this purpose, a diffuse-interface immersed boundary method is adopted in the numerical simulations. We expand the parameter space considered previously, provide the phase diagrams and identify the key phenomena in the impact dynamics. Then, we propose the scaling models to interpret the critical conditions for the occurrence of sphere entrapment, accounting for the wettability of the sphere. The models are shown to provide a good correlation among the impact inertia of the drop, the surface tension, the wettability and the density ratio of the sphere to the liquid.