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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.

We investigate by direct numerical simulation the active control of laminar-turbulent transition in a hypersonic flat-plate boundary layer at a freestream Mach number of 5.86. The control mechanism is a synthetic jet. Based upon the linear stability theory of Mack, in hypersonic flow the important path to transition involves a high-frequency, second-mode fundamental resonance. Through systematic investigation, we reveal that the forcing the boundary layer with a synthetic jet at appropriate combinations of amplitude and frequency suppresses the second mode and delays transition. To gain physical insights into the major control mechanism, we employ the momentum potential theory (MPT) to analyze the flows with and without control. Essentially, the underlying control mechanism relies on an intriguing effect of the synthetic jet via generating the outward radiated wave structures, which are identified to split the upstream acoustic and vortical components. The splitting treatment presents the second-mode energy to drop sharply after the flow passes through the synthetic jet slot. The MPT source-term analysis reveals that the significantly suppressed near-wall source terms are responsible for suppressing the second mode downstream. Compared with the vortical and thermal source terms, the acoustic source term is found to be suppressed most. The kinetic budget analysis further reveals that the splitting treatment is related to the non-parallel effect and the nonlinear interaction.

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.

Direct numerical simulation of spanwise-rotation-driven flow transitions in viscoelastic plane Couette flow from a drag-reduced inertial to a drag-enhanced elasto-inertial turbulent flow state followed by full relaminarization is reported for the first time. Specifically, this novel flow transition begins with a drag-reduced inertial turbulent flow state at a low rotation number $0\leqslant Ro \leqslant 0.1$ , and then transitions to a rotation/polymer-additive-driven drag-enhanced inertial turbulent regime, $0.1\leqslant Ro \leqslant 0.3$ . In turn, the flow transitions to a drag-enhanced elasto-inertial turbulent state, $0.3\leqslant Ro \leqslant 0.9$ , and eventually relaminarizes at $Ro=1$ . In addition, two novel rotation-dependent drag enhancement mechanisms are proposed and substantiated. (1) The formation of large-scale roll cells results in enhanced convective momentum transport along with significant polymer elongation and stress generated in the extensionally dominated flow between adjacent roll cells at $Ro\leqslant 0.2$ . (2) Coriolis-force-generated turbulent vortices cause strong incoherent transport and homogenization of significant polymer stress in the bulk via their vortical circulations at $Ro=0.5 - 0.9$ .

The nonlinear evolution of mixing layer in cylindrical Rayleigh-Taylor (RT) turbulence is studied theoretically and numerically. The scaling laws including the hyperbolic cosine growth for outward mixing layer and the cosine growth for inward mixing layer of the cylindrical RT turbulence are proposed for the first time and verified reliably by direct numerical simulation of the Navier-Stokes equations. It is identified that the scaling laws for the cylindrical RT turbulence transcend the classical power law for the planar RT turbulence and can be recovered to the quadratic growth as cylindrical geometry effect vanishes. Further, characteristic time- and length scales are reasonably obtained based on the scaling laws to reveal the self-similar evolution features for the cylindrical RT 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.

The stability of the inverted flexible plate with non-uniform stiffness distribution in a free stream is studied by numerical simulation and mathematical theory. In our study, the bending stiffness distribution is expressed as the function of the leading edge's bending stiffness [Formula: see text] and the polynomial of the plate's coordinate. Based on the former theoretical work on the stability of inverted plates with uniform stiffness distribution, we derive the upper limit value of [Formula: see text] at which the zero-deflection equilibrium loses its stability for the plate with non-uniform stiffness distribution. The critical [Formula: see text] derived from the mathematical theory agrees well with that obtained from the numerical simulation. An effective bending stiffness is defined, which can be used to unify the regimes of the motion modes between uniform plates and non-uniform plates. Moreover, three orders of mass ratio [[Formula: see text], and [Formula: see text]] are investigated, and the underlying mechanism for large amplitude flapping is clarified for the inverted plate with different mass ratios. An appropriate bending stiffness distribution can greatly improve the deformation of the plate. The findings shed some light on the energy harvesting of the inverted plate.

When controlling the trailing-edge (TE) interference noise of airfoil, the design of the TE serration shape is still an open issue. To this end, the flow and noise generation for different TE serration shapes are explored by the wall-resolved implicit large-eddy simulation and acoustic analogy. The feather-like serrations are found to achieve the most prominent noise reduction among the four types of curved serrations, especially in the low-frequency range. With the aid of acoustic analogy, the coherence analysis of far-field noise produced by the dipole sources on the airfoil surface is performed. The results show that destructive interference is still the critical mechanism responsible for noise reduction. Considering only the dipole sources, we find that the feather-like serrated TE shape can obtain the best noise reduction performance among all the serrated cases. Furthermore, since flow structures are reorganized near the TE serrations, we investigated the flow noise sources quantitatively in the near field. In these cases, the noise source due to flow structures is suppressed to a greater extent in the feather-like serrated case near the TE serration roots. Consequently, the above findings indicate that the feather-like serration favors suppressing dipole and flow noise sources in the near field, which makes it an efficient configuration for reducing airfoil noise.

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.

It is fascinating that fish groups spontaneously form different formations. The collective locomotions of two and multiple undulatory self-propelled foils swimming in a fluid are numerically studied and the deep reinforcement learning (DRL) is applied to control the locomotion. We explored whether typical patterns emerge spontaneously under the driven two DRL strategies. One strategy is that only the following fish gets hydrodynamic advantages. The other is that all individuals in the group take advantage of the interaction. In the DRL strategy, we use swimming efficiency as the reward function, and the visual information is included. We also investigated the effect of involving hydrodynamic force information, which is an analogy to that detected by the lateral line of fish. Each fish can adjust its undulatory phase to achieve the goal. Under the two strategies, collective patterns with different characteristics, i.e., the staggered-following, tandem-following phalanx and compact modes emerge. They are consistent with the results in the literature. The hydrodynamic mechanism of the above high-efficiency collective traveling modes is analyzed by the vortex-body interaction and thrust. We also found that the time sequence feature and hydrodynamic information in the DRL are essential to improve the performance of collective swimming. Our research can reasonably explain the controversial issue observed in the relevant experiments. The paper may be helpful for the design of bionic fish.

The locomotion of a flapping flexible plate with different shapes and non-uniform chordwise stiffness distribution in a stationary fluid is studied numerically. The normalized effective bending stiffness K∗ for three-dimensional plates with arbitrary stiffness distribution and shape parameters is proposed, and the overall bending stiffness of non-uniform plates with different shapes is reasonably characterized. It is found that the propulsion performance in terms of cruising speed and efficiency of the self-propelled flapping plate mainly depends on the effective bending stiffness. Plates with moderate flexibility K∗ show better propulsion performance. Meanwhile, both a large area moment of the plate and a flexible anterior are favorable to significantly improve their propulsive performance. The evolution of vortical structures and the pressure distribution on the upper and lower surfaces of the plate are analyzed, and the inherent mechanism is revealed. These findings are of great significance to the optimal design of propulsion systems with different fins or wings.