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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The force and power of flapping plates are studied by vortex dynamic analysis. Based on the dynamic analysis of the numerical results of viscous flow past three-dimensional flapping plates, it is found that the force and power are strongly dominated by the vortical structures close to the body. Further, the dynamics of the flapping plate is investigated in terms of viscous vortex-ring model. It is revealed that the model can reasonably reflect the essential properties of the ring-like vortical structure in the wake, and the energy of the plate transferred to the flow for the formation of each vortical structure possesses a certain relation. Moreover, simplified formulae for the thrust and efficiency are proposed and verified to be reliable by the numerical solutions and experimental measurements of animal locomotion. The results obtained in this study provide physical insight into the understanding of the dynamic mechanisms relevant to flapping locomotion. [ABSTRACT FROM PUBLISHER]

The flow topologies of compressible turbulent boundary layers at Mach 2 are investigated by means of direct numerical simulation (DNS) of the compressible Navier–Stokes equations, and statistical analysis of the invariants of the velocity gradient tensor. We identify a preference for an unstable focus/compressing topology in the inner layer and an unstable node/saddle/saddle (UN/S/S) topology in the outer layer. The dissipation and dissipation production originate mainly from this UN/S/S topology. The enstrophy depends mainly on an unstable focus/stretching (UFS) topology, and the enstrophy production relies on a UN/S/S topology in the inner layer and on a UFS topology in the outer layer. The compressibility effect on the statistical properties of the topologies is investigated in terms of the ‘incompressible’, compressed and expanding regions. It is found that the locally compressed region tends to be more stable and the locally expanding region tends to be more dissipative. The compressibility is mainly related to unstable focus/compressing and stable focus/stretching topologies. Moreover, the features of the average dissipation, enstrophy, dissipation production and enstrophy production of the various topologies are clarified in the locally compressed and expanding regions. [ABSTRACT FROM PUBLISHER]

The rotation of a neutrally buoyant spheroidal particle in a Couette flow is studied by a multi-relaxation-time (MRT) lattice Boltzmann method. We find several new periodic and steady rotation modes for a prolate spheroid for Reynolds numbers ($\mathit{Re}$) exceeding 305. The simulations cover the regime up to $\mathit{Re}\leq 700$. The rotational behaviour of the spheroid appears to be not only sensitive to the Reynolds number but also to its initial orientation. We discuss the effects of initial orientation in detail. For $305\lt \mathit{Re}\lt 345$ we find that the prolate spheroid reaches a periodic mode characterized by precession and nutation around an inclined axis which is located close to the middle plane where the velocity is zero. For $345\lt \mathit{Re}\lt 385$, the prolate spheroid precesses around the vorticity direction with a nutation. For $\mathit{Re}$ close to the critical ${\mathit{Re}}_{c} \approx 345$, a period-doubling phenomenon is observed. We also identify a motionless mode at higher Reynolds numbers ($\mathit{Re}\gt 445$) for the prolate spheroid. For the oblate spheroid the dynamic equilibrium modes found are log rolling, inclined rolling and different steady states for $\mathit{Re}$ increasing from 0 to 520. The initial-orientation effects are studied by simulations of 57 evenly distributed initial orientations for each $\mathit{Re}$ investigated. Only one mode is found for the prolate spheroid for $\mathit{Re}\lt 120$ and $385\lt \mathit{Re}\lt 445$. In other $\mathit{Re}$ regimes, more than one mode is possible and the final mode is sensitive to the initial orientation. However, the oblate spheroid dynamics are insensitive to its initial orientation. [ABSTRACT FROM PUBLISHER]

Numerical investigation of a sonic jet from a blunt body opposing a supersonic flow with a free stream Mach number ${M}_{\infty } = 2. 5$ was carried out using large-eddy simulation for two total pressure ratios of the jet to the free stream, i.e. $\mathscr{P}= 0. 816$ and 1.633. Results have been validated carefully against experimental data. Various fundamental mechanisms dictating the flow phenomena, including shock/jet interaction, shock/shear-layer interaction, turbulent shear-layer evolution and coherent structures, have been studied systematically. Based on the analysis of the flow structures and features, two typical flow states, i.e. unstable and stable states corresponding to the two values of $\mathscr{P}$, are identified and the behaviours relevant to the flow states are discussed. Small-scale vortical structures mainly occur in the jet column, and large-scale vortices develop gradually in a recirculation region when the jet terminates through a Mach disk and reverses its orientation as a conical free shear layer. The turbulent fluctuations are enhanced by the rapid deviation of the shear layer and the interaction with shock waves. Moreover, the coherent structures of the flow motion are analysed using the proper orthogonal decomposition technique. It is found that the dominant mode in the cross-section plane exhibits an antisymmetric character for the unstable state and an axisymmetric one for the stable state, while statistical analysis of unsteady loads indicates that the side loads can be seen as a rotating vector uniformly distributed in the azimuthal direction. Further, we clarify a feedback mechanism whereby the unsteady motion is sustained by the upstream-propagating disturbance to the Mach disk through the recirculation subsonic region and downstream propagation in the conical shear layer. Feedback models are then proposed which can reasonably well predict the dominant frequencies of the two flow states. The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to the opposing jet/supersonic flow interaction. [ABSTRACT FROM PUBLISHER]

Numerical investigation of the compressible flow past a wavy cylinder was carried out using large-eddy simulation for a free-stream Mach number M∞ = 0.75 and a Reynolds number based on the mean diameter Re = 2 × 105. The flow past a corresponding circular cylinder was also calculated for comparison and validation against experimental data. Various fundamental mechanisms dictating the intricate flow phenomena, including drag reduction and fluctuating force suppression, shock and shocklet elimination, and three-dimensional separation and separated shear-layer instability, have been studied systematically. Because of the passive control of the flow over a wavy cylinder, the mean drag coefficient of the wavy cylinder is less than that of the circular cylinder with a drag reduction up to 26%, and the fluctuating force coefficients are significantly suppressed to be nearly zero. The vortical structures near the base region of the wavy cylinder are much less vigorous than those of the circular cylinder. The three-dimensional shear-layer shed from the wavy cylinder is more stable than that from the circular cylinder. The vortex roll up of the shear layer from the wavy cylinder is delayed to a further downstream location, leading to a higher-base-pressure distribution. The spanwise pressure gradient and the baroclinic effect play an important role in generating an oblique vortical perturbation at the separated shear layer, which may moderate the increase of the fluctuations at the shear layer and reduce the growth rate of the shear layer. The analysis of the convective Mach number indicates that the instability processes in the shear-layer evolution are derived from oblique modes and bi-dimensional instability modes and their competition. The two-layer structures of the shear layer are captured using the instantaneous Lamb vector divergence, and the underlying dynamical processes associated with the drag reduction are clarified. Moreover, some phenomena relevant to the compressible effect, such as shock waves, shocklets and shock/turbulence interaction, are analysed. It is found that the shocks and shocklets which exist in the circular cylinder flow are eliminated for the wavy cylinder flow and the wavy surface provides an effective way of shock control. As the shock/turbulence interaction is avoided, a significant drop of the turbulent fluctuations around the wavy cylinder occurs. The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to the passive control of the compressible flow past a wavy surface. [ABSTRACT FROM AUTHOR]

The dynamics of moving contact lines in a two-phase Couette flow is investigated by using a matched asymptotic procedure. The walls are assumed to be partially wetting, and the microscopic contact angle is finite but sufficiently small so that the lubrication approach can be used. Explicit formulas are derived to characterize the shear-induced interface deformation and the critical capillary number for the onset of wetting transition. It is found that the apparent contact angle vanishes for liquid–air systems and remains finite for liquid–liquid systems when the wetting transition occurs. [ABSTRACT FROM PUBLISHER]