The spatio-temporal characteristics of turbulent separations beneath semi-submerged bluff bodies with different undersurface roughness conditions are studied using a time-resolved particle image velocimetry. The Reynolds number based on the free-stream velocity and submergence depth was fixed to 14 400. Three different undersurface conditions – smooth, sandpaper roughness and cube roughness – were examined. The results showed that wall roughness reduces the mean reattachment length, and suppresses the Reynolds stresses in the second half of the mean separation bubble. The Kelvin–Helmholtz instability is observed at the leading edge of the smooth bluff body, but is bypassed in the rough cases. In the first half of the mean separation bubble, the frequencies in the separated shear layer migrate to lower values in a discrete manner through the vortex pairing mechanism. Consequently, multiple vortex shedding motions at different frequencies are nested in the separated shear layer, and the cores of shed vortices are aligned near the isopleth of free-stream velocity. The shed vortex is accompanied with multiple vortices along the edge of mean flow reversal in the upstream locations. These vortices are influenced significantly by wall roughness. A low-frequency flapping motion manifests as enlargement/shrinkage of reverse flow areas in the first half of the mean separation bubble. The frequencies of flapping motion in the smooth and sandpaper cases are similar, but are relatively lower than that in the cube roughness case. This flapping motion is associated with an extremely large vortex shed from the mean reattachment point to the free-stream region.

Gas–liquid coaxial injectors invariably involve a shear layer between a fast-moving gas stream and a slow-moving liquid stream. This shear layer within the confinement of a recess has a region of absolute instability beyond a critical momentum flux ratio. This causes the spray to exhibit self-pulsation at discrete natural frequencies. We apply sinusoidal acoustic forcing to the gas jet over a range of frequencies and amplitudes to explore the frequency response of the spray. The fluctuating spray width near the injector orifice is measured as a time-resolved tracer characteristic, and its power spectral density is used to determine the spectral response of the spray. The non-pulsating spray that involves a primarily convectively unstable shear layer responds unconditionally to all the forcing frequencies. However, for a self-pulsating spray, when the forcing frequency is far from the natural frequency and both are incommensurate, the spectral response involves both the frequencies, their linear combinations and harmonics representing a state of quasi-periodicity. When the forcing frequency is close enough or the amplitude is high enough, 1 : 1 lock-in is observed where the natural mode is suppressed completely and the spray behaves just like the unforced flow with the peak shifted to the forcing frequency. Combining the experimental observations and application of the van der Pol oscillator model, we could demonstrate the analogous behaviour of this multiphase system with other hydrodynamically self-excited systems with external forcing. The results presented here can prove significant in understanding the dynamics of the atomization process in thermoacoustic coupling and possible control of it.

A combined theoretical and experimental investigation is conducted with the objective of evaluating the lift aerodynamic admittances of an airfoil in various turbulent flow fields. Current theoretical approaches and concepts are reviewed and extended, enabling us to use a strategy to measure the one-wavenumber aerodynamic admittance in the turbulent flow field. The key of the strategy is to separate the spanwise effect from the generalized aerodynamic admittances which can be directly determined by the one-dimensional lift spectrum and one-dimensional turbulent velocity spectrum. With this strategy, the experimental values of one-wavenumber aerodynamic admittances of a two-dimensional airfoil with a NACA 0015 profile in three turbulent flow fields are obtained. As expected, due to the influence of the spanwise effect, the generalized aerodynamic admittances vary with different turbulent flow fields, exhibiting a significant dependence on flow field, and are much less than the Sears function. Contrarily, the one-wavenumber aerodynamic admittances, which are obtained in three turbulent flow fields, are generally consistent, confirming that the one-wavenumber aerodynamic admittance is mainly related to the cross-sectional shape itself. The experimental values of one-wavenumber aerodynamic admittances are compared with the Sears function. The results of all cases indicate that the experimental results agree well with the Sears function at low frequencies, while decaying faster at high frequencies.

A quasi-dynamic subgrid-scale (SGS) kinetic energy one-equation eddy-viscosity model is introduced in this paper for large-eddy simulation (LES) of compressible flows. With the additional SGS kinetic energy equation, the SGS kinetic energy can be predicted properly. Then, using the dual constraints of SGS kinetic energy and the SGS kinetic energy flux, the eddy-viscosity model can be determined exactly. Taking a similar scheme as the expansion of the SGS stress, other unclosed quantities in the equations to be solved could be well modelled separately. Therefore, with the advance of the equations, all the model coefficients can be determined dynamically. Differing from the classic dynamic procedure, the new methodology needs no test filtering, and thus it could also be called a quasi-dynamic procedure. Using direct numerical simulation of compressible turbulent channel flow, the $a$ $priori$ test shows that the key modelled quantities of the suggested model display high correlations with the real values. In LES of compressible turbulent channel flows of the Mach number being $1.5$ and 3.0, the proposed model can precisely predict some important quantities, including the mean velocity, Reynolds stress and turbulent flux, and it can also supply more abundant turbulent structures. For the compressible flat-plate boundary layer, the new model can correctly predict the transition process, mean velocity and turbulence intensities in the turbulent region. The results show that the proposed model has the advantage of scale adaptivity. Finally, the new model is applied to LES of turbulent mixing in spherical converging Richtmyer–Meshkov instability, and the accurate results show that the new model has a good ability for LES of complex fluids.

The effect of perforation on the wake of a thin flat plate placed normal to the free stream at Reynolds number ($Re$) 250 (based on plate width $d$, and inflow velocity $U_o$) is studied by means of direct numerical simulation. The perforated plate of length $6d$ consist of six equidistant square holes of varying sizes corresponding to porosity $\beta$ (ratio of open area to total plate area) of 0 %, 4 %, 9 %, 12.25 %, 16 %, 20.25 % and 25 %. It is observed that the bleed or jet flow through perforations pushes the shear layer interaction farther downstream with increasing $\beta$. This causes a monotonic decrease in the drag coefficient with increasing porosity, and a sharp fall seeming to begin at $\beta \approx 4\,\%$. On the other hand, the Strouhal number increases with $\beta$ up to 16 % (at $\beta =16\,\%$, loss of flow three-dimensionality leads to a ‘quasi-laminar’ state of flow). This is followed by a sharp fall in the Strouhal number at $\beta \approx 20\,\%$. The behaviour of the large-scale vortical structures in the far wake is influenced by the near-wake behaviour of the bleed flow, where the local $Re$ based on the perforation hole size determines the overall flow three-dimensionality. It is also observed that the jet or bleed flow undergoes meandering instability when pitch separation is equivalent to the hole size (at $\beta =25\,\%$). The low-$Re$ turbulent flow for a non-perforated plate is altered to a transitional state by the presence of perforation. The streamwise vortex pairs (secondary instabilities) become fairly organized as $\beta$ is increased from 0 % to 16 %. The secondary instability at $\beta =16\,\%$ appears similar to mode-B with wavelength ${\approx }1d$. On the contrary, the secondary instability at $\beta =25\,\%$ appears similar to mode-A with a wavelength of ${\approx }2d$.

In labscale Faraday experiments, meniscus waves respond harmonically to small-amplitude forcing without threshold, hence potentially cloaking the instability onset of parametric waves. Their suppression can be achieved by imposing a contact line pinned at the container brim with static contact angle $\theta _s=90^{\circ }$ (brimful condition). However, tunable meniscus waves are desired in some applications as those of liquid-based biosensors, where they can be controlled adjusting the shape of the static meniscus by slightly underfilling/overfilling the vessel ($\theta _s\ne 90^{\circ }$) while keeping the contact line fixed at the brim. Here, we refer to this wetting condition as nearly brimful. Although classic inviscid theories based on Floquet analysis have been reformulated for the case of a pinned contact line (Kidambi, J. Fluid Mech., vol. 724, 2013, pp. 671–694), accounting for (i) viscous dissipation and (ii) static contact angle effects, including meniscus waves, makes such analyses practically intractable and a comprehensive theoretical framework is still lacking. Aiming at filling this gap, in this work we formalize a weakly nonlinear analysis via multiple time scale method capable of predicting the impact of (i) and (ii) on the instability onset of viscous subharmonic standing waves in both brimful and nearly brimful circular cylinders. Notwithstanding that the form of the resulting amplitude equation is in fact analogous to that obtained by symmetry arguments (Douady, J. Fluid Mech., vol. 221, 1990, pp. 383–409), the normal form coefficients are here computed numerically from first principles, thus allowing us to rationalize and systematically quantify the modifications on the Faraday tongues and on the associated bifurcation diagrams induced by the interaction of meniscus and subharmonic parametric waves.

Compared to the streamwise instability, the cross-flow instability in high-enthalpy flows has received relatively less attention, but the latter is of vital importance in the flow transition for practical configurations. This work aims to investigate the cross-flow primary and secondary instabilities in hypersonic and high-enthalpy boundary layers, considering thermochemical non-equilibrium (TCNE) effects. The numerical tools adopted include a high-order shock-fitting solver, nonlinear parabolized stability equations and secondary instability theory (SIT). The flow over a swept parabola is calculated at a free-stream Mach number of 16. It is found that TCNE has a destabilizing effect on the cross-flow mode with a non-catalytic wall. Two important non-dimensional parameters are summarized to explain this effect. One is the ratio between the wall and boundary-layer edge temperatures, and the other is the cross-flow Mach number. Due to nonlinear effects, the stationary cross-flow vortices evolve and exhibit the classic rollover structures as in lower-speed flows. Two different disturbance energy norms are used in the energy budget analysis to classify the secondary cross-flow instability modes. The results from SIT highlight the importance of type-IV modes in TCNE flows at the downwash region of the vortex. The type-IV modes arise with the combined contribution from the wall-normal (on top and trough of the vortex) and spanwise (in the downwash region) production terms. The type-I mode is dominant in the calorically perfect gas case with an adiabatic wall, whereas the type-IV mode has the largest growth rate in the TCNE cases irrespective of wall temperature variation.

The stability and dynamics of a falling liquid film over an anisotropic porous medium are studied using a one-domain approach. Our stability analysis shows a significant departure from the effective no-slip boundary condition in the isotropic case. Anisotropy does not affect the threshold of linear instability. However, a non-trivial dual effect of anisotropy on the film stability is observed depending on the permeability of the porous medium. This dual effect results from the net balance of the enhancement of viscous diffusion at the top Brinkman sublayer and the mitigation of viscous damping in the core Darcy sublayer. Three-equation models have been derived from the lubrication theory approximation in terms of the exact mass balance and averaged momentum balances in the porous and liquid layers. In the nonlinear regime, anisotropy has a dual effect by damping capillary waves at large permeabilities and enhancing them at low permeabilities. Anisotropy also affects wave speeds and shapes, modifies travelling-wave branches of solutions, affects the development of a time-periodic wavetrain by inlet forcing and alters the noise-driven dynamics of the flow. These effects result from the mitigation of mass exchange at the liquid–porous interface and the contribution of the cross-stream permeability in the Brinkman top sublayer to the viscous diffusion.

This work studies the detachment of a micron-sized spherical particle from a surface with concave roughness in a linear shear flow. The concave roughness is described as regularly spaced hollow hemispheres below a flat surface and is characterised by two dimensionless parameters, i.e. dimensionless asperity distance and asperity size ratio. The hydrodynamic force and torque on the particle are calculated by performing lattice Boltzmann simulations for particle Reynolds numbers ranging from 0.02 to 40. Empirical correlations of the drag, lift and torque coefficients of the particle as functions of the particle Reynolds number and the asperity size ratio are proposed. For detachment by lifting, sliding and rolling, a numerical approach to calculate the critical particle Reynolds number (i.e. above which the particle can detach from the surface) is proposed. It is found that the dimensionless asperity distance and the distribution of asperities on the rough surface have a minor influence on the hydrodynamic force and torque on the particle, and the detachment of the particle becomes more difficult as the particle sits deeper in a larger hole. Both the empirical correlations and the numerical approach can be implemented into Lagrangian particle tracking and can accurately predict the detachment of particles from the surface with concave roughness or the detachment of particles embedded in a flat surface.

We investigate the steady motion of solid particles through successive jumps over a horizontal, rigid, bumpy bed driven by the shearing of a viscous fluid in the absence of turbulence, lubrication forces and collisions above the bed. We employ a discrete element method for the particles coupled to a mean field continuum model for the fluid to run quasi-two-dimensional simulations that we compare with the predictions of a simple model which assumes that all the particles follow identical periodic trajectories determined by the intensity of the shearing and compatible with previously suggested laws relating the particle velocities before and after the impact with the bed. We solve the periodic model both numerically and analytically, and identify the solutions that are linearly stable to small perturbations. We show that the stable solutions of the periodic model are in qualitative and quantitative agreement with the discrete simulations, as long as the number of moving particles in the system is not too large. The discrete simulations further reveal that there are two distinct families of particle trajectories, and that the simple periodic model is actually a good representation of the more energetic particles, that spend most of their time in the upper flow layers where they can gain momentum from the flow.

An experimental Lagrangian study based on particle tracking velocimetry has been completed in an incompressible turbulent round water jet freely spreading into water. The jet is seeded with tracers only through the nozzle: inhomogeneous seeding called nozzle seeding. The Lagrangian flow tagged by these tracers therefore does not contain any contribution from particles entrained into the jet from the quiescent surrounding fluid. The mean velocity field of the nozzle seeded flow, $\langle \boldsymbol {U}_{\boldsymbol {\varphi }} \rangle$, is found to be essentially indistinguishable from the global mean velocity field of the jet, $\langle \boldsymbol {U} \rangle$, for the axial velocity while significant deviations are found for the radial velocity. This results in an effective compressibility of the nozzle seeded flow for which $\boldsymbol {\nabla }\boldsymbol {\cdot } \langle \boldsymbol {U}_{\boldsymbol {\varphi }} \rangle \neq 0$ even though the global background flow is fully incompressible. By using mass conservation and self-similarity, we quantitatively explain the modified radial velocity profile and analytically express the missing contribution associated with entrained fluid particles. By considering a classical advection–diffusion description, we explicitly connect turbulent diffusion of mass (through the turbulent diffusivity $K_T$) and momentum (through the turbulent viscosity $\nu _T$) to entrainment. This results in new practical relations to experimentally determine the non-uniform spatial profiles of $K_T$ and $\nu _T$ (and hence of the turbulent Prandtl number $\sigma _T = \nu _T/K_T$) from simple measurements of the mean tracer concentration and axial velocity profiles. Overall, the proposed approach based on nozzle seeded flow gives new experimental and theoretical elements for a better comprehension of turbulent diffusion and entrainment in turbulent jets.

We study the morphology of Eulerian vortical structures and their interaction with density interfaces in increasingly turbulent stably stratified shear layers. We analyse the three-dimensional, simultaneous velocity and density fields obtained in the stratified inclined duct laboratory experiment (SID). We track, across 15 datasets, the evolution of coherent structures from pre-turbulent Holmboe waves, through intermittent turbulence, to full turbulence and mixing. We use the rortex–shear decomposition of the local vorticity vectors into a rortex vector capturing rigid-body rotation and a shear vector. We describe the morphology of ubiquitous hairpin-like vortical structures (revealed by the rortex), similar to those commonly observed in boundary-layer turbulence. These are born as relatively weak vortices around the strong three-dimensional shearing structures of confined Holmboe waves, and gradually strengthen and deform under increasing turbulence, transforming into pairs of upward- and downward-pointing hairpins propagating in opposite directions on the top and bottom edge of the shear layer. The pair of legs for each hairpin are counter-rotating and entrain fluid laterally and vertically, whereas their arched-up ‘heads’, which are transverse vortices, entrain fluid vertically. We then elucidate how this large-scale vortex morphology stirs and mixes the density field. Essentially, vortices located at the sharp density interface on either edge of the mixing layer (mostly hairpin heads) engulf blobs of unmixed fluid into the mixing layer, whereas vortices inside the mixing layer (mostly hairpin legs) further stir it, generating strong, small-scale shear, enhancing mixing. These findings provide new insights into the role of turbulent coherent structures in shear-driven stratified mixing.

In this study, we present a three-dimensional numerical model for the interaction of flow with submerged flexible vegetation, based on a large-eddy simulation and the immersed boundary method. The model innovatively realises the interaction between the flow and highly flexible vegetation with clustered leaves. Besides being a three-dimensional model of motion with full degrees of freedom, this study improves the consideration of the motion of the vegetation in all directions, and in addition the energy and momentum transfer in the spanwise direction. Furthermore, we perform a flume experiment for the flow with submerged flexible vegetation, the results of which are used to validate the simulation effects of the numerical model. It is found that the numerical model can effectively simulate the velocity profiles and the movement of vegetation induced by the flow. Using the model to analyse the flow–vegetation interaction, we find that the movement of vegetation is closely related to the flow velocity. As the flow velocity increases, both the offset angle and the vegetation swaying amplitude increase. Compared to vertical rigid vegetation, the tilting of flexible vegetation does not significantly change the velocity difference and the magnitude of the turbulent kinetic energy between the inside and the outside of the vegetation canopy, but it does weaken the disturbance to flow, thus reducing the resistance to flow. However, the swaying of vegetation dose significantly increase the velocity difference between the inside and the outside of the canopy. It forms Kelvin–Helmholtz hairpin vortices intensifying the turbulence production, and enhancing the disturbance and resistance to flow.

Laminar miscible displacement flows in narrow, vertical, eccentric annuli show a wide range of interesting physical phenomena, e.g. static layers and channels, dispersive spikes/fronts and various instabilities. These are of relevance to the primary cementing of wells, where gas leakage and greenhouse gas emissions can result from ineffective cementing. The current popular way to model this process is via a Hele-Shaw approach, reducing the Navier–Stokes equations via scaling arguments and then averaging across the annular gap: the two-dimensional (2-D) gap averaged (2DGA) model. This leads to a reduced model that is computationally efficient and represents some important features of cementing flows, but is also deficient in capturing the effects of dispersion. While three-dimensional (3-D) simulations are able to capture dispersion and most other physical phenomena, they suffer from excessive computational times due to the extreme aspect ratios of cementing geometries and non-Newtonian properties of the fluids. Here we extend the 2DGA approach by modelling the high Péclet number limit of miscible duct displacement flows, to take into account the leading-order effects of dispersion. Our modified dispersive 2DGA model is well able to approximate dispersive effects that are observed by gap-averaging the results of 3-D computations, including geometric effects of eccentricity and instabilities. This represents a marked improvement over the 2DGA approach, while keeping the computational advantages of a 2-D model.

Large-eddy simulation (LES) is performed to investigate the dynamics of flow and canopy motions and the energy transfer in turbulent canopy flows. Different from the traditional approach that models the canopy as a continuous medium with a drag coefficient prescribed a priori, an immersed boundary method together with a beam model is employed to explicitly capture the dynamics of individual stems and resolve monami. The simulation cases cover a broad range of stem flexibilities from rigid stems to oscillatory stems to stems yielding to the flow. For highly flexible canopies, the stem fluctuation is small such that the canopy behaves like a rigid canopy, which is used to explain the similarities of the flow features between rigid and highly flexible canopies. Analyses of the turbulent kinetic energy (TKE) budget show that, in the flexible canopy cases, the waving term associated with the canopy drag–flow velocity correlation can be as large as one-half of the shear production term near the canopy top. Spectral TKE budget analyses further reveal dominant effects at two characteristic scales: the monami scale associated with the coherent structures in the mixing layer and the wake scale associated with the interval between adjacent stems. For the TKE in flexible canopies, the waving term is found to play an important role in the interscale and wall-normal transport terms. Our LES data show that the spectral shortcut mechanism proposed by previous studies is caused by the waving term.

The transient flow of a circular liquid jet impinging on a horizontal disk, and the hydraulic jump formation, are examined theoretically and numerically. The interplay between inertia and gravity is particularly emphasised. The flow is governed by the thin-film equations, which are solved along with a force balance across the jump. The unsteadiness of the flow is caused by a linearly accelerating jet from an initial to a final steady state. To validate the predicted boundary-layer flow evolution, an analytical development is conducted for small distance from impingement, and for small time. In addition, the predictions of the film profile and jump location are compared against numerical simulation for the transient flow, and are further validated against experiment for steady flow. The evolutions of the film thickness and the wall shear stress in the developing boundary-layer region are found to be similar to those reported for a fluid lying on a stretching surface. The flow responds to the jet acceleration quasi-steadily near impingement but exhibits a long-term transient behaviour near the jump. Analysis of the jump evolution is considered in the range 5 < Fr < 40 for the Froude number (based on the jet radius and velocity). For Fr < 10, the jump reaches the final state instantly when the jet acceleration ceases. At higher Froude number, the jump settles at a later time, exhibiting an overshoot in the thickness due to the dominance of inertia.

A modified fully nonlinear model of an air–water system in deep water is presented in which the effect of wind in the air is simply represented by a direct link between the air–water interface pressure and the interface slope. The water system is a fully nonlinear Euler model of incompressible and irrotational fluid flow. Our main aim is to establish and compare with a reduced model represented by a forced nonlinear Schrödinger (FNLS) equation that describes wave groups in a weakly nonlinear asymptotic limit. Wave groups are described by the soliton and breather solutions generated by four cases of initial conditions in the relevant parameter regime. Numerical simulations of wave group formation in both models are compared, both with and without wind forcing. The FNLS model gives a good prediction to the modified fully nonlinear model when the wavenumber and wave frequency of the initial carrier waves are close to unity in dimensionless units based on typical carrier wavenumber and wave frequency. Wind forcing induces an exponential growth rate in the maximum amplitude wave. When the wave steepness becomes high in the fully nonlinear model some wave breaking is observed, but the FNLS model continues to predict large waves without breaking and there is then agreement only in the initial stage for the relevant initial conditions and parameter value ranges.

A synchronised multi-axis digital holographic interferometry set-up is presented for the study of 3-D flow fields with large density gradients. This optical configuration provides instantaneous interferograms with fine spatial resolution in six directions of projection. A regularised tomographic approach taking into account the presence of possible shock waves is furthermore considered to reconstruct 3-D density fields. Applied to a screeching under-expanded supersonic jet with helical dynamics, this set-up is used to provide dense optical phase measurements in the initial region of the jet. The jet mean density field is shown to be satisfactorily estimated with sharply resolved density gradients. In addition, an approach based on azimuthal Fourier transform and snapshot proper orthogonal decomposition (POD) applied to the instantaneous flow observations is proposed to study the main coherent dynamics of the jet. Relying on a cluster analysis of the azimuthal POD mode coefficients, a reduced dynamical model in the POD mode phase space is used as an approximation of the two observed limit cycles. A clear 3-D representation of the density field of a helical instability associated with screech mode C is then evidenced, with two equally probable directions of rotation. Switching between the two directions is reported, highlighting intermittency in the feedback loop. This helical structure is particularly seen to extend to the jet core, driving its internal dynamics and inducing out-of-phase density fluctuations between the outer and inner shear layers. These out-of-phase motions are related to the non-uniform radial distribution of fluctuation phase associated with the outer-layer Kelvin–Helmholtz instability wave.

Surface reactions such as the adsorption and desorption at boundaries are very common for solute dispersion in many applications of chemistry, biology, hydraulics, etc. To study how reversible adsorption affects the transient dispersion, Zhang, Hesse & Wang (J. Fluid Mech., vol. 828, 2017, pp. 733–752) have investigated the temporal evolution of moments using the Laplace transform method. Owing to difficulties introduced by the adsorption–desorption boundary condition, great challenges arise from the inverse Laplace transform: dealing with the singularities by the residue theorem can tremendously increase complexities. This work provides a much simpler analytical method to derive solutions in a more compact form that is valid for the entire range of the reactive transport process. Such a progress demonstrates that the classic framework of separation of variables can be extended and applied to this more general adsorption–desorption condition, based on which higher-order statistics including skewness and kurtosis can be explicitly explored in practice. Also extended is Gill's generalised dispersion model for solute concentration distributions, which can now address the entire transient dispersion characteristics, instead of just applied for the long-time asymptotic reactive process as done previously. Regarding the most classic Taylor dispersion problem, we investigate the influence of the reversible adsorption–desorption on the solute cloud in a tube flow. Not only the transient dispersion characteristics of transverse-average concentration distribution but also those of the bulk, surface and total-average distributions are discussed. We further investigate the influence of initial conditions on the non-uniformity of the transient dispersion over the cross-section.

The effects of compressibility on the statistics and coherent structures of a temporally developing mixing layer are studied using numerical simulations at convective Mach numbers ranging from $M_c=0.2$ to $1.8$ and at Taylor Reynolds numbers up to 290. As the convective Mach number increases, the streamwise dissipation becomes more effective to suppress the turbulent kinetic energy. At $M_c=1.8$, the streamwise dissipation increases much faster than the other two components in the transition region, even larger than pressure–strain redistribution, correlating with the streamwise elongated vortical structures at a higher level of compressibility. We confirm the existence of the large-scale high- and low-speed structures in the mixing layers, which accompany the spanwise Kelvin–Helmholtz rollers at low convective Mach number and dominate the mixing layer at higher convective Mach number. Conditional statistics demonstrate that the large-scale low-speed structures are lifted upwards by a pair of counter-rotating quasi-streamwise rollers flanking the structures. The small-scale vortical structures have an apparent preference for clustering into the top of the low-speed regions, which is directly associated with high-shearing motions on top of the low-speed structures. The high-speed structures statistically exhibit central symmetry with the low-speed structures. The statistics and dynamics of large-scale high- and low-speed structures in the compressible mixing layers resemble those in the outer region of the turbulent boundary layers, which reveals the universality of the large-scale structures in free shear and wall-bounded turbulence. A conceptual model is introduced for the large-scale high- and low-speed structures in turbulent mixing layers.