We recently lost Juan Lasheras, a valued member of our community. The following tribute provides an overview of his life.

A three-layer asymptotic structure for turbulent pipe flow is proposed revealing, in terms of intermediate variables, the existence of a Reynolds-number-invariant logarithmic region for the streamwise mean velocity and variance. The formulation proposes a local velocity scale (which is not the friction velocity) for the intermediate layer and results in two overlap layers. We find that the near-wall overlap layer is governed by a power law for the pipe for all Reynolds numbers, whereas the log law emerges in the second overlap layer (the inertial sublayer) for sufficiently high Reynolds numbers ($Re_{\tau }$). This provides a theoretical basis for explaining the presence of a power law for the mean velocity at low $Re_{\tau }$ and the coexistence of power and log laws at higher $Re_{\tau }$. The classical von Kármán ($\kappa$) and Townsend–Perry ($A_1$) constants are determined from the intermediate-scaled log-law constants; $\kappa$ shows a weak trend at sufficiently high $Re_{\tau }$ but falls within the commonly accepted uncertainty band, whereas $A_1$ exhibits a systematic Reynolds-number dependence until the largest available $Re_{\tau }$. The key insight emerging from the analysis is that the scale separation between two adjacent layers in the pipe is proportional to $\sqrt {Re_{\tau }}$ (rather than $Re_{\tau }$) and therefore the approach to an asymptotically invariant state can be expected to be slow.

The interaction of fluids with surface-mounted obstacles in canopy flows leads to strong turbulence that dominates dispersion and mixing in the neutrally stable atmospheric surface layer. This work focuses on intermittency in the Lagrangian velocity statistics in a canopy flow, which is observed in two distinct forms. The first, small-scale intermittency, is expressed by non-Gaussian and not self-similar statistics of the velocity increments. The analysis shows an agreement in comparison with previous results from homogeneous isotropic turbulence (HIT) using the multifractal model, extended self-similarity and velocity increments’ autocorrelations. These observations suggest that the picture of small-scale Lagrangian intermittency in canopy flows is similar to that in HIT and, therefore, they extend the idea of universal Lagrangian intermittency to certain inhomogeneous and anisotropic flows. Second, it is observed that the root mean square of energy increments along Lagrangian trajectories depends on the direction of the trajectories’ time-averaged turbulent velocity. Subsequent analysis suggests that the flow is attenuated by the canopy drag while leaving the structure function's scaling unchanged. This observation implies the existence of large-scale intermittency in Lagrangian statistics. Thus, this work presents a first empirical evidence of intermittent Lagrangian velocity statistics in a canopy flow that exists in two distinct senses and occurs due to different mechanisms.

Coating of filtration membranes with a polymer brush holds great promise for efficiently preventing the deposition of fouling particles. The polymer chains are compressed by incoming particles, carried with the permeation flow towards the membrane, and consequently exert a repulsive force that acts to keep the particles away from the membrane surface. Here, we theoretically investigate the effect of a polymer brush coating on the permeation-induced hydrodynamic force, $F_{h}$, pulling a particle towards the membrane, and its balance with the steric repulsion exerted by the compressing brush, resisting the particle's approach. Lubrication theory yields an ordinary differential equation for the pressure, from which $F_{h}$ is calculated numerically. Further, an asymptotic analysis is performed for the limiting cases of a dilute or dense brush, providing analytic expressions that demonstrate how brush properties affect $F_{h}$. Finally, the equilibrium position of a particle is evaluated by considering a balance between the opposing forces. The results provide an upper boundary for the brush properties, beyond which the brush is barely compressed under conditions typical of membrane filtration processes. Further increasing the brush density or thickness only decreases the total system permeance, resulting in increased energy consumption. The results shed light on the mechanisms by which a polymer brush affects the forces acting on a foulant particle, providing quantitative measures for assessing the potential efficacy of brush coatings.

An experimental campaign was conducted to examine the impact of an abrupt change in surface geometry on hypersonic boundary-layer instability waves. The primary test configuration consisted of a $5^{\circ }$ half-angle, nominally sharp cone with a $15^{\circ }$ half-angle flare attachment. Tests were conducted at Mach 6 with the unit Reynolds number varying from $3.0\times 10^6$ to $4.9\times 10^6\ \textrm {m}^{-1}$. The $10^{\circ }$ compression was sufficient to create a small separation region at the cone–flare junction at these conditions. Ultra-high-speed schlieren (822 kHz) revealed the propagation of second-mode disturbances with frequencies between 200 and 300 kHz within the upstream boundary layer; when these reached the separation region, radiation of disturbance energy along the separation shock was observed. Tests conducted at low unit Reynolds numbers demonstrated inhibited instability growth (compared to the straight-cone case) through the separation region and the development of low-frequency (${\sim }75\ \textrm {kHz}$) instabilities within the separated shear layer. At higher Reynolds numbers, however, the corner interaction was found to cause rapid breakdown near reattachment, leading to earlier transition than for a straight cone. Analysis of the schlieren images using spectral proper orthogonal decomposition provided a global picture of the structure and development of the second-mode and shear-generated instabilities.

Exact solutions are found for an $N$-fold rotationally symmetric, steadily rotating hollow vortex where a continuous real parameter governs its deformation from a circular shape and $N \ge 2$ is an integer. The vortex shape is found as part of the solution. Following the designation ‘V-states’ assigned to steadily rotating vortex patches (Deem & Zabusky, Phys. Rev. Lett., vol. 40, 1978, pp. 859–862) we call the analogous rotating hollow vortices ‘H-states’. Unlike V-states where all but the $N=2$ solution – the Kirchhoff ellipse – must be found numerically, it is shown that all H-state solutions can be written down in closed form. Surface tension is not present on the boundaries of the rotating H-states but the latter are shown to be intimately related to solutions for a non-rotating hollow vortex with surface tension on its boundary (Crowdy, Phys. Fluids, vol. 11, 1999a, pp. 2836–2845). It is also shown how the results here relate to recent work on constant-vorticity water waves (Hur & Wheeler, J. Fluid Mech., vol. 896, 2020, R1) where a connection to classical capillary waves (Crapper, J. Fluid Mech., vol. 2, 1957, pp. 532–540) is made.

Extreme cavitation scenarios, such as water column separations in hydraulic systems during transient processes caused by large cavitation bubbles, can lead to catastrophic destruction. In the present paper, we study the onset criteria and dynamics of large cavitation bubbles in a tube. A new cavitation number $Ca_2 = {l^*}^{-1} Ca_0$ is proposed to describe the maximum length $L_{max}$ of the cavitation bubble, where $l^*$ is a non-dimensional length of the water column indicating its slenderness, and $Ca_0$ is the classic cavitation number. Combined with the onset criteria for acceleration-induced cavitation ($Ca_1<1$, Pan et al., Proc. Natl Acad. Sci. USA, vol. 114, 2017, pp. 8470–8474), we show that the occurrence of large cylindrical cavitation bubbles requires both $Ca_2<1$ and $Ca_1<1$ simultaneously. We also establish a Rayleigh-type model for the dynamics of large cavitation bubbles in a tube. The bubbles collapse at a finite end speed, and the time from the maximum bubble size to collapse is $T_c=\sqrt {2}\sqrt {lL_{max}}\sqrt {{\rho }/{p_\infty }}$, where $l$ is the length of the water column, $L_{max}$ is the maximum bubble length, $\rho$ is the liquid density and $p_{\infty }$ is the reference pressure in the far field. The analytical results are validated against systematic experiments using a modified ‘tube-arrest’ apparatus, which can decouple acceleration and velocity. The results in the current work can guide design and operation of hydraulic systems encountering transient processes.

The phenomena of self-sustained shock-wave oscillations over conical bodies with a blunt axisymmetric base subject to uniform high-speed flow are investigated in a hypersonic wind tunnel at Mach number $M = 6$. The flow and shock-wave dynamics is dictated by two non-dimensional geometric parameters presented by the three length scales of the body, two of which are associated with the conical forebody and one with the base. Time-resolved schlieren imagery from these experiments reveals the presence of two disparate states of shock-wave oscillations in the flow, and allows for the mapping of unsteadiness boundaries in the two-parameter space. Physical mechanisms are proposed to explain the oscillations and the transitions of the shock-wave system from steady to oscillatory states. In comparison with the canonical single-parameter problem of shock-wave oscillations over spiked-blunt bodies reported in literature, the two-parameter nature of the present problem introduces distinct elements to the flow dynamics.

The dynamics of intense vorticity is investigated by means of synchronisation experiments in direct numerical simulations of isotropic turbulence. By imposing similar dynamics above the dissipative range, the same structures of intense vorticity appear in two independent turbulent flows, showing that intense vorticity synchronises to large-scale dynamics. Remarkably, this synchronisation takes place despite the presence of chaos, and affects mostly the intense vorticity, but not so much the weak vorticity background, which remains comparatively asynchronous. These results pinpoint the role of large-scale dynamics in the formation of intense vorticity structures, the so-called ‘worms’, and rule out the possibility that they emerge primarily due to interactions within the dissipative range, and then grow or coalesce into elongated structures. The stretching of the vorticity vector by the large-scale rate-of-strain tensor is identified as the mechanism responsible for the synchronisation of intense vorticity, supporting the extended view of vortex stretching as a fundamental inter-scale mechanism in turbulence.

Although the morphology of oblique detonation waves (ODWs) has been widely studied, it remains impossible to predict the wave systems in the initiation region, which is a critical component in promoting engine applications. Such wave systems are usually viewed as secondary ODWs or compression waves (CWs), introducing some structural ambiguities and contradictions with recent observations. In this study, ODWs are simulated numerically in a stoichiometric hydrogen–air mixture and their morphological features are analysed. To cover a wide range of flight conditions physically, the control parameters are the flight altitude $H_{0}$ and Mach number $M_{1}$ of an ODW-based engine. Numerical results reveal the morphological variations with respect to $H_{0}$ and $M_{1}$, within which two special wave systems arise. One wave system indicates that the CW might induce an abrupt transition, and the other indicates that the classical secondary ODW might evolve into a normal detonation wave, another illustration of the well-known ‘detonation-behind-shock’ wave configurations. To clarify the mechanism of wave system variation, a geometric analysis of two characteristic heights demonstrates that the wave system could be predicted from the viewpoint of CW convergence. Moreover, analysis of the induction zone Mach number, compared with the corresponding Chapman–Jouguet Mach number, provides a criterion for the normal detonation wave formation. These semi-theoretical approaches collectively enhance our understanding of the wave system physically.

In the Stokesian limit, the streamline topology around a single neutrally buoyant sphere is identical to the topology of pair-sphere pathlines, both in an ambient simple shear flow. In both cases there are fore–aft symmetric open and closed trajectories spatially demarcated by an axisymmetric separatrix surface. We show that the topology of the fluid pathlines around a neutrally buoyant freely rotating spheroid, in simple shear flow, is profoundly different, and will have a crucial bearing on transport from such particles in shearing flows. An inertialess non-Brownian spheroid in a simple shear flow rotates indefinitely in any one of a one-parameter family of Jeffery orbits. The parameter is the orbit constant $C$, with $C = 0$ and $C = \infty$ denoting the limiting cases of a spinning (log-rolling) spheroid, and a spheroid tumbling in the flow–gradient plane, respectively. The streamline pattern around a spinning spheroid is qualitatively identical to that around a sphere regardless of its aspect ratio. For a spheroid in any orbit other than the spinning one ($C >0$), the velocity field being time dependent in all such cases, the fluid pathlines may be divided into two categories. Pathlines in the first category extend from upstream to downstream infinity without ever crossing the flow axis; unlike the spinning case, these pathlines are fore–aft asymmetric, suffering a net displacement in both the gradient and vorticity directions. The second category includes primarily those pathlines that loop around the spheroid, and to a lesser extent those that cross the flow axis, without looping around the spheroid, reversing direction in the process. The residence time, in the neighbourhood of the spheroid, is a smooth function of upstream conditions for pathlines belonging to the first category. In contrast, the number of loops, and thence, the residence time associated with pathlines in the second category, is extremely sensitive to upstream conditions. Plots reveal a fractal structure with singularities distributed on a Cantor-like set, suggesting the existence of a chaotic saddle in the vicinity of the spheroid.

It has been recognized that, generally, large particles enhance the turbulence intensity, while small particles attenuate the turbulence intensity. However, there has been no consensus on the quantitative criterion for particle-induced turbulence enhancement or attenuation. In the present study, interface-resolved direct numerical simulations of particle-laden turbulent flows in an upward vertical channel are performed with a direct forcing/fictitious domain method to establish a criterion for turbulence enhancement or attenuation. The effects of the particle Reynolds number ($Re_p$), the bulk Reynolds number ($Re_b$), the particle size, the density ratio and the particle volume fraction on the turbulence intensity are examined at $Re_b=5746$ (i.e. $Re_\tau =180.8$) and 12 000 ($Re_\tau =345.9$), the ratio of the particle radius to the half channel width $a/H=0.05\text {--}0.15$, the density ratio 2–100, the particle volume fraction $0.3\,\%$–$2.36\,\%$ and $Re_p < 227$. Our results indicate that at low $Re_p$ the turbulent intensity across the channel is all diminished; at intermediate $Re_p$ the turbulent intensity is enhanced in the channel centre region and attenuated in the near-wall region; and at sufficiently large $Re_p$ the turbulent intensity is enhanced across the channel. The critical $Re_p$ increases with increasing bulk Reynolds number, particle size and particle–fluid density ratio, while increasing with decreasing particle volume fraction, particularly for the channel centre region. Criteria for enhancement or attenuation are provided for the total turbulence intensity in the channel and the turbulence intensity at the channel centre, respectively, and both are shown to agree well with the experimental data in the literature. The reason for the dependence of the critical particle Reynolds number on the other parameters is discussed.

Some microscopic flying insects have evolved bristled wings. In the low-Reynolds-number regime they reside in, these porous wings perform like membranous wings because the virtual fluid barriers formed by strong viscous diffusion effectively block the gaps between bristles. In this study, the unsteady aerodynamic responses of a two-dimensional bristled wing to a single intermittent head-on gust are investigated numerically for a wide range of the Reynolds number, gust profile and gap width between the bristles. A comparison of a bristled wing with a corresponding flat wing shows that the gap flow alleviates the undesired aerodynamic loading induced by gusts. The Womersley number, which represents the ratio of the gap width to the length scale of unsteady viscous diffusion, is introduced to better characterize the unsteady drag and lift acting on the bristled wing. Under various model conditions, unsteady drag asymptotically converges beyond a specific value of the Womersley number, and unsteady lift exhibits peak values in a limited range of the Womersley number. Because of the linear property of the low-Reynolds-number flow, the unsteady force induced by the intermittent gusty flow is independent of the steady force produced by the basic steady and uniform free stream. For a large Womersley number, the aerodynamic interaction between the bristles is weak under a gusty flow, and thus the unsteady drag and lift forces can be analytically predicted, using the linear superposition approach of the velocity vector perturbed by a single isolated bristle.

The parametric subharmonic instability (PSI) of finite-width internal gravity wave beams is revisited using a formal linear stability analysis based on Floquet theory. The Floquet stability eigenvalue problem is studied asymptotically in the limit where PSI arises, namely for a small-amplitude beam of frequency $\omega$ subject to fine-scale perturbations under nearly inviscid conditions. It is found that, apart from the two dominant subharmonic perturbation components with frequency $\omega /2$, PSI also involves two smaller components with frequency $3\omega /2$, which affect the instability growth rate and were ignored in the earlier models for PSI by Karimi & Akylas (J. Fluid Mech., vol. 757, 2014, pp. 381–402) and Karimi & Akylas (Phys. Rev. Fluids, vol. 2, 2017, 074801). After accounting for these components, the revised PSI models are in excellent agreement with numerical solutions of the Floquet eigenvalue problem. The Floquet stability analysis also reveals that PSI is restricted to a finite range of perturbation wavenumbers: as the perturbation wavenumber is increased (for fixed beam amplitude), higher-frequency components eventually come into play due to the advection of the perturbation by the underlying wave beam, so the components at $\omega /2$ no longer dominate. By adopting a frame riding with the wave beam, this advection effect is factored out and it is shown that small-amplitude beams that are not generally susceptible to PSI may develop an essentially inviscid instability with broadband frequency spectrum.

The probability density function (p.d.f.) of the streamwise velocity has been shown to indicate the presence of uniform momentum zones in wall-bounded turbulent flows. Most studies on the topic have focused on the instantaneous characteristics of this p.d.f. In this work, we show how the use of time-resolved particle image velocimetry data highlights robust features in the temporal behaviour of the p.d.f. and how these patterns are associated with the change of the number of zones present in the flow over time. The use of a limited resolvent model provides a clear link between this experimentally observed behaviour and the underlying velocity structures and their phase characteristics. This link is further supported by an extended resolvent model consisting of self-similar hierarchies centred in the logarithmic region, with triadically consistent members, yielding much more complex patterns in the p.d.f. Results indicate that the geometric similarity of these members instantaneously, as well as their relative evolution in time (dictated by their wall-normal varying wave speed), both inherent to the model, can reproduce many experimentally identified features.

The interaction between various wave-like structures in screeching jets is considered via both experimental measurements and linear stability theory. Velocity snapshots of screeching jets are used to produce a reduced-order model of the screech cycle via proper orthogonal decomposition. Streamwise Fourier filtering is then applied to isolate the negative and positive wavenumber components, which for the waves of interest in this jet correspond to upstream- and downstream-travelling waves. A global stability analysis on an experimentally derived base flow is conducted, demonstrating a close match to the results obtained via experiment, indicating that the mechanisms considered here are well represented in a linear framework. In both the global stability analysis and the experimental decomposition, three distinct wave-like structures are evident; these waves are also solutions to the cylindrical vortex-sheet dispersion relation. One of the waves is the well-known downstream-travelling Kelvin–Helmholtz mode. Another is the upstream-travelling guided jet mode that has been a topic of recent discussion by a number of authors. The third component, with positive phase velocity, has not previously been identified in screeching jets. Via a local stability analysis, we provide evidence that this downstream-travelling wave is a duct-like mode similar to that recently identified in high-subsonic jets. We further demonstrate that both of the latter two waves are generated by the interaction between the Kelvin–Helmholtz wavepacket and the shock cells in the flow. Finally, we consider the periodic spatial modulation of the coherent velocity fluctuation evident in screeching jets, and show that this modulation can be at least partially explained by the superposition of the three wave-like structures, in addition to any possible modulation of the Kelvin–Helmholtz wavepacket by the shocks themselves.

Recent numerical experiments have shown that the temporal dynamics of isolated energy-containing eddies in the hierarchy of wall-bounded turbulence are governed by the self-sustaining process (SSP). However, high-Reynolds-number turbulence is a multi-scale phenomenon and exhibits interaction between the structures of different scales, but the dynamics of such multi-scale flows are poorly understood. In this study, the temporal dynamics of near-wall turbulent flow with two integral length scales of motion are investigated using a shear stress-driven flow model (Doohan et al., J. Fluid Mech., vol. 874, 2019, pp. 606–638), with a focus on identifying scale interaction processes through the governing equations and relating these to the SSPs at each scale. It is observed that the dynamics of the energy cascade from large to small scales is entirely determined by the large-scale SSP and the timing of the corresponding inter-scale turbulent transport coincides with the large-scale streak breakdown stage. Furthermore, the characteristic time scales of the resulting small-scale dissipation match those of the large-scale SSP, indicative of non-equilibrium turbulent dissipation dynamics. A new scale interaction process is identified, namely that the transfer of wall-normal energy from large to small scales drives small-scale turbulent production via the Orr mechanism. While the main outcome of this driving process appears to be the transient amplification of localised small-scale velocity structures and their subsequent dissipation, it also has an energising effect on the small-scale SSP. Finally, the feeding of energy from small to large scales is impelled by the small-scale SSP and coincides with the small-scale streak instability stage. The streamwise feeding process seems to be related to the subharmonic sinuous streak instability mode in particular and leads to the formation of the wall-reaching part of high-speed large-scale streaks.

It is commonly accepted that the breakup criteria of drops or bubbles in turbulence is governed by surface tension and inertia. However, also buoyancy can play an important role at breakup. In order to better understand this role, here we numerically study two-dimensional Rayleigh–Bénard convection for two immiscible fluid layers, in order to identify the effects of buoyancy on interface breakup. We explore the parameter space spanned by the Weber number $5\leqslant We \leqslant 5000$ (the ratio of inertia to surface tension) and the density ratio between the two fluids $0.001 \leqslant \varLambda \leqslant 1$, at fixed Rayleigh number $Ra=10^8$ and Prandtl number $Pr=1$. At low $We$, the interface undulates due to plumes. When $We$ is larger than a critical value, the interface eventually breaks up. Depending on $\varLambda$, two breakup types are observed. The first type occurs at small $\varLambda \ll 1$ (e.g. air–water systems) when local filament thicknesses exceed the Hinze length scale. The second, strikingly different, type occurs at large $\varLambda$ with roughly $0.5 < \varLambda \leqslant 1$ (e.g. oil–water systems): the layers undergo a periodic overturning caused by buoyancy overwhelming surface tension. For both types, the breakup criteria can be derived from force balance arguments and show good agreement with the numerical results.

Shock-wave–turbulence interactions are important problems with ubiquitous applications in high-speed flight and propulsion. The complex physical processes during the interaction are not fully understood, where contemporary high-fidelity numerical simulations have brought into question classical linear interaction analyses (LIA). The differences are most pronounced at high Mach number ($>$2). The objective of this study was to experimentally examine the role of a normal shock wave on the modification of velocity and temperature fluctuations to provide an empirical basis to help close the emerging knowledge gap between classical and contemporary theories. The experiments were performed in a pulsed wind tunnel facility at Mach 4.4. The free-stream disturbances provided the test bed for the study. A Mach-stem normal shock was generated through the interaction of two mirrored oblique shock waves. Molecular tagging velocimetry and two-line planar laser induced fluorescence thermometry were conducted upstream and downstream of the normal shock wave and the fluctuating intensities were compared. The measured axial velocity fluctuation amplification factor was nominally 1.1–1.2 over the Reynolds number range tested. The measured values were more consistent with LIA than contemporary theory. The temperature fluctuation amplification factor was found to vary between 3.0 and 4.5, where the lowest Reynolds number condition saw the highest free-stream disturbances and largest amplification. The free-stream fluctuations were primarily in the entropic mode, which is believed to lead to the significantly higher amplification of the entropic mode reported in these measurements.

Three-dimensional (3-D) measurements of flame stretch are experimentally challenging. In this paper, two-dimensional (2-D) and 3-D measurements of flame stretch and turbulence–flame interactions were examined using direct numerical simulation (DNS) data of turbulent premixed flames, and models to estimate 3-D statistics of flame stretch-related quantities by correcting 2-D measurements were developed. A variety of DNS cases were simulated, including three freely propagating planar flames without a mean shear and a slot-jet flame with a mean shear. The main findings are summarized as follows. First, the mean shear mainly influences the flame orientations. However, it does not change the flame stretch and turbulence–flame interactions qualitatively. The distributions of out-of-plane angle of all cases are nearly isotropic. Second, models were proposed to approximate the 3-D statistics of flame stretch-related quantities using 2-D measurements, the performance of which was verified by comparing modelled and actual 3-D surface averages and probability density functions of tangential strain rate, curvature and displacement velocity. Third, 2-D measurements of flame stretch capture properly the trends of the 3-D results, with flame surface area being produced in low curvature regions and destroyed in highly curved regions. However, the magnitude of flame stretch was under-estimated in 2-D measurements. Finally, 2-D and 3-D turbulence–flame interactions were examined. The flame normal vector is aligned with the most compressive strain rate in both 2-D and 3-D measurements. Meanwhile, the flame normal vector is misaligned (weakly aligned) with the most extensive strain rate in 3-D (2-D) measurements, highlighting the difference in 2-D and 3-D results of turbulence–flame interactions.